A linguistic multi-attribute decision making method based on normal cloud similarity

Abstract

The present invention relates to a linguistic multi-attribute decision-making method based on normal cloud similarity, comprising the steps of: obtaining the linguistic variables of each expert on different attributes and converting them into normal cloud concepts to obtain the cloud decision matrix of each solution; based on the cloud decision matrix, performing a first cloud synthesis on the normal cloud concept to obtain the comprehensive cloud concept of each solution under different attributes; finding the weight of each attribute, performing a second cloud synthesis on the comprehensive cloud concept to obtain the final comprehensive cloud concept; calculating the positive ideal cloud concept and the negative ideal cloud concept; calculating the similarity between the final comprehensive cloud concept and the positive and negative ideal cloud concepts, as well as the relative cloud concept similarity of each solution; sorting by relative cloud concept similarity, the larger the value, the better the solution, thereby selecting the optimal solution. The present invention applies the calculation of normal cloud concept similarity to linguistic multi-attribute decision-making, fully expresses the uncertain information of the expert group, and makes a comprehensive judgment.

Description

Technical Field

[0001] The present invention relates to the technical field of linguistic multi-attribute decision making, and in particular to a linguistic multi-attribute decision making method based on normal cloud similarity. Background Art

[0002] With the development of social economy and the increasing complexity of the environment, multi-attribute decision-making is widely used in planning, strategy and other fields. However, the complexity of the decision-making environment and the subjectivity and limitations of decision-makers make it difficult for decision-makers to make judgments in an accurate and quantitative form. Therefore, how to effectively express and process uncertain language information has become the focus of decision-making research.

[0003] Existing technologies show that the quality of multi-attribute decision-making depends largely on the characterization and description of uncertainty and fuzziness. The cloud model is a model that characterizes the randomness and fuzziness in uncertainty. The cloud model is a model that can describe uncertainty conversion using qualitative language and quantitative numerical values, and its application effectiveness has been recognized and promoted. As an uncertainty model for qualitative-quantitative conversion, the cloud model can fully reflect the randomness and fuzziness of language concepts and is an effective tool for achieving qualitative-quantitative conversion. The quality of the cloud model similarity measurement method is closely related to the actual application effect of the cloud model.

[0004] There are many deficiencies in the calculation of cloud model similarity in the prior art. For example, the similarity between cloud models is measured by calculating the distance between cloud droplets. This method has too high time complexity and unstable results. The three digital features of the cloud model are regarded as three elements of the vector, and the cosine value of the two vectors is calculated using the cosine law to determine the similarity of the two cloud models. This method ignores the role of entropy and super entropy, resulting in weak discrimination ability. The similarity of the two cloud models is calculated by integrating the overlapping area of ​​the expected curve and the maximum boundary curve of the two cloud models. When there are many cloud concepts, the computational complexity of this method will increase sharply. In summary, how to quickly and effectively calculate the similarity of cloud concepts is an issue worth exploring. Summary of the invention

[0005] The purpose of the present invention is to apply the calculation of normal cloud concept similarity to linguistic multi-attribute decision making, fully express the uncertain information of the expert group, make a comprehensive judgment, and provide a linguistic multi-attribute decision making method based on normal cloud similarity.

[0006] In order to achieve the above-mentioned object of the invention, the embodiment of the present invention provides the following technical solutions:

[0007] A linguistic multi-attribute decision-making method based on normal cloud similarity includes the following steps:

[0008] Step 1: Based on the language evaluation set, the language variables of each expert on different attributes are obtained, and the language variables are converted into normal cloud concepts. The cloud decision matrix of each solution is obtained through the normal cloud concept;

[0009] Step 2: Based on the cloud decision matrix, the normal cloud concepts of each solution under different experts are first integrated to obtain the integrated cloud concepts of each solution under different attributes;

[0010] Step 3, using the comprehensive cloud concept to find the weight of each attribute, and performing a second cloud synthesis on the comprehensive cloud concept according to the attribute weight to obtain the final comprehensive cloud concept;

[0011] Step 4, calculating the positive ideal cloud concept and the negative ideal cloud concept according to the final comprehensive cloud concept of each scheme;

[0012] Step 5, calculating the similarity between the final comprehensive cloud concept and the positive ideal cloud concept, the negative ideal cloud concept, and the relative cloud concept similarity of each solution;

[0013] Step 6: Based on the TOPSIS idea, the relative cloud concept similarity is used for sorting. The larger the value of the relative cloud concept similarity is, the better the solution is, so the optimal solution is selected.

