Method for determining the recruitment process of pilots using artificial intelligence based fuzzy multi-criteria decision making models

Abstract

The invention relates to a method for determining the recruitment process of pilots using artificial intelligence-based fuzzy multi-criteria decision-making models, which creates an artificial intelligence-based decision-making model by considering numerous criteria such as socio-cognitive abilities, performance competencies, communication skills, visual perspective perception, and spatial working range in the selection process of airline pilots; processes and evaluates uncertain, vague, and subjective data with fuzzy logic techniques (fuzzy TOPSIS, fuzzy VIKOR, and fuzzy PROMETHEE) and enables the ranking of candidates; transforms non-numerical linguistic terms into fuzzy mathematical models; ensures the integration of qualitative and quantitative data and the transformation of uncertain data into reliable results in pilot selections; facilitates the successful ranking of candidate pilots and the selection of competent personnel for safe operations by companies; improves the recruitment process of pilots and utilizes an artificial intelligence-based decision-making model application in their selection

Description

[0001] METHOD FOR DETERMINING THE RECRUITMENT PROCESS OF PILOTS USING ARTIFICIAL INTELLIGENCE BASED FUZZY MULTI-CRITERIA DECISION MAKING MODELS

[0002] Technical Field of the Invention

[0003] The present invention relates to a method for determining the recruitment process of pilots by using artificial intelligence-based fuzzy multi-objective decision-making models that take into account the main criteria such as socio-cognitive abilities, performance competencies, communication competencies, visual perspective perception and spatial working range and 39 sub-criteria of these criteria, using multi-criteria artificial intelligence-based decision-making techniques such as fuzzy TOPSIS, fuzzy VIKOR and fuzzy PROMETHEE and clarifying the fuzzy data contained in these techniques, in order to select the best among the pilot candidates.

[0004] State of the Art

[0005] Airline organizations have to allocate considerable financial resources to pilot selection and time for training. Pilots make sudden, high-risk decisions in emergency situations, taking into account many criteria. Most of the accidents that usually occur in the aviation industry are caused by piloting errors. The decision problems encountered in real life have a quite complex structure. Pilot selection is also a complex decision-making problem. The source of this complex structure can be attributed to the necessity of evaluating multiple factors and objectives simultaneously, the frequent conflict between objectives, the uncertainties inherent in decision-making situations, the involvement of multiple individuals in the decision-making process, and the fact that the consequences of decisions often affect many people. Currently, the following classic multi-purpose decision-making techniques are still used:

[0006] Bayes Theorem in Decision-Making: Decision makers often use subjective approaches when determining the probabilities of real situations. The inaccuracy of the probabilities obtained by using subjective approaches also affects the process that the decision maker follows in determining which decision option to choose. Assigning a low-valued probability to a natural state that is likely to occur with high probability will reduce the probability of reaching the right conclusion or the right decision option, as it will reduce the amount of contribution that the actual state will make, especially to the expected value calculation.

[0007] Analytic Hierarchy Process (AHP): The technique provides the opportunity to combine quantitative (numerical) and qualitative criteria, taking into account the priorities of the group or individual in decision-making. However, decision makers' judgments cannot be expected to be fully consistent across all pairwise comparisons. The analytical hierarchy process models the decision problem in a hierarchical structure in a unidirectional manner and the criteria are assumed to be independent of each other.

[0008] Analytic network process (ANP): This method expresses the formation of a decision network by considering the relationships between the criteria of the decision problem, the preferences between the options and the criteria, and presenting a decision problem with these relationships. Thus, the requirement to model the problem in a single direction is eliminated, when there is a relationship (dependency) between criteria or options at the same level, or within them, AHP is insufficient for modeling the problem. Compared to AHP, the concept of level in AHP corresponds to the concept of set in ANP.

[0009] TOPSIS Method (Technique for Order Preference by Similarity to Ideal Solution): This method performs the evaluation of decision options by revealing positive ideal solutions and negative ideal solutions. For the method to be applied, there must be at least two decision options. The TOPSIS method, which has an analysis process that does not involve complex algorithms and mathematical models, finds application in many fields due to its ease of use and easy understanding and interpretation of the results. In addition to these advantages, the method also has some problems.

[0010] VIKOR (Vise Kriterijumska Optimizacija Kompromisno Resenje) method: This is a method which evaluates these criteria based on whether they are close to the minimum or maximum values after the weights of the decision criteria are established and selects among the alternatives. In addition to a compromise solution obtained with input weights, the VIKOR algorithm also determines the weight stability intervals.

[0011] The main difference of PROMETH EE (The Preference Ranking Organization Method For Enrichment Evaluation) from other decision-making methods is that it can define separate preference functions for each criterion and takes into account the internal relationship of each criterion. The method allows the weight values given at the beginning of the decision-making process to be changed when desired. The algorithm is easy to use and very efficient in decision-making.

[0012] Currently, major airlines use a limited number of criteria in the challenging and critical process of evaluating and selecting pilot candidates. Since almost all pilot selection criteria cannot be measured numerically, previous methods, criteria, and evaluation methods are insufficient and are unable to ensure an objective decision. In a decisionmaking problem, criteria can be quantitative (numerical) criteria or qualitative criteria. Likerd's method is currently used for the evaluation of quantitative and qualitative (non-numerical) criteria. This method is a suitable approach for assessing quantitative criteria. However, when qualitative criteria are used in decision-making processes, classical methods do not provide accurate and reliable results. In this case, it is difficult to reach the right conclusions in a decision problem by considering qualitative criteria such as pilots' flight hour experience, technical knowledge about the airplane, and psychological state.

[0013] The VIKOR (Vise Kriterijumska Optimizacija Kompromisno Resenje) algorithm was developed as a multi-objective decision-making method used to solve decision-making problems involving incomparable, conflicting criteria. This method focuses on the approach of selection and ranking of the set of alternatives. Thus, the method aims at a compromise solution for problems with disparate criteria and objectives. Considering that each alternative is evaluated according to each criterion in decision-making problems, the consensus ranking can be fulfilled by comparing the criteria close to the ideal alternative. Since the method is based only on the ranking position of the criteria, it can sometimes give different ranking results than other decision-making methods. However, fuzzy VIKOR may be insufficient in assigning weights for missing information and evaluating the consistency of judgments. This problem can only be overcome by using the fuzzy AHP method.

[0014] The disadvantage of the PROMETH EE method is that it is insufficient for criteria using imprecise, ambiguous linguistic expressions. The distinguishing point of the method is its ability to perform normalization as well as the use of different function types for each evaluation criterion in pairwise comparisons. This method is based on the similarity of coefficients between alternatives.

[0015] For example, techniques that a decision maker who has to make decisions in an uncertain environment using the TOPSIS method can use are based on compromise data for optimism and pessimism. These data are generally criteria designed to reflect the psychological state of the decision maker. If a new alternative is added to the problem or an alternative is removed, the ranking of alternatives may change completely. When evaluating alternative pilot candidates, some criteria cannot be measured by numerical values, yet they are evaluated based on numerical figures relying on the personal judgment of decision makers, and therefore previous methods are insufficient. However, fuzzy linguistic terms that we use very commonly in daily life can solve this problem very easily. The traditional criteria used in the methods currently in practice; flight time and / or psychological characteristics of the pilot cannot be measured, predicted and modeled. Although criteria related to emotional intelligence, personal vetting, as well as cognitive ability tests can significantly affect a pilot's ability to provide safe flights, they will not be sufficient to select pilot candidates when non-linear criteria are used.

[0016] With existing methods, it is difficult to determine which set of criteria and decision makers to use, and which is more advantageous to achieve a balanced score regarding the ranking of pilot candidates. On the other hand, in traditional engineering problems that require large-scale group decision making, decision makers often disagree and fail to reach consensus. Since the criteria are expressed in fuzzy terms that are vague and imprecise in nature, it is almost impossible to define the weights that determine the relationship between these criteria in pilot selection. Therefore, in areas where intuitionistic fuzzy numbers are used, many approaches are widely used to define criteria that include vague, imprecise, and subjective fuzzy information.

