A fuzzy multi-attribute decision evaluation method and system

Abstract

This invention discloses a fuzzy multi-attribute decision-making evaluation method and system. The method includes defining a hesitant fuzzy language terminology set; determining the evaluation object and its influencing factors based on the hesitant fuzzy language terminology set to form a factor set, and assigning weights to each influencing factor to determine the membership function of each factor; performing fuzzy synthesis operations on the membership function of each factor and its corresponding weights to obtain a comprehensive membership value; and performing fuzzy evaluation on the evaluation object based on the comprehensive membership value to obtain a fuzzy comprehensive evaluation result of the evaluation object. This invention's multi-attribute decision-making method, capable of handling incomplete and imprecise fuzzy information, plays a crucial role in ensuring the rationality and accuracy of investment risk assessment.

Description

Technical Field

[0001] This invention relates to the field of fuzzy attribute decision-making technology, and in particular to a fuzzy multi-attribute decision-making evaluation method and system. Background Technology

[0002] Decision-making is the process by which people select and execute a solution from multiple alternatives to achieve a goal or complete a task. The decision-making process typically includes: identifying and defining the problem; determining the goal and standards and developing corresponding alternatives; evaluating the alternatives and selecting the implementation plan. As human society progresses with scientific development, more and more decision-making problems are constrained and influenced by complex factors, and simple experience-based decision-making can no longer meet the increasingly complex decision-making needs. Under this trend, multi-attribute decision-making has emerged as an important branch of modern decision theory. Multi-attribute decision-making refers to the process of selecting the optimal solution from a finite number of alternatives with limited attributes. Specifically, given a set of alternative action plans to be evaluated, each plan is expressed through multiple attributes representing the current state. Decision-makers need to evaluate each plan's attributes according to certain evaluation criteria and obtain a comprehensive ranking of the plans through a specific method to find the best decision plan. It can be seen that the key elements of the multi-attribute decision-making process mainly include four aspects: decision goal, alternatives, attributes, and attribute weights.

[0003] With the continuous development of society and the economy, people are facing increasing complexity and uncertainty in decision-making problems, as well as the ambiguity of human thinking. In the actual decision-making process, decision information often carries ambiguity and uncertainty, manifesting in the following forms:

[0004] (1) In the decision-making process, decision-makers often lack a full understanding of the decision object due to the limitations of their subjective judgment and the finiteness of their knowledge and experience. They struggle to provide precise information or accurate probability distribution characteristics of the object being evaluated. To address this issue, Professor Zadeh of the University of California published the paper "Fuzzy Sets," pioneering the concept of fuzzy sets. Fuzzy set theory posits that the relationship between an object and a set is not simply one of belonging or not belonging; rather, there exists a transitional state. An object's transition from belonging to a set to not belonging to that set involves a continuous process of change from quantitative to qualitative change, and fuzzy sets are used to describe this process of change.

[0005] (2) Due to the complexity and uncertainty of objective things and the ambiguity of human thinking, decision-makers tend to use language to provide evaluation information in some situations. For example, teachers use comments such as "Excellent," "Good," "Average," and "Poor" to evaluate students' overall performance during their time at school. However, sometimes decision-makers find it difficult to provide evaluation information with a single comment and may believe that the level of the evaluated object is between two comments. In this case, they will use "between Excellent" and "Good" to express it. Uncertain linguistic variables are used to describe this situation, and such multi-attribute decision problems are called uncertain linguistic multi-attribute decision problems.

[0006] (3) Sometimes, people may hesitate or have some knowledge gaps during the process of understanding things, resulting in three possible outcomes: affirmation, negation, or a hesitation that falls between affirmation and negation. For example, in the process of voting, in addition to support and opposition, there may also be abstentions. Summary of the Invention

[0007] The present invention aims to at least partially solve one of the technical problems in the related art.

[0008] To address this, the present invention proposes a fuzzy multi-attribute decision evaluation method, which provides decision-makers with more options when assigning evaluation information to evaluation indicators, better expresses the uncertainty of evaluation information, and thus preserves complete decision information to the greatest extent.

[0009] Another objective of this invention is to propose a fuzzy multi-attribute decision evaluation system.

[0010] To achieve the above objectives, this invention proposes a fuzzy multi-attribute decision evaluation method, comprising:

[0011] Define a set of hesitant and ambiguous language terms;

[0012] Based on the hesitant fuzzy language terminology set, the evaluation object and its influencing factors are determined to form a factor set, and a weight is assigned to each influencing factor to determine the membership function of each factor;

[0013] The membership function of each factor and its corresponding weight are combined using fuzzy synthesis to obtain a comprehensive membership value.