[0014] Compared with the prior art, the present invention has the following beneficial effects:

[0015] Starting from the characteristic curve, the present invention considers the normal cloud similarity of the entropy expectation curve, uses the Wasserstein distance to characterize the similarity measurement method, and conducts an example analysis on the given method to illustrate the feasibility and effectiveness of the method. BRIEF DESCRIPTION OF THE DRAWINGS

[0016] In order to more clearly illustrate the technical solutions of the embodiments of the present invention, the drawings required for use in the embodiments are briefly introduced below. It should be understood that the following drawings only show certain embodiments of the present invention and therefore should not be regarded as limiting the scope. For ordinary technicians in this field, other related drawings can be obtained based on these drawings without creative work.

[0017] Figure 1 is a flow chart of the method of the present invention;

[0018] Figure 2 It is a schematic diagram of the normal cloud expectation curve and the entropy expectation curve;

[0019] FIG3 is a schematic diagram showing a comparison of the classification accuracy of the method proposed in Example 2 of the present invention and other traditional methods on four types of training data sets, wherein FIG3(a) shows the classification accuracy of different methods on the A1 type training data set, FIG3(b) shows the classification accuracy of different methods on the B1 type training data set, FIG3(c) shows the classification accuracy of different methods on the C1 type training data set, and FIG3(d) shows the classification accuracy of different methods on the D1 type training data set;

[0020] Figure 4 This is a schematic diagram showing a comparison of CPU running time between the method proposed in Example 2 of the present invention and other traditional methods at different numbers of cloud concepts. DETAILED DESCRIPTION

[0021] The technical solutions in the embodiments of the present invention will be clearly and completely described below in conjunction with the drawings in the embodiments of the present invention. Obviously, the described embodiments are only a part of the embodiments of the present invention, rather than all the embodiments. The components of the embodiments of the present invention generally described and shown in the drawings here can be arranged and designed in various different configurations. Therefore, the following detailed description of the embodiments of the present invention provided in the drawings is not intended to limit the scope of the claimed invention, but merely represents selected embodiments of the present invention. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without making creative work belong to the scope of protection of the present invention.

[0022] It should be noted that similar numbers and letters represent similar items in the following figures, so once an item is defined in one figure, it does not need to be further defined and explained in subsequent figures. At the same time, in the description of the present invention, the terms "first", "second", etc. are only used to distinguish the description, and cannot be understood as indicating or implying relative importance, or implying any such actual relationship or order between these entities or operations. In addition, the terms "connected", "connected", etc. can be directly connected between elements, or indirectly connected via other elements.

[0023] Concept introduction:

[0024] 1. Cloud model and its concepts

[0025] Let U be a quantitative domain represented by exact numerical values, C be a qualitative concept on the domain U, there exists a quantitative value x∈U which is a random realization of the qualitative concept C, and its membership to C μ(x)∈[0,1] is a random number with a stable tendency, that is, μ:U→[0,1], x→μ(x), then the division of the membership μ(x) on the domain U is referred to as a cloud, denoted by C(U), and each (x,μ(x)) is called a cloud droplet. If: x~N(Ex,En` 2), if En`~N(En,He 2 ), and the certainty of C satisfies The distribution on the domain is called a normal cloud.

[0026] Normal cloud expectation curve is an important method to study the geometric characteristics of normal cloud. If the random variable x~N(Ex,En` 2 ), if En`~N(En,He 2 ), and En≠0, then It is called the expected entropy curve of the normal cloud.