[0017] In real life, decision makers often use linguistic expressions rather than numerical values to evaluate criteria. For example, saying "this candidate pilot's reasoning ability is 5" is not very meaningful; instead, using fuzzy linguistic expressions such as "this candidate's reasoning ability is excellent, good, or poor" is extremely explanatory. When such fuzzy linguistic expressions are evaluated using previous methods and a large number of people are involved in the decision process, it is not possible to reach meaningful results. On the other hand, decision-making processes often involve incompatible criteria. Negative aspects arising from the structure of the criteria lead to different objectives and qualities, resulting in different expectations. For example, pilots' flight time can be measured in units of time, while their ability to focus can be expressed in qualitative techniques, therefore some criteria can be measured quantitatively, while other criteria can only be defined subjectively. For example, while a pilot candidate's English writing and reading skills and numerical ability can be measured numerically, criteria such as perception, leadership, stress tolerance, self-discipline, and reliability can only be measured qualitatively. This is because many of these criteria are subjective.

[0018] Subjective judgments are often ambiguous, and people use linguistic terms to make judgments regarding these vague criteria. Sometimes uncertainties may also arise due to missing data or incomplete information regarding the criteria, and in some cases, information on certain criteria may be completely or partially unavailable. If the number of criteria is large, the problem can become much more complex. Therefore, it is often not possible to reach a definitive conclusion in evaluations made with previous methods. On the other hand, when there is insufficient and consistent numerical information regarding the criteria, the inconsistency between the criteria may be greater, furthermore, in cases where there are uncertainties in subjective decisions and different preferences among decision makers, the final evaluation results may not be definitive.

[0019] Due to the problems mentioned above, the approach that airlines and military institutions need to consider a sufficient number of criteria and the technical specifications of the criteria in order to determine and evaluate the recruitment processes of pilot candidates, which is a challenging and vital issue, using optimal methods arises. Without appropriate methods to combine data of different characters, the decision process and the reliability of the process will be unrealistic. For this reason, it is crucial to develop a method that determines the recruitment process of pilots using artificial intelligence-based fuzzy multi-objective decision-making models.

[0020] Summary and Objects of the Invention

[0021] The present invention relates to a method for determining the recruitment process of pilots that take into account the main criteria such as socio-cognitive abilities, performance competencies, communication competencies, visual perspective perception and spatial working range and 39 sub-criteria of these criteria, using multicriteria artificial intelligence-based multi-purpose decision-making techniques such as fuzzy TOPSIS, fuzzy VIKOR and fuzzy PROMETHEE, and clarifying the fuzzy data generated by these techniques, in order to select the best among the pilot candidates.

[0022] An object of the invention is to identify a large number of qualitative and quantitative criteria that have not been considered so far and to ensure that they are taken into account in the decision-making process. For this purpose, five main criteria and thirty-nine sub-criteria of the main criteria were identified (Table 3).

[0023] Another object of the invention is to combine measurable numerical data with vague ambiguous data to enable the performance ranking of candidates. Thus, a multi-criteria artificial intelligence-based decision-making model was developed.

[0024] Another object of the invention is to enable the use of data of parameters of different characters in the calculations of the decision process, which is one of the most difficult operations of the fuzzy logic technique. Fuzzy data: are obtained from three individuals: one instructor pilot, one expert from the human resources department, and one technical staff.

[0025] Another object of the invention is to resolve conflicts that may arise from personal preferences among decision makers based on uncertain and non-linear fuzzy linguistic terms that cannot be measured numerically.

[0026] Another object of the invention is to enable the modeling of real-life uncertainty and variability using trapezoidal fuzzy numbers. In this way, decision makers are not limited to a precise number or a single criterion when evaluating candidates. Evaluation results are more flexible and the actual ranking of candidates can be determined more accurately.

[0027] Another object of the invention is to enable the synthesis and evaluation of the numerical values obtained in the fuzzification process using a new defuzzification approach.

[0028] Another object of the invention is that the results obtained will enable airline organizations to recruit qualified and skilled pilots to ensure safe and efficient operations. Another object of the invention is to eliminate ambiguous statements in subjective evaluations involving uncertainty, thereby eliminating uncertainty arising from lack of data or insufficient information. In this way, criteria for which no data were available could be assessed with a new approach and the mismatch between criteria for which there was insufficient or inconsistent quantitative information was eliminated.

[0029] Another object of the invention is to collect information and define terms for all criteria that affect a pilot's ability to fly safely. In this way, even in cases where data collection was difficult with existing methods, the fuzzy logic technique was used to describe the pilot's characteristics such as perception, leadership, stress tolerance, self-discipline and reliability with qualitative and subjective statements such as "excellent, good, normal, poor or very poor" and the selection of candidates was carried out smoothly.

[0030] Description of the Drawings

[0031] Fig. 1. The graphical drawing of the ranking of candidate pilots for recruitment subject to the invention.

[0032] Fig. 2. The graph showing the best fj* and worst fj values of the criterion functions subject to the invention.

[0033] Fig. 3. The graph showing a) Q values and b) (Sj), (Rj) values according to the fuzzy VIKOR approach subject to the invention.

[0034] Fig.4. The graph showing the fuzzy leaving flow (φ+) and fuzzy entering flow (φ-) values of the alternative subject to the invention.

[0035] Detailed Description of the Invention

[0036] The present invention relates to a method for determining the recruitment process of pilots by using artificial intelligence-based fuzzy multi-objective decision-making models that take into account the main criteria such as socio-cognitive abilities, performance competencies, communication competencies, visual perspective perception and spatial working range and 39 sub-criteria of these criteria, using multi-criteria artificial intelligence-based decision-making techniques such as fuzzy TOPSIS, fuzzy VIKOR and fuzzy PROMETHEE and clarifying the fuzzy data contained in these techniques, in order to select the best among the pilot candidates. The method of determining the recruitment process of candidate pilots using artificial intelligence-based fuzzy multi-objective decision-making techniques includes the process of expressing 5 main and 39 sub-criteria in linguistic terms and translating them into numerical data. In this method, the weights of the criteria are determined with the fuzzy analytic hierarchy process (AHP) and preference functions are created using fuzzy TOPSIS, fuzzy VIKOR, which provides compromising solutions, and fuzzy PROMETH EE. The user interface presents the results in graphical and report format, allowing the candidates to be ranked according to the ideal solution.

[0037] Data collection and processing for the invention of an artificial intelligence-based decision-making model for improving the recruitment process of pilots is as follows;

[0038] • In this approach, there is no data acquisition problem as the data is obtained from experts in pilot recruitment, the most important point to be considered is the correct definition of the decision variables of the problem and the correct definition of the linguistic expressions defining the criteria.

[0039] • System data are obtained from Tables 1, 2 and 3 developed for this problem.

[0040] Data collection process: three individuals were appointed: an instructor pilot, an expert from the human resources department, and a technical staff member, and the evaluation of each candidate based on the criteria by these 3 decision makers has been taken as the basis.

[0041] • Candidates' performance rankings were determined by combining criteria defined by explicit, specific, and numerical data with data expressed using ambiguous linguistic terms, thereby developing a multi-criteria artificial intelligence-based decision-making model.

[0042] • For the criteria given in Table 1 and Table 2, which cannot be measured numerically, a set of fuzzy linguistic terms and trapezoidal values expressing these numerically are defined and conflicts that may arise from personal preferences among decision makers are resolved.

[0043] • Since the terms related to the criteria are well defined, uncertainties due to missing data and criteria for which no numerical data are available are used as a new approach to solve the problem. • The artificial intelligence system and experts in the field evaluated the pilot candidates and five main criteria and thirty-nine sub-criteria sets were identified and the criteria were ranked as shown in Table 3.

[0044] • During the calculations of the decision-making process, fuzzy logic techniques were used, according to this approach, after defining the decision problem, the linguistic factors affecting the problem (Table 3) were determined, the linguistic expressions defining these factors were defined by experts in the field (Tables 2 and 3), and numerical values were assigned to these terms. The numeric values defining the linguistic expressions are usually in the range [0,1] and are chosen for the linguistic expressions describing the pilot candidates. It comprises steps of consisting solely of a set of terms defined by the artificial intelligence system for the evaluation of candidate pilots and being expressed by these terms, • In this approach, there is no data acquisition problem since the data is obtained from field experts, Obtaining the artificial intelligence system data from Table 2, which we developed for this problem,

[0045] • Developing a multi-criteria artificial intelligence-based decision-making model by combining explicit, specific numerical data with linguistic data and ranking the performance of candidates,

[0046] • Defining the linguistic terms by artificial intelligence and the fuzzy equivalents corresponding to numerical values (those determined by fuzzy logic) being listed as follows;

[0047] The set of fuzzy linguistic terms used by the artificial intelligence system for the evaluation of the criteria and the trapezoidal numerical equivalents thereof;

[0048] - very low (VL) (0, 0, 0.1, 0.2)

[0049] - low (L) (0.1, 0.2, 0.2, 0.3)

[0050] - fairly low (FL) (0.2, 0.3, 0.4, 0.5)

[0051] - fair (F) (0.4, 0.5, 0.5, 0.6)

[0052] - fairly good (FG) (0.5, 0.6, 0.7, 0.8)

[0053] - good (G) (0.7, 0.8, 0.8, 0.9)

[0054] - very good (VG) (0.8, 0.9, 1.0, 1.0)

[0055] list of main and sub-criteria;

[0056] - very poor (VP) (0, 0, 0.1, 0.2)

[0057] - poor (P) (0.1, 0.2, 0.2, 0.3)

[0058] - moderately poor (MP) (0.2, 0.3, 0.4, 0.5)

[0059] - fair (F) (0.4, 0.5, 0.5, 0.6) - Moderately good (MG) (0.5, 0.6, 0.7, 0.8)

[0060] - good (G) (0.7, 0.8, 0.8, 0.9)

[0061] - very good (VG) (0.8, 0.9, 1.0, 1.0)

[0062] • expressing the main criteria and sub-criteria in linguistic terms as a result of artificial intelligence calculations.

[0063] Very Low (VL) (0, 0, 0.1, 0.2)

[0064] Low (L) (0.1, 0.2, 0.2, 0.3)

[0065] Fairly Low (FL) (0.2, 0.3, 0.4, 0.5)

[0066] Fair (F) (0.4, 0.5, 0.5, 0.6)

[0067] Fairly Good (FG) (0.5, 0.6, 0.7, 0.8)

[0068] Good (G) (0.7, 0.8, 0.8, 0.9)

[0069] Very Good

[0070]

[0071] (VG) (0.8, 0.9, 1.0, 1.0)

[0072] Table 1: The set of fuzzy linguistic terms used to determine the weights of the criteria and trapezoidal numerical equivalents thereof

[0073] Very Poor (VP) (0, 0, 0.1, 0.2)

[0074] Poor (P) (0.1, 0.2, 0.2, 0.3)

[0075] Moderately Poor (MP) (0.2, 0.3, 0.4, 0.5)

[0076] Fair (F) (0.4, 0.5, 0.5, 0.6)

[0077] Moderately Good (MG) (0.5, 0.6, 0.7, 0.8)

[0078] Good (G) (0.7, 0.8, 0.8, 0.9)

[0079] Very Good (VG) (0.8, 0.9, 1.0, 1.0)

[0080] Table 2: The set of fuzzy linguistic terms used to rate criteria and trapezoidal numerical equivalents thereof

[0081] Main criteria Sub-criteria

[0082] - Working memory

[0083] - Reasoning ability

[0084] Pilot's socio-cognitive ability _ Attention to detail

[0085] (SCA) _ Quick thinking ability

[0086] - Active listening ability >

[0087] - Information processing ability

[0088] - Memory strength - Logic (ability to establish context)

[0089] - Strong focus

[0090] - Perception speed - Cognitive speed - Commitment

[0091] - Decision-making Performance competence competence

[0092] (PC) (behavioral criteria) > Flexibility

[0093] - Reliability / discipline - Stress resistance - Trust

[0094] - Self-discipline

[0095] - Stress management - Ability to remain calm under pressure

[0096] - Ability to cooperate - Conflict resolution Interpersonal relations > Self-assessment competence (IC) > English writing ability - English reading ability - Active listening ability - Teamwork ability - Leadership ability Multitasking ability - Spatial visualization - Numerical ability Spatial working memory > Ability to translate (SWM) information

[0097] - Ability to process information

[0098] > - Ability to understand technical information

[0099] - Strong focus logic

[0100] - High attention and Visual perspective-taking alertness

[0101] (VPT) - Ability to plan ahead

[0102] - Determination

[0103] - Empathy skills

[0104] Table 3: List of main and sub-criteria

[0105] The process for solving the decision-making problem of pilot selection consists of six stages.

[0106] The first stage is to define the decision problem: decision problem is defined as follows. “Determining the recruitment process of pilots using artificial intelligence-based fuzzy multi-objective decision-making models”.

[0107] The second stage is to identify decision-making criteria: for this purpose, five main criteria and 39 sub-criteria of the main criteria were identified. The list of criteria is given in Table 3.

[0108] The third stage is to identify the solution alternatives for the decision problem: In fuzzy set theory, the degree of membership of an element is defined in the range [0,1], if the membership is close to 1, it is assumed that the element is a high member of that set, and if the membership degree is close to zero, it is assumed to be outside the fuzzy set. Fuzzy logic theory, which can be applied in many areas, is used to solve vague, uncertain, subjective problems and judgments with undefined boundaries. Since it is not possible to express these uncertainties with numerical values, linguistic variables and terms describing these variables are used instead of numerical values. In our study, criteria for selecting the five best candidates among 12 pilot candidates and a set of terms expressing these criteria were identified. In addition, trapezoidal fuzzy numbers were defined in the membership functions and these numbers were defined with four parameters (Table 1, Table 2). In the invention, these letters are defined by the = ( fc / t’a^i’Pkji> ^kji) parameters, I and h denote the lower and upper bounds of the fuzzy number, respectively, and a and denote the middle values.

[0109] In the method of determining the recruitment process of pilots using artificial intelligence-based fuzzy multi-objective decision-making models, fuzzy TOPSIS, fuzzy VIKOR and fuzzy PROMETHEE from extended fuzzy MCDM (Multi-Criteria Decision Making) methods were used for the decision-making process. Fuzzy mathematical operations related to the weights of criteria and sub-criteria were performed using the minimum- average-maximum (min-average-max) composition rule, wherein Ri,..., Rmare the fuzzy sub-criteria relationships defined in the universes X, Y, and U. Here, Xmis the sub-criteria set defined by trapezoidal fuzzy numbers (TFN) indicating the membership degrees (MDs) of working memory, reasoning, etc.; Ymis the membership degrees (MDs) of the sub-criteria set and its space (Um) is the MDs of the main criteria set. These sub-criteria are sub-criteria of the main criteria Socio-cognitive ability, performance competence. In this method, the weights of the criteria are determined by the following equation.