[0027] 2. Introduction to Wasserstein distance

[0028] Let μ, v be the probability space R n The measurement on The p-Wasserstein distance is defined as: in, For R n ×R n The set of joint probability measures γ on the upper bound, whose marginal distributions are μ, v, and d(x, y) is R l For any distance on , p ≥ 1.

[0029] For two multidimensional normal distributions P1 and P2, the Wasserstein distance between them is:

[0030]

[0031] Among them, m1 and m2 are the mean vectors of P1 and P2 respectively, and M1 and M2 are the covariance matrices of P1 and P2 respectively.

[0032] Based on the definition of Wasserstein distance, the present invention obtains two one-dimensional normal distributions X and Y, and their Wasserstein distance d(X, Y) is: Among them, μ1 and μ2 are the means of X and Y respectively, and σ1 and σ2 are the variances of X and Y respectively.

[0033] 3. Similarity calculation based on Wasserstein distance

[0034] The present invention combines Figure 2 The characteristics of the entropy expectation curve and Wasserstein distance of the normal cloud shown in the figure, and the normal cloud concept similarity calculation based on Wasserstein distance is obtained. The specific steps are as follows:

[0035] (1) Let C1 = (Ex1, En1, He1) and C2 = (Ex2, En2, He2) be two normal cloud concepts. According to the expected entropy curve of the normal cloud Get the expectation (Ex1, Ex2) and variance corresponding to the two normal cloud concepts

[0036] (2) According to the characteristic that Wasserstein distance can describe the distance between two probability distributions, the Wasserstein distance d(C1, C2) between two normal cloud concepts C1 and C2 is calculated as:

[0037]

[0038] (3) An exponential function is introduced as a normalization function to convert the distance d(C1, C2) between two normal cloud concepts C1 and C2 into similarity sim(C1, C2), that is:

[0039]

[0040] Embodiment 1:

[0041] The present invention is achieved through the following technical solutions: Figure 1 As shown, a linguistic multi-attribute decision-making method based on normal cloud similarity includes the following steps:

[0042] Step 1: Based on the language evaluation set, the language variables of each expert on different attributes are obtained, and the language variables are converted into normal cloud concepts. The cloud decision matrix of each solution is obtained through the normal cloud concept.

[0043] Assume that the decision maker needs to choose one solution from m solutions. There are l experts who evaluate the m solutions based on n attributes. i The Cloud Decision Matrix Among them, i represents the i-th solution, i = 1, 2, ..., m; r represents the r-th expert, r = 1, 2, ..., l; j represents the j-th attribute, j = 1, 2, ..., n.

[0044] Given a language evaluation set H = {h k |k=-t,...,0,...,t,t∈N},h k represents a language variable, there exists a function f that can convert h k Transformed into the corresponding parameter θ k ,θ k ∈[0,1], that is:

[0045]

[0046] The value of a can be determined by experimental method or subjective method. The experimental method shows that the value range of a is [1.36,1.4], and the subjective method shows that a≈1.37.

[0047] Given an expert domain [X min ,X max ], let h k ∈H after transformation, the corresponding normal cloud concept is C k =(Ex k ,En k ,He k ), and its conversion model is as follows:

[0048] (1) Calculation of Ex k :

[0049] Ex k =X min +θ k (X max -X min )

[0050] (2) Calculate En k :

[0051]

[0052] (3) Calculate He k :

[0053]

[0054]

[0055]

[0056] The normal cloud concept is calculated as C k =(Ex k ,En k ,He k ), assuming that the expert domain is [X min ,X max ]=[2,8], t=3, then the normal cloud concept of the language evaluation set is shown in Table 1.

[0057] Table 1 Normal cloud concepts of language evaluation set

[0058]

[0059] For example, a company wants to choose an intelligent identification system. There are three options X = {X1, X2, X3} available for the company to choose from. When making the choice, the decision makers mainly consider the attributes c1 (functionality), c2 (effectiveness), and c3 (economy). Among them, c1 and c2 are benefit attributes, c3 is a cost attribute, and the weight of each attribute is unknown.