[0110] (%, u), min( / tXii,., / tXjnl), Ave. (( / tX12+.. + / iXm2)

[0111] / m), Ave. max(^i4,., / tXjn4),

[0112] e r.e u\

[0113]

[0114] Equation-1

[0115] The fuzzy TOPSIS approach is based on the fundamental concepts of fuzzy sets and systems and aggregates the opinions of multiple decision makers using fuzzy linguistic terms. A fuzzy set represents parameters with continuous membership degrees (MD) and is therefore one of the preferred methods for solving MCDM problems. Therefore, in a universe U and a sub-criteria set X defining TFNs, the fuzzy set denoted by 'A' can be defined by the membership function [iAin a given framework. The membership function (MF) is an effective mathematical tool for handling ambiguity and uncertainty in fuzzy sets and hence in MCDM problems. For example, let x ∈ X be a real number and let μ(x) ∈ [0, 1] denote the MD of x in fuzzy set A. A fuzzy sub set of a real number can be denoted by u: R → [0,1] and is called a fuzzy number when it satisfies the u(x) = 1 criterion when u is ∃ x ∈ R. As defined by Zadeh (1975), fuzzy linguistic variables (e.g. socio-cognitive ability etc. in our study) can be expressed in linguistic terms (very poor, poor, moderately poor, good, excellent, etc.) or in natural language sentences. In this method, fuzzy numerical matrices expressing fuzzy linguistic terms, A and B, are defined as fuzzy trapezoidal numbers and shown as à = (l̃ji, ãji, β̃ji, h̃ji) and B̃ = (ãji, b̃ji, c̃ji, d̃ji) for two different fuzzy sets. The distance of ideal and anti-ideal points can be measured by various adaptations of the fuzzy TOPSIS method involving fuzzy TOPSIS method, TFNs (trapezoidal fuzzy numbers) instead of triangular numbers. Therefore, the fuzzy extension of the TOPSIS method is explained in the following steps:

[0116] Step 1: The alternative candidates are denoted as Aj ={al, a2,...,an},j=1, 2, 3,...,n; the criteria set is denoted as

[0117]

[0118] Ci={Ci,..., Cm}, i=1, 2, and the sub-criteria set, which represents the parameters dependent on the ‘m’ criteria set, is denoted as Ci= {ci,...,cm}. Similarly, Dk= {d1,...,dk} is defined as a set of decision makers (DMs). In this case, it is represented as the fuzzy rating of the d-th decision maker for Alternative 'Aj' and criterion 'Ci', where Xji represents trapezoidal fuzzy numbers.

[0119] r(4) _ nW W n(d)

[0120] kji ~.lkji’ukji’Pkji’,lkji)

[0121] Equation-2

[0122] Similarly, the weighting of the criteria is shown in the figure below.

[0123] ’ Wkji ~ iwkjl ’Wkja’WkjP’Wkjh)

[0124]

[0125] Equation-3

[0126] Step 2: The ratings given by decision makers (DM) have been compiled in relation to the jth alternative and ith criterion and calculated using the following equations.

[0127] lkjt = akji=

[0128]

[0129] Pkji =hkji = maxd{hW} Equation -4

[0130] Here = (Z^-, a^, h ') is the fuzzy relative importance of the d-th DM, which

[0131]

[0132] encompasses many degrees of importance. Therefore, the fuzzy decision matrix is expressed in terms of criteria and alternatives and multiple membership values (DM) are defined using the following equation.

[0133] xlllx122 "■xklm

[0134] *221 *222 "■xk2m

[0135] ^mxn(xkji) ~

[0136]

[0137] ■xknlxkn2xknm-

[0138] Equation-5

[0139] Step 3: Normalized matrix R = [ry is obtained using fuzzy decision matrix D through the following equations.

[0140] _ Ijiaji Pji hji

[0141] r

[0142]

[0143] ji~

[0144] Equation-6

[0145] Wherein, h*i is expressed as maxj{hji} of the benefit factor for all 'i's.

[0146]

[0147] Equation-7

[0148] Wherein, l(-) i is expressed as minj{lji} of the non-beneficial factors for all 'i's.

[0149] Step 4: Using the vector of criteria weights, the fuzzy decision matrix is calculated and normalized. Normalized fuzzy weight decision matrix Vjt is as follows.

[0150] V

[0151]

[0152] JH*■ = R * W) L.(D)

[0153] Equation-8 Step 5: The fuzzy positive ideal solution (FPIS) and the fuzzy negative ideal solution (FNIS) are calculated in the following order.

[0154] FPIS = A(*) = (ṽ(*) 1, ṽ(*) 2, ..., ṽ(*) n), and v(*) i = maxj{vkji}

[0155] Equation-9

[0156] F

[0157]

[0158] NIS A^ = v^,vn~l)’anc* v[ = minj{vkji}

[0159] Equation-10

[0160] Step 6: Accordingly, the following method is proposed to calculate the distance between numbers.

[0161] JI 2 2 2

[0162] —^kji) + (j%kji ^kji) + ( / ? kj i ~ ^kji) + (J^-kji ~ ^-kji)2^

[0163]

[0164] Equation-11

[0165] The distance of the alternative (A;) from the normalized weighted matrix to FPIS and FNIS is calculated using the following equations respectively.

[0166] m

[0167] D(*) j = Σ d(ṽkji, ṽ(*) i), j = 1, 2, ···, n, i = 1, 2, ···, m

[0168] i=l

[0169] Equation-12

[0170] m

[0171] D(-) j = Σ d(ṽkji, ṽ(-) i), j = 1, 2, ···, n, i = 1, 2, ···, m

[0172]

[0173] Equation-13

[0174] Step 8: The Closeness Coefficient CCj of each alternative is calculated as follows.

[0175] of'

[0176]

[0177] 7 =nw+ nH’J

[0178] Equation-14 The VIKOR method was initially formulated and later extended by Opricovic and Tzeng (2007) and Opricovic (2009) to address decision-making problems characterized by criteria where conflict in opinions is assumed. The decision maker (DM), by evaluating alternatives in the domain of all the established criteria in VIKOR, searches for the best approach to rank the solution that is closest to the ideal solution and determine the compromise solution. Similarly, fuzzy VIKOR is used to search for a consensus-based solution in a fuzzy environment with incomplete, uncertain and subjective linguistic variables and to evaluate the knowledge of decision makers. The fuzzy VIKOR studied by Rostamzadeh et al. (2015) consists of the following steps when used with trapezoidal fuzzy numbers: 1) Identify the objectives of the decision process and define the scope of the problem, 2) form a group of decision makers and identify a finite set of relevant attributes, 3) select appropriate linguistic variables, 4) combine the views of the decision makers and construct a fuzzy decision matrix to obtain the fuzzy weighting of the criteria and the combined fuzzy evaluation of the alternatives. 5) Convert the fuzzy decision matrix and the fuzzy weights of each criterion into exact values. Since the linguistic weights indicate the importance of the criteria, the trapezoidal fuzzy numbers need to be subjected to a defuzzification process using appropriate approaches. In this study, the Center of the Area (COA) method was used to obtain the final number of final counts that have been defuzzified. Defuzzification is expressed using the following relationships.

[0179] f x-[i(x)dx Defuzzification ( / ?) =

[0180] f ii(x)dx

[0181] “kii( -^hlL-Xxdx+f^1xdx+fRkJi(hhkfX\xdx

[0182] Iji \akji ^kli)akji 0kji \fkji PkjiJ

[0183] r, Mx}dX+^kiidx+^kii[hhkfx)dx

[0184] ^kji \akjilkjiJakji ^kji y^kji “kjij

[0185] — l * a + / h h +j(h - / ?)2— (a — Z)2

[0186] — I — a + f + h

[0187] Equation-15

[0188]

[0189] Step 6: Determining the best ( / *) and worst (Jj ) values for all criterion functions.

[0190] f(*) i = maxj fkji, f(-) i = minj fkji, j = 1, 2, ···, n, and i = 1, 2, ···, m.

[0191]

[0192] Equation-16

[0193] i'th function is maximized (benefit) and minimized (cost) respectively. f(*) i = minj fkji, f(-) i = maxj fkji, j = 1, 2, ···, and i = 1, 2, ···, m.

[0194]

[0195] Equation-17

[0196] Step 7: Sj and Rj values are found through the following equations.

[0197] Equation-18

[0198] R

[0199]

[0200] J =mtax[vvi( / i(*)“ - / i(-))]'7 = l,2,-,n,and i = l,2,-,m.

[0201] Equation-19

[0202] Step 8: Qj values are found through the following equations.

[0203] Q

[0204]

[0205] j = v(Sj - S*) / (S- - S*) + (1 - v^Rj - R*) / (R~ — R*),j = 1,2, -,n.

[0206] Equation-20

[0207] wherein S(*) = minj Sj; S(-) = maxj Sj; R(*) = minj Rj; R(-) = maxj Rj; and 'v' refers

[0208]

[0209] j J j J

[0210] to the weight for "maximum group benefit", while the weight for individual regret is denoted by (1 — v).

[0211] Step 9: Alternatives are ranked by sorting S, R, and Q values in ascending order.

[0212] Step 10: The best sorted / ranked alternative

[0213]

[0214] according to Q (minimum) is recommended as a compromise solution if the following two conditions are met:

[0215] Cl - Acceptable advantage,

[0216]

[0217] Q(A(2)) − Q(A(1)) ≥ DQ

[0218] Equation-21 Wherein A(2) is the second-ranked alternative with Q measure and is given by DQ = 1 / (m — 1).

[0219] C2 - Acceptable stability in the decision-making process: Alternative

[0220]

[0221] must maintain superior ranking with S and / or R. This compromise solution ensures stability in the decision-making process, encompassing strategies of maximum group benefit (v > 0.5), "consensus" ( « 0.5), or "veto" (v < 0.5). If one of the two conditions is not met, a compromise solution set is proposed, this set consisting of the following alternatives Only if the C2 condition is not met, the alternatives

[0222]

[0223] and; if the acceptable advantage (Cl) condition is not met, then

[0224]

[0225] A(2), •••, A® alternatives are determined for the maximum I according to the relation A®,

[0226]

[0227] < DQ (the positions of these alternatives are "within closeness").

[0228] The fuzzy-PROMETHEE method incorporates the principles of fuzzy sets theory and treats input data as fuzzy numbers to account for data uncertainties. In this method, fuzzy set theory is combined with the classical PROMETH EE procedure to improve the integration of trapezoidal fuzzy interval numbers. Trapezoidal fuzzy numbers occur when the two most promising values are equal; this represents a transition from a trapezoidal fuzzy number to a triangular fuzzy number and allows the Decision maker (DM) to express their view of the alternatives. As a result, trapezoidal fuzzy numbers provide greater flexibility in representing a wider range of scenarios. Trapezoidal fuzzy interval of two sets is expressed i

[0229]

[0230] n A = (lkji,akji, fkji,hkji) and B = (akji, &kji, ckji, dk7£) notations. The mathematical expression of the membership function for trapezoidal fuzzy intervals is as follows.

[0231] r0 for x < Iji or,

[0232] 1“ for lA ~ Pi1 < x < lA’

[0233] / z(x) = 'llf

[0234] 1 for Iji < x < aji,

[0235]

[0236] 1“ f°r aA< X~aA+ hA

[0237] Equation-22

[0238] Therefore, the proposed fuzzy PROMETHEE approach can be described in the following steps. Step 1: A generalized preference functionp

[0239]

[0240] k(d;) is determined for each criterion ( ).

[0241] Step 2: A vector containing fuzzy weights is defined as in Equation 1 and it is not necessary to normalize i

[0242]

[0243] t as Wkij = 1- Step 3: Fuzzy outranking relation for all alternatives ay, anG A is defined as ft(aj, an).

[0244] π(aj, an) = Σ(k=1 to K) wk · pk(Ci(aj) − Ci(an))

[0245]

[0246] i—ik=iv

[0247] Equation-23

[0248] Here, the trapezoidal expressions are C£(

[0249]

[0250] oy) = (lkji,akji> ftkji>h-kji) and Cn(an) = (akji> ^kji<ckji< dkjt) and the preference degrees for comparing alternatives ay and anaccording to criterion C£were calculated using fuzzy arithmetic according to the equation given in Step 3.

[0251] (c£((Zy) — C£((Zn)) — pk{^(j-kji>akji> Pkji’hkji) ~ (akji< ^kji<ckji< Equation-24

[0252] Wherein:

[0253]

[0254] ^kji ~ Pk(j-kji ^kji);akji ~ Pk(j-kjiakji)j Pkji ~ Pk(j-kji ^kji) Pk(j-kji ^kji P

[0255]

[0256] kji ~ dkjt), — Pfc(dkji + hkji +ckji)—Pk kji ~akji) ■

[0257] In the next step, the fuzzy outranking relation 'n' is determined using the following relationships.

[0258] — (J-kji>akji> Pkji’hkji) Equation-25

[0259] Here, ■ 1%). a’kJI= ), / ??), = •

[0260]

[0261] β(π) kji = Σ(k=1 to m)(l(w) kji · β(pk) kji + l(pk) kji · β(w) kji − β(w) kji · β(pk) kji), and h(π) kji = Σ(k=1 to m)(α(w) kji · h(pk) kji + α(pk) kji · h(w) kji + h(w) kji · h(pk) kji) Step 4: In contrast, for each alternative a / s fuzzy leaving flow is calculated as follows.

[0262] 1n

[0263] 0+(aj) = —^7l(-aj>an')

[0264] i=i

[0265] i*i

[0266] Equation-26

[0267]

[0268] Step 5: dj G A, is a measure of the weakness of alternatives, therefore a s fuzzy entering flow is determined by the following equation.

[0269] 1n

[0270] i=i

[0271] i*i

[0272]

[0273] Equation-27

[0274] Step 6: As a final step in defining the outranking relation, the weighted preference ratings calculated for each criterion k are added as in Equation (1). In the final stage of the definition of the outranking relation represented by "pe", the weighted preference ratings calculated for each criterion "k" were realized according to the formula presented in Equation- 1.

[0275] The fourth stage is the selection of the best alternatives: in this method, the pilot recruitment process, which is a challenging issue especially for large airlines, is examined and a ranking is made using three different fuzzy MCDM methods, fuzzy VIKOR, fuzzy TOPSIS and fuzzy PROMETHEE to evaluate and compare candidate pilots. Candidate pilots were assessed on five main factors, socio-cognitive ability (SCA), performance competence (PC), interpersonal competence (IC), visual perspectivetaking (VPT) and spatial working memory (SWM). To demonstrate the complexity of the comparison process, two different challenges were assessed using fuzzy linguistic terms (Tables 1 and 2) and a set of criteria and sub-criteria (Table 3) with ambiguous and uncertain meanings, in addition to the psychological characteristics of the candidates, to ensure a fair comparison and comprehensive evaluation. Three experts (DMs) were consulted for the study: The criteria set in Table 3 was used to evaluate a pilot group of twelve candidates by three decision makers: a fleet officer from Saudi Airlines, an officer from the General Authority of Civil Aviation (GACA), and an instructor pilot (IP). The evaluation process was initiated by determining the sub-criteria weights and ranking them using trapezoidal fuzzy numbers (TFNs) and term sets given in Tables 1 and 2 respectively.

[0276] Equation 11 shows the proposed method for calculating the distance (dj(B̃)) between trapezoidal fuzzy values. Therefore, the distances of alternatives (

[0277]

[0278] Aj) from the normalized weighted matrix to the respective FPIS and FNIS were calculated. On the other hand, the coefficient of closeness (CCj) of each alternative in the fuzzy TOPSIS ranking were determined and the results are given in Table 4. The results clearly show that alternative #1 (A1 ) is the best candidate pilot with the highest coefficient of closeness (CC) value of 0.359, followed by A6 with 0.3445, A5 with 0.3088 and A9 with 0.2947. The values of the other alternatives (CC) are presented in Fig. 1. In this context, according to the results of (CC), the ranking positions of the alternatives of all candidate pilots were determined and the best pilot was selected among twelve alternatives. Table 4 and Fig. 1 show the CC values of all alternative candidate pilots and the ranking order of the candidate pilots. Therefore, the data (B matris) in Table 7 were obtained from data presented in Tables 3 and 4. Step 3 shows the normalized matrix obtained from the fuzzy decision matrix / ). Equations 12 and 13 are used for the calculations of this matrix. Positive ideal (D*) and negative ideal (Dj values are used in calculating each candidate pilot's degree of closeness (CCj) to the ideal solution. The identification of positive and negative ideal solutions is used to determine the ranking of candidate pilots according to the fuzzy TOPSIS method.