[0060] There are 5 experts D = {d1, d2, d3, d4, d5} who evaluate 3 solutions. Assume that the importance of the experts’ evaluation is the same, that is, the weight of each expert is λ r is 0.2, each expert has a 7-scale language evaluation set H = {h -3 = Very bad, h -2 = difference, h -1 = poor, h0 = average, h1 = good, h2 = good, h3 = very good} to select language variables and evaluate each solution. The decision information given by the experts is shown in Table 2.

[0061] Table 2 Decision information of each plan given by experts

[0062]

[0063] When the value of a and the domain [X min ,X max ] After being determined, Table 1 is a fixed value, then the specific cloud decision matrix of the decision information of each scheme in Table 2 is shown in Tables 3-5.

[0064] Table 3 Cloud decision matrix for solution 1

[0065]

[0066] Table 4 Cloud decision matrix for solution 2

[0067]

[0068] Table 5 Cloud decision matrix for solution 3

[0069]

[0070] Step 2: Based on the cloud decision matrix, the normal cloud concepts of each solution under different experts are first integrated to obtain the comprehensive cloud concepts of each solution under different attributes.

[0071] Based on the Cloud Decision Matrix Each plan X i Normal cloud concept under different experts Perform the first cloud synthesis and obtain each solution X i In different attributes c j Comprehensive cloud concept under X i c j :C=(Ex ij ,En ij ,He ij ),in:

[0072]

[0073]

[0074]

[0075] Among them, λ r is the weight of the rth expert.

[0076] Based on the cloud decision matrix shown in Tables 2 to 5, the normal cloud concepts of each solution under different experts are first integrated to obtain the X i In different attributes c j Comprehensive cloud concept under X i c j :C=(Ex ij ,En ij ,He ij ) as shown in Table 6.

[0077] Table 6 Comprehensive cloud concept of each attribute for each solution decision information

[0078]

[0079] Step 3: Use the comprehensive cloud concept to find the weight of each attribute, perform a second cloud synthesis on the comprehensive cloud concept according to the attribute weight, and obtain the final comprehensive cloud concept.

[0080] Using Ex ij and En ij Find the attributes c j The weight w j :

[0081]

[0082] According to the attribute weight w j For each plan X i In the attribute c j Comprehensive cloud concept under X i c j :C=(Ex ij ,En ij ,He ij ) Perform the second cloud synthesis to obtain each solution X i The ultimate comprehensive cloud concept X i :C=(Ex i ,En i ,He i ),in:

[0083]

[0084]

[0085]

[0086] The final comprehensive cloud concept of each solution is:

[0087] X1:C=(4.269,1.359,0.818)

[0088] X2:C=(4.588,1.363,0.825)

[0089] X3:C=(4.918,1.389,0.840)

[0090] Step 4: Calculate the positive ideal cloud concept and the negative ideal cloud concept based on the final comprehensive cloud concept of each solution.

[0091] Final comprehensive cloud concept based on each solution X i :C=(Ex i ,En i ,He i ), we get the positive ideal cloud concept XPIC and the negative ideal cloud concept XNIC:

[0092]

[0093]

[0094] The obtained positive ideal cloud concept and negative ideal cloud concept are:

[0095] XPIC=(4.918,1.359,0.818)

[0096] XNIC=(4.269,1.389,0.839)

[0097] Step 5: Calculate the similarity between the final integrated cloud concept and the positive ideal cloud concept, the negative ideal cloud concept, and the relative cloud concept similarity of each solution.

[0098] Computing the Ultimate Comprehensive Cloud Concept X i : The similarity between C and the positive ideal cloud concept XPIC and the negative ideal cloud concept XNIC is sim(X i :C,XPIC),sim(X i :C,XNIC), and each scheme X i The relative cloud concept similarity RCS(X i ):

[0099]

[0100] The similarity results are shown in Table 7.