[0279] Table 4. The coefficient of closeness (CCj) of alternative candidates according to fuzzy TOPSIS

[0280] Fuzzy TOPSIS

[0281] D D~ CCi Ranking

[0282] A1 2.938 1.646 0.3590 1

[0283] A2 3.246 0.311 0.0874 9

[0284] A3 3.580 0.253 0.0659 10

[0285] A4 2.993 0.134 0.0427 12

[0286] A5 2.712 1.211 0.3088 3

[0287] A6 3.267 1.717 0.3445 2 A7 2.951 0.385 0.1155 7

[0288] A8 3.104 1.211 0.2806 5

[0289] A9 3.141 1.312 0.2947 4

[0290] A10 2.922 0.157 0.0510 11

[0291] A11 2.732 0.332 0.1083 8

[0292] A12 2.784 0.957 0.2558 6

[0293] In the fuzzy VIKOR approach, the trapezoidal fuzzy numbers (TFNs) are defuzzified and the defuzzification process is carried out are using Equation 15 for combining TFNs. In this study, the center-of-area (COA) method was used for the defuzzification and the results are presented in Table 5. The fuzzy VIKOR findings given in Table 5 represent the performance values of candidates, which are obtained by combining the TFNs of each candidate pilot (A1,...,12) corresponding to the main criteria and expressing the evaluation scores of the decision makers about the candidates and converting them into a single number.

[0294] Table 5. Decision matrix and fuzzy weights for alternative candidates

[0295] Can dictate Sncie- Performance Jaterparsortel Spatial Visual

[0296] Pi Jots cognitive cempotence working perspectiveability memory taking

[0297]

[0298] The best (fj*) and worst (fj⁻) values of all criterion functions (Fig. 2) were obtained using Equations 16 and 17 given in step 6 to obtain the functions that should be maximized (benefit) and the functions that should be minimized (cost), respectively. The results of the best and worst values are obtained from Table 5 and presented in Table 6. The results are an array of best and worst values for all criteria functions.

[0299] The inputs are an array of the best and worst performances of the alternative candidates and the minimum / maximum operations of the criteria. The outputs are two vectors containing the Sj (variables) and Rj values given in step 7. Equations 18 and 19 were used to calculate the values (Sj) and (Rj), respectively, and the results are given in Table 6. Therefore the following was found: S*(min Sj) value as 1.220 and S⁻(max Sj) = 2.846. Similarly, R*(min Rj) value was detected as 0.59 and R⁻(max Rj) = 0.868.

[0300] Table 6. Calculation of Si and Ri values

[0301] Candidate Socio- Performance Interpersonal Spatial Visual Si RI Pilots cognitive competence competence working perspective^

[0302] ability memory taking Al 0. A4? JUTS O. SS f 0.533 O.0(K> CKGLS7

[0303] A2 0. XM (U4? 0.775 0. J50 2.244 0?‘?5

[0304] A3 0 S61 Q LU 077? (U4C- 06<x? 2. ML A4 0 (100 0.000 O.72S 0.722 Q.369 0.72S

[0305] A5 0306 0.654 0 104 0.000 0. -6S L233 0,654

[0306] A6 (1304 0.339 0,56? 0.420 0,302 2,37$ O. Tffcl

[0307] A? O JJy 0.£00 0023 0.005 1,(555 0300

[0308] .48 0.614 G.27S 0.104 0.420 0.660 2.0'6 0660

[0309] A$ (1.505 0222 0.6QS 6.667 0,36-9 2.372 0.66*

[0310] Al« a.< M! 0.445 0.164 0.667 0.4?s i.'SS O.6S7

[0311] AU O tidS 0.002 0.000 0.193 007& 1.220 0.§6S

[0312]

[0313] AJ2 0.4S4 044? Q.21J 0.590 0.546 IW O.59O

[0314] Step 8 aims to calculate the Qivalues using Equation 20; wherein, V is defined as a weight for the 'maximum group benefit' strategy, while (1 - v) represents the individual regret weight. For this study, V values were set as 0.25, 0.5 and 0.75 and the results and findings are given in Table 7.

[0315] Table 7. Calculation of Qivalues for v = 0.25, 0.50 and 0.75

[0316] Q0.250.152 0.615 0.941 0.423 0.134 0.445 0.593 0.280 0.345 0.246 0.708 -0.016

[0317] Q0.50.214 0.647 0.987 0.433 0.119 0.561 0.511 0.389 0.493 0.296 0.499 0.049

[0318]

[0319] 0.237 0.638 0.994 0401 0.064 0.637 0.390 0.458 0.601 0.307 0.250 0.073

[0320] Fig. 3 shows the ranking positions of the alternatives. Therefore, using step 10 and Equation 21 for the ranking position of the alternatives, the A3> A2> A6> A9> A8> A4> A7> A10> A11> A1> A12> A5 ranking of candidate pilots was obtained.

[0321] Fuzzy-PROMETHEE approach was also used to perform pilot selection using fuzzy linguistic data. The principles of fuzzy sets theory and the PROMETHEE approach are integrated using the TFNs given in Table 8 for the calculations. A generalized preference function pk(d;) for each decision criterion ( ) has been determined using the TFNs given in the D matrix in Table 8 (as seen in Equation 21). With the idea of combining total weights, a vector containing fuzzy weights that do not need to be normalized to 1 has been determined. The fuzzy outranking relation ft aj,an) for all alternative candidates ((a7), ane ) was determined using Equations 23, 24, and 25, respectively, and the results are presented in Table 9. These relations show the pairwise comparison of the candidate pilots to calculate the leaving flow (<(>+) and the entering flow (<(>-) to determine the ranking positions of the candidate pilots.

[0322] Table 8. Fuzzy trapezoidal numerical values determined for candidate pilots according to the criteria sets

[0323]

[0324] Table 9. Fuzzy outranking relation of candidate pilots

[0325] Combined Preference Leaving Function Aa A2Aie An flow,<|>+ Aj 0 0.324 0.591 0.233 0.156 Q. I34 0.273 0.197 0.362 0 173 0.491 0.350 3.28 As 0.136 0 0.0S3 0.254 0.214 0 109 0.269 0204 0.116 0.317 0.123 0.429 2.25 As 0.122 0.27 0 0.34 0266 0.221 0.374 0.258 0.230 0.237 0.312 0.456 3.09 A» 0.190 0.137 0.096 0 0.211 0.162 0.182 0.257 0.044 0.164 0,212 0.235 1.89 As 0.154 0.257 0.360 0.249 0 0 188 0.093 0 110 0.130 0 132 0.211 0.173 2.06 As 0.199 0.311 0.385 0.270 0.136 0 0.329 0.261 0.106 0.179 0.122 0.312 2.61 A- 0.171 0.280 0 191 0.224 0 196 0.162 0 0.299 0.188 0.252 0.278 0.318 2.56 As 0.177 0.172 0.084 0,307 0.021 0.102 0.002 0 0.136 0 150 0.287 0.291 1.73 As 0.146 0.450 0.273 0.168 0.108 0224 0.346 0313 0 0252 0.398 0.278 2.96 Aw 0.198 0.224 0276 0.152 0.156 0.133 0.293 0.123 0.087 0 0.339 0.186 2.17 0.086 0.236 0053 0.237 0 108 0.048 0271 0.072 0.106 0.212 0 0.166 1.59 Au 0.067 0.195 0.081 0.084 0.084 0052 0.225 0080 0.000 0053 0.170 0 1.09 Entering flow,

[0326]

[0327] 4>- 1.65 2.85 2.47 2.52 1.66 1.53 2.66 2.14 2.51 2.12 2.64 2.89

[0328] The fuzzy leaving flow of each alternative candidate in A, called the positive outranking flow (<(>+), is a number that indicates how much this activity is preferred over all other activities in A. The higher this value, the more preferred this alternative candidate is for the decision maker. Accordingly, the definition of positive outranking flow is given in Equation 26 and the findings are presented in Table 10. On the other hand, aj∈ A is a measure of weakness of alternative candidates, and a s fuzzy entering flow (<()-) is determined by Equation 27. As shown in Table 9 and Fig. 4, the negative outranking flow (<))-) is an indicator of the extent to which all other alternative candidates are preferred over all other alternatives, in line with the positive flow. Net flows are shown in Table 10. Therefore, according to fuzzy PROMETHEE, the ranking position of the candidates is A1 > A6 > A3 > A9 > A5 > A10 > A7 > A8 > A2 > A4 > A11 > A12.