[0101] Table 7 Similarity between the comprehensive cloud concept of each scheme and the positive and negative ideal cloud concepts and the relative cloud concept similarity

[0102]

[0103] Step 6: Based on the TOPSIS idea, the relative cloud concept similarity is used for sorting. The larger the value of the relative cloud concept similarity is, the better the solution is, so the optimal solution is selected.

[0104] According to the results in Table 7, the TOPSIS method is used to analyze the relative cloud concept similarity RCS (X i ) to sort, RCS(X i ) value is larger, indicating that the scheme X i The better, the ranking of the three solutions is X3>X2>X1, which means that solution X3 is the best solution.

[0105] Embodiment 2:

[0106] This embodiment analyzes the test results based on the above embodiment 1. Time series data is a type of data collected at different times, which is used to describe the changes of phenomena over time. It has high-dimensional characteristics and can well test the accuracy of the classification method. In the classification process, the quality of the similarity measurement method plays a decisive role in the classification results. The time series data set commonly used in the database (UCI KDD) is often used for classification and clustering because it has the characteristics of multiple changing trends, large fluctuations, and complex and variable time series. It can better test the quality of similarity measurement methods. The data set consists of 600 rows and 60 columns of data, with 100 rows for each category, a total of 6 categories, and these 6 categories of data represent 6 types of time series with different changing trends.

[0107] The present invention uses the UCI knowledge discovery database as the research object. During the experiment, the last 20 rows of each category are selected as the test set, and the rest are the training set. The method proposed by the present invention is compared and analyzed with the existing traditional methods. The KNN algorithm is used to classify the data set, and the number of nearest neighbors K is 1 to 10. In order to improve the calculation efficiency, the first 80 rows of data in each category are evenly divided into 4 parts, forming a total of 4 training data sets, each with 120 data, represented by A1, B1, C1, and D1, and their classification accuracy is calculated respectively.

[0108] Please refer to Figure 3, which is a schematic diagram comparing the classification accuracy of the method proposed in the present invention and other traditional methods on four types of training data sets, wherein Figure 3 (a) is the classification accuracy of different methods on the A1 type training data set, Figure 3 (b) is the classification accuracy of different methods on the B1 type training data set, Figure 3 (c) is the classification accuracy of different methods on the C1 type training data set, and Figure 3 (d) is the classification accuracy of different methods on the D1 type training data set. It can be seen that the classification accuracy of the method (WCM) proposed in the present invention is above 80%, which has a strong advantage over other traditional methods.

[0109] See also Figure 4 , Figure 4 This is a schematic diagram of the CPU running time comparison between the method proposed in this invention and other traditional methods at different numbers of cloud concepts. It can be seen that the method proposed in this invention (WCM) has obvious advantages in CPU running time cost compared with ECM, MCM and other methods with higher classification accuracy, and effectively improves the classification efficiency of time series. In general, the method proposed in this invention (WCM) is better and is a more feasible method for calculating similarity.

[0110] In summary, quantitative analysis of uncertain information has always been an important research direction in information processing, and cloud model theory has made great contributions in this research direction. The amount of uncertain information and related measurement calculation processing in linguistic multi-attribute decision-making determine the rationality and scientificity of the decision results. Aiming at the problem of cloud concept similarity calculation in linguistic multi-attribute decision-making, the present invention proposes a linguistic multi-attribute decision-making method based on normal cloud similarity. Starting from the characteristic curve, the method considers the normal cloud similarity of the entropy expectation curve, and uses the Wasserstein distance to characterize the similarity measurement method. The given method is analyzed by example to illustrate the feasibility and effectiveness of the method. Based on this, a linguistic multi-attribute decision-making method based on normal cloud similarity is given. Finally, this method is applied to the decision-making selection example of the intelligent recognition system to verify the practicality and scientificity of the method.

[0111] The above is only a specific embodiment of the present invention, but the protection scope of the present invention is not limited thereto. Any person skilled in the art can easily think of changes or substitutions within the technical scope disclosed by the present invention, which should be included in the protection scope of the present invention. Therefore, the protection scope of the present invention should be based on the protection scope of the claims.

Claims

1. A linguistic multi-attribute decision-making method based on normal cloud similarity, characterized by: The following steps are involved: Step 1: Based on the language evaluation set, the language variables of each expert on different attributes are obtained, and the language variables are converted into normal cloud concepts. The cloud decision matrix of each solution is obtained through the normal cloud concept; Step 2: Based on the cloud decision matrix, the normal cloud concepts of each solution under different experts are first integrated to obtain the integrated cloud concepts of each solution under different attributes; Step 3: Use the comprehensive cloud concept to find the weight of each attribute, and perform a second cloud synthesis on the comprehensive cloud concept according to the attribute weight to obtain the final comprehensive cloud concept X i :C=(Ex i ,En i ,He i ); Step 4: Final comprehensive cloud concept based on each solution i :C=(Ex i ,En i ,He i ), calculate the positive ideal cloud concept and the negative ideal cloud concept; The step 4 specifically comprises the following steps: Final comprehensive cloud concept based on each solution X i :C=(Ex i ,En i ,He i ), we get the positive ideal cloud concept XPIC and the negative ideal cloud concept XNIC: Step 5, calculating the similarity between the final comprehensive cloud concept and the positive ideal cloud concept, the negative ideal cloud concept, and the relative cloud concept similarity of each solution; The step 5 specifically comprises the following steps: Computing the Ultimate Comprehensive Cloud Concept X i : The similarity between C and the positive ideal cloud concept XPIC and the negative ideal cloud concept XNIC is sim(X i :C,XPIC),sim(X i :C,XNIC), and each scheme X i The relative cloud concept similarity RCS(X i ): in: Step 6: Based on the TOPSIS idea, the relative cloud concept similarity is used for sorting. The larger the value of the relative cloud concept similarity is, the better the solution is, so the optimal solution is selected.

2. The linguistic multi-attribute decision making method based on normal cloud similarity according to claim 1, characterized in that: The step 1 specifically comprises the following steps: Given a language evaluation set H = {h k |k=-t,...,0,...,t,t∈N},h k represents a language variable, there exists a function f that converts h k Transformed into the corresponding parameter θ k ,θ k ∈[0,1], we have: Given an expert domain [X min ,X max ], let h k ∈H after transformation, the corresponding normal cloud concept is C k =(Ex k ,En k ,He k ), and its conversion model is: Calculate Ex k : Ex k =X min +θ k (X max -X min ) Calculate En k : Calculate He k : The normal cloud concept is calculated as C k =(Ex k ,En k ,He k ), the cloud decision matrix of each solution is obtained through the concept of normal cloud Among them, i represents the serial number of the plan, i=1,2,...,m; r represents the serial number of the expert, r=1,2,...,l; j represents the serial number of the attribute, j=1,2,...,n.

3. The linguistic multi-attribute decision making method based on normal cloud similarity according to claim 2 is characterized by: The step 2 specifically includes the following steps: Based on the Cloud Decision Matrix Each plan X i Normal cloud concept under different experts Perform the first cloud synthesis and obtain each solution X i In different attributes c j Comprehensive cloud concept under X i c j :C=(Ex ij ,En ij ,He ij ),in: Among them, λ r is the weight of the rth expert.

4. The linguistic multi-attribute decision making method based on normal cloud similarity according to claim 3 is characterized by: The step 3 specifically includes the following steps: Using Ex ij and En ij Find the attributes c j The weight w j : According to the attribute weight w j For each plan X i In the attribute c j Comprehensive cloud concept under X i c j :C=(Ex ij ,En ij ,He ij ) Perform the second cloud synthesis to obtain each solution X i The ultimate comprehensive cloud concept X i :C=(Ex i ,En i ,He i ),in:

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