[0329] Table 10. Ranking of alternative candidates according to fuzzy PROMETHEE

[0330]

[0331] The rankings of candidate pilots as a result of fuzzy-TOPSIS, fuzzy-VIKOR and fuzzy-PROMETHEE methods are given above. Although the fuzzy-TOPSIS and fuzzy-VIKOR approaches are distance-based methods of consensus ranking, fuzzy PROMETHEE is an outranking method for comparing alternatives. In this study, all five sets of evaluation criteria are considered as benefit criteria. In the fuzzy PROMETHEE approach, the comparative analysis of results involves the comparison of ranking positions, while the other two approaches take into account similarity coefficients in the selection of alternatives. Accordingly, maximum similarity was observed between the ranking positions of fuzzy TOPSIS and fuzzy PROMETHEE methods. On the other hand, the results from the fuzzy VIKOR approach showed sharp differences when compared to those obtained from other approaches. For example, alternative #1 (A1) was found to be the best candidate for recruitment according to the results of fuzzy TOPSIS and fuzzy PROMETHEE methods. However, while the ranking position of this alternative was found to be 23.77 (Table 11), it ranked tenth in the fuzzy VIKOR method. Pilot #6 was recruited as the second candidate according to the calculations of fuzzy TOPSIS and fuzzy PROMETHEE approaches. However, this candidate ranked third in the fuzzy VIKOR approach. Pilot #3 ranked third for recruitment according to the fuzzy TOPSIS and fuzzy PROMETHEE approaches while ranking first according to the fuzzy VIKOR approach. Interestingly, pilot #9 ranked fourth according to the calculations of all three MCDM approaches, and candidate 8 ranked fifth for the fuzzy TOPSIS and fuzzy VIKOR methods while ranking eighth according to the fuzzy PROMETHEE approach. The ranking positions of the remaining candidates are shown in Table 11.

[0332] The ranking positions of candidate pilots are shown as a result of the fuzzy -TOPSIS, fuzzy -VIKOR, and fuzzy -PROMETHEE methods. Although the fuzzy-TOPSIS and fuzzy-VIKOR approaches are distance-based methods of consensus ranking, fuzzy PROMETHEE is an outranking method for comparing alternatives. In this study, all five sets of evaluation criteria are considered as benefit criteria. In the fuzzy PROMETHEE approach, the comparative analysis of results involves the comparison of ranking positions, while the other two approaches take into account similarity coefficients in the selection of alternatives. Accordingly, maximum similarity was observed between the ranking positions of fuzzy TOPSIS and fuzzy PROMETHEE methods. On the other hand, the results from the fuzzy VIKOR approach showed sharp differences when compared to those obtained from other approaches. For example, alternative #1 (A1) was found to be the best candidate for recruitment according to the results of fuzzy TOPSIS and fuzzy PROMETHEE methods. However, while the ranking position of this alternative was found to be 23.77 (Table 11), it ranked tenth in the fuzzy VIKOR method. Pilot #6 was recruited as the second candidate according to the calculations of fuzzy TOPSIS and fuzzy PROMETHEE approaches. However, this candidate ranked third in the fuzzy VIKOR approach. Pilot #3 ranked third for recruitment according to the fuzzy TOPSIS and fuzzy PROMETHEE approaches while ranking first according to the fuzzy VIKOR approach. Interestingly, pilot #9 ranked fourth according to the calculations of all three MCDM approaches, and candidate 8 ranked fifth for the fuzzy TOPSIS and fuzzy VIKOR methods while ranking eighth according to the fuzzy PROMETHEE approach. The ranking positions of the remaining candidates are shown in Table 11.

[0333] Table 11. Ranking positions of candidates according to different MCDM methods AT

[0334] AS

[0335]

[0336] The operation of said method is as follows;

[0337] - Identifying qualitative and quantitative criteria for the recruitment process of pilots and taking these into account in the decision-making process,

[0338] - Uploading interviews conducted by experts on pilot recruitment processes and evaluation data (main criteria and sub-criteria) to the server,

[0339] - Converting criteria expressed in linguistic data into numerical data (trapezoidal numerical equivalents) by artificial intelligence using fuzzy logic method, - Introducing a set of fuzzy criteria and terms consisting of main and sub-criteria expressed in numerical data or converted into numerical data to the server with artificial intelligence,

[0340] - Evaluating, by a decision-making team consisting of at least one expert, the criteria (main criteria and sub-criteria), identifying candidate pilots and presenting the system working within the framework determined by expert opinions to artificial intelligence,

[0341] - Using fuzzy analytic hierarchy process (AHP) with artificial intelligence, determining, by the server, how decision makers evaluate each criterion and which criteria are more important using fuzzy logic by determining the degree of importance of each criterion, establishing a hierarchy among the criteria based on the opinions of experts, and calculating a weight value for each criterion, - Evaluating, by the server with artificial intelligence, the candidates with the fuzzy TOPSIS method, defuzzifying the trapezoidal numerical values with the positive ideal solution (best candidate) and negative ideal solution (worst candidate), and determining the performance of the candidates,

[0342] - Calculating, by the server (good) with artificial intelligence, the ideal closeness (CCj) using fuzzy TOPSIS based on the degrees of the positive ideal solution (best candidate) and the negative ideal solution, ranking the candidates using the coefficient of closeness to the ideal solution,

[0343] - Comparing, by the server with artificial intelligence, the results to determine the best candidate according to the scores of the candidates in each criterion, determining the candidate closest to the positive solution,

[0344] - Finding, by the server with artificial intelligence, the best compromise solution among the alternatives in the system by using the fuzzy VIKOR method based on the weights entered into the system by the decision makers, evaluating the minimum error and maximum success of the candidates in each criterion, and ranking the most suitable pilot candidates,

[0345] - Creating, by the artificial intelligence system, separate preference functions for each criterion with the fuzzy PROMETHEE method considering the internal relationship of the criteria, analyzing the differences between the candidates, and evaluating the performance of the candidates,

[0346] - Ranking candidates, by the server with artificial intelligence, starting with the most successful one (who scored the highest) for each criterion, and reporting, by the server, how successful each candidate is in which criteria,

[0347] - Presenting a report, by the server, to decision makers through an application, including comparisons between the candidates, the success ranking of each candidate on the criteria, and their final ranking,

[0348] - Selecting, by the decision makers, the most suitable pilot candidate based on the report received from the server.

[0349] In the process step of converting criteria expressed in linguistic data into numerical data by artificial intelligence using fuzzy logic method, the set of fuzzy linguistic terms used to determine the weights of the criteria and trapezoidal numerical equivalents thereof are as follows: very low (0, 0, 0.1, 0.2), low (0.1, 0.2, 0.2, 0.3), fairly low (0.2, 0.3, 0.4, 0.5), fair (0.4, 0.5, 0.5, 0.6), fairly good (0.5, 0.6, 0.7, 0.8), good (0.7, 0.8, 0.8, 0.9), very good (0.8, 0.9, 1.0, 1.0).

[0350] In the process step of converting criteria expressed in linguistic data into numerical data by artificial intelligence using fuzzy logic method, the set of fuzzy linguistic terms used to rate the criteria and trapezoidal numerical equivalents thereof are as follows: medium (0.4, 0.5, 0.5, 0.6), moderately good (0.5, 0.6, 0.7, 0.8), good (0.7, 0.8, 0.8, 0.9), very good (0.8, 0.9, 1.0, 1.0). In the process step of introducing a set of fuzzy criteria and terms consisting of main and sub-criteria expressed in numerical data or converted into numerical data to the server with artificial intelligence, the pilot's ‘socio-cognitive ability’comprising the main criteria is determined according to the criteria of performance competence, interpersonal relations competence, spatial working memory, visual perspective-taking ability.

[0351] In the process step of introducing a set of fuzzy criteria and terms consisting of main and sub-criteria expressed in numerical data or converted into numerical data to the server with artificial intelligence, the sub-criteria of the pilot's ‘socio-cognitive ability’ main criterion are determining their performance taking into account their working memory, reasoning ability, attention to detail, quick thinking ability, active listening ability, information processing ability, memory strength, logic (ability to establish context), strong focus, perception speed, and cognitive speed.

[0352] In the process step of introducing a set of fuzzy criteria and terms consisting of main and sub-criteria expressed in numerical data or converted into numerical data to the server with artificial intelligence, the 'performance competence’ main criterion of the candidate pilot is determined based on the following sub-criteria: commitment, decision-making competence, flexibility, reliability / discipline, stress resistance, trust, self-discipline, stress management, and the ability to remain calm under pressure criteria.

[0353] In the process step of introducing a set of fuzzy criteria and terms consisting of main and sub-criteria expressed in numerical data or converted into numerical data to the server with artificial intelligence, the sub-criteria of ‘interpersonal relations competence’ main criterion of the candidate pilot are determined according to the ability to cooperate, conflict resolution, self-assessment, English writing ability, English reading ability, active listening ability, teamwork ability, leadership ability, and multitasking ability.

[0354] In the process step of introducing a set of fuzzy criteria and terms consisting of main and sub-criteria expressed in numerical data or converted into numerical data to the server with artificial intelligence, the sub-criteria of the 'spatial working memory' main criterion of the candidate pilot are measured according to spatial visualization, numerical ability, ability to translate information, ability to process information, and ability to understand technical information. In the process step of introducing a set of fuzzy criteria and terms consisting of main and sub-criteria expressed in numerical data or converted into numerical data to the server with artificial intelligence, the sub-criteria of the 'visual perspective-taking' main criterion are measured based on the criteria of strong focus logic, high attention and alertness, ability to plan ahead, determination, and ability to empathize.

Claims

CLAIMS1. Method of determining the recruitment process of pilots using artificial intelligence-based fuzzy multi-objective decision-making models, characterized in that it comprises the process steps of:- Identifying qualitative and quantitative criteria for the recruitment process of pilots and taking these into account in the decision-making process,- Uploading interviews conducted by experts on pilot recruitment processes and evaluation data to the server,- Converting criteria expressed in linguistic data into numerical data by artificial intelligence using fuzzy logic method,- Introducing a set of fuzzy criteria and terms consisting of main and sub-criteria expressed in numerical data or converted into numerical data to the server with artificial intelligence,- Evaluating, by a decision-making team consisting of at least one expert, the criteria, identifying candidate pilots and presenting the system working within the framework determined by expert opinions to artificial intelligence,- Using fuzzy analytic hierarchy process (AHP) with artificial intelligence, determining, by the server, how decision makers evaluate each criterion and which criteria are more important using fuzzy logic by determining the degree of importance of each criterion, establishing a hierarchy among the criteria based on the opinions of experts, and calculating a weight value for each criterion, - Evaluating, by the server with artificial intelligence, the candidates with the fuzzy TOPSIS method, defuzzifying the trapezoidal numerical values with the positive ideal solution and negative ideal solution, and determining the performance of the candidates,- Calculating, by the server with artificial intelligence, the ideal closeness (CCj) using fuzzy TOPSIS based on the degrees of the positive ideal solution and the negative ideal solution, ranking the candidates using the coefficient of closeness to the ideal solution,- Comparing, by the server with artificial intelligence, the results to determine the best candidate according to the scores of the candidates in each criterion, determining the candidate closest to the positive solution,- Finding, by the server with artificial intelligence, the best compromise solution among the alternatives in the system by using the fuzzy VIKOR method basedon the weights entered into the system by the decision makers, evaluating the minimum error and maximum success of the candidates in each criterion, and ranking the most suitable pilot candidates,- Creating, by the artificial intelligence system, separate preference functions for each criterion with the fuzzy PROMETHEE method considering the internal relationship of the criteria, analyzing the differences between the candidates, and evaluating the performance of the candidates,- Ranking candidates, by the server with artificial intelligence, starting with the one who scored the highest for each criterion, and reporting, by the server, how successful each candidate is in which criteria,- Presenting a report, by the server, to decision makers through an application, including comparisons between the candidates, the success ranking of each candidate on the criteria, and their final ranking,- Selecting, by the decision makers, the most suitable pilot candidate based on the report received from the server.

2. A method of determining the recruitment process of pilots using artificial intelligence-based fuzzy multi-objective decision-making models according to claim 1, characterized in that; in the process step of converting criteria expressed in linguistic data into numerical data by artificial intelligence using fuzzy logic method, the set of fuzzy linguistic terms used to determine the weights of the criteria and trapezoidal numerical equivalents thereof are as follows: very low (0, 0, 0.1, 0.2), low (0.1, 0.2, 0.2, 0.3), fairly low (0.2, 0.3, 0.4, 0.5), fair (0.4, 0.5, 0.5, 0.6), fairly good (0.5, 0.6, 0.7, 0.8), good (0.7, 0.8, 0.8, 0.9), very good (0.8, 0.9, 1.0, 1.0).

3. A method of determining the recruitment process of pilots using artificial intelligence-based fuzzy multi-objective decision-making models according to claim 1, characterized in that; in the process step of converting criteria expressed in linguistic data into numerical data by artificial intelligence using fuzzy logic method, the set of fuzzy linguistic terms used to rate the criteria and trapezoidal numerical equivalents thereof are as follows: medium (0.4, 0.5, 0.5, 0.6), moderately good (0.5, 0.6, 0.7, 0.8), good (0.7, 0.8, 0.8, 0.9), very good (0.8, 0.9, 1.0, 1.0).

4. A method of determining the recruitment process of pilots using artificial intelligence-based fuzzy multi-objective decision-making models according to claim 1,characterized in that in the process step of introducing a set of fuzzy criteria and terms consisting of main and sub-criteria expressed in numerical data or converted into numerical data to the server with artificial intelligence, the main criteria are the candidate pilot's socio-cognitive ability, performance competence, interpersonal relations competence, spatial working memory, visual perspective-taking ability.

5. A method of determining the recruitment process of pilots using artificial intelligence-based fuzzy multi-objective decision-making models according to claim 1 or claim 4, characterized in that in the process step of introducing a set of fuzzy criteria and terms consisting of main and sub-criteria expressed in numerical data or converted into numerical data to the server with artificial intelligence, the sub-criteria of the pilot's socio-cognitive ability main criterion are: working memory, reasoning ability, attention to detail, quick thinking ability, active listening ability, information processing ability, memory strength, logic, strong focus, perception speed, and cognitive speed.

6. A method of determining the recruitment process of pilots using artificial intelligence-based fuzzy multi-objective decision-making models according to claim 1 or claim 4, characterized in that in the process step of introducing a set of fuzzy criteria and terms consisting of main and sub-criteria expressed in numerical data or converted into numerical data to the server with artificial intelligence, the sub-criteria of the performance competence main criterion are: commitment, decision-making competence, flexibility, reliability / discipline, stress resistance, trust, self-discipline, stress management, and the ability to remain calm under pressure.

7. A method of determining the recruitment process of pilots using artificial intelligence-based fuzzy multi-objective decision-making models according to claim 1 or claim 4, characterized in that in the process step of introducing a set of fuzzy criteria and terms consisting of main and sub-criteria expressed in numerical data or converted into numerical data to the server with artificial intelligence, the sub-criteria of interpersonal relations competence main criterion are: ability to cooperate, conflict resolution, self-assessment, English writing ability, English reading ability, active listening ability, teamwork ability, leadership ability, and multitasking ability.

8. A method of determining the recruitment process of pilots using artificial intelligence-based fuzzy multi-objective decision-making models according to claim 1 or claim 4,characterized in that in the process step of introducing a set of fuzzy criteria and terms consisting of main and sub-criteria expressed in numerical data or converted into numerical data to the server with artificial intelligence, the sub-criteria of the spatial working memory main criterion are: spatial visualization, numerical ability, ability to translate information, ability to process information, and ability to understand technical information.

9. A method of determining the recruitment process of candidate pilots using artificial intelligence-based fuzzy multi-objective decision-making models according to claim 1 or claim 4, characterized in that in the process step of introducing a set of fuzzy criteria and terms consisting of main and sub-criteria expressed in numerical data or converted into numerical data to the server with artificial intelligence, the sub-criteria of 'visual perspective-taking ability’ main criterion are: strong focus logic, high attention and alertness, ability to plan ahead, determination, and empathy skills.

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