[0014] Based on the comprehensive membership value, a fuzzy evaluation is performed on the evaluation object to obtain the fuzzy comprehensive evaluation result of the evaluation object.

[0015] To achieve the above objectives, the present invention proposes a fuzzy multi-attribute decision evaluation system, comprising:

[0016] The terminology set definition module is used to define the terminology set for hesitant and ambiguous language.

[0017] The membership function determination module is used to determine the evaluation object and its influencing factors based on the hesitant fuzzy language terminology set to form a factor set, and to assign weights to each influencing factor to determine the membership function of each factor;

[0018] The membership value calculation module is used to perform fuzzy synthesis operation on the membership function of each factor and the corresponding weight to obtain a comprehensive membership value through fuzzy synthesis.

[0019] The fuzzy evaluation module is used to perform fuzzy evaluation on the evaluation object based on the comprehensive membership value to obtain the fuzzy comprehensive evaluation result of the evaluation object.

[0020] The fuzzy multi-attribute decision evaluation method and system of this invention applies multi-attribute decision-making and fuzzy theory. Based on fuzzy sets, and considering the weight of each attribute, it evaluates the evaluation object by single factors and then synthesizes the results to obtain a comprehensive evaluation result, making the evaluation result more accurate.

[0021] Additional aspects and advantages of the invention will be set forth in part in the description which follows, and in part will be obvious from the description, or may be learned by practice of the invention. Attached Figure Description

[0022] The above and / or additional aspects and advantages of the present invention will become apparent and readily understood from the following description of the embodiments taken in conjunction with the accompanying drawings, wherein:

[0023] Figure 1 This is a flowchart of a fuzzy multi-attribute decision evaluation method according to an embodiment of the present invention;

[0024] Figure 2 This is a schematic diagram of the structure of a fuzzy multi-attribute decision evaluation system according to an embodiment of the present invention. Detailed Implementation

[0025] It should be noted that, unless otherwise specified, the embodiments and features described in the present invention can be combined with each other. The present invention will now be described in detail with reference to the accompanying drawings and embodiments.

[0026] To enable those skilled in the art to better understand the present invention, the technical solutions of the present invention will be clearly and completely described below with reference to the accompanying drawings of the embodiments of the present invention. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort should fall within the scope of protection of the present invention.

[0027] The following description, with reference to the accompanying drawings, illustrates a fuzzy multi-attribute decision evaluation method and system proposed according to embodiments of the present invention.

[0028] The fuzzy multi-attribute decision evaluation method of this invention is as follows: Figure 1 As shown, it includes:

[0029] S1 defines the set of hesitant and ambiguous language terms;

[0030] S2, Based on the set of hesitant and fuzzy language terms, determine the evaluation object and its influencing factors to form a factor set, and assign weights to each influencing factor to determine the membership function of each factor;

[0031] S3, perform fuzzy synthesis operation on the membership function of each factor and the corresponding weight to obtain a comprehensive membership value through fuzzy synthesis;

[0032] S4. Based on the comprehensive membership value, perform fuzzy evaluation on the evaluation object to obtain the fuzzy comprehensive evaluation result of the evaluation object.

[0033] It is understandable that the key elements of a multi-attribute decision-making process are mainly four: decision objective, alternative solutions, attributes, and attribute weights.

[0034] (1) Decision-making objectives

[0035] Decision objectives refer to the ultimate goal and expected outcome of a decision; they serve as the highest guiding principle and action plan for the decision-making process. Without decision objectives, it is impossible to evaluate the actual effectiveness of alternative and implementation plans, and thus impossible to determine decision efficiency. The purpose of investment risk assessment for offshore photovoltaic power generation projects is to determine the risk level of the investment project and provide risk analysis opinions for investors to make investment decisions.

[0036] (2) Alternative solutions

[0037] Alternative options, also known as decision objects, are the objects of evaluation in the decision-making process. They can be used to characterize the objects to be evaluated in a project, such as strategies or actions. In multi-attribute decision-making, alternative options are a finite number of known solutions or objects, and can be either definite or uncertain.

[0038] (3) Attributes

[0039] Attributes, also called criteria, are the foundation of the decision-making process. Each decision objective contains several attributes that reflect the state characteristics of alternative solutions and measure the degree to which the decision objective is achieved. Attributes can be divided into two categories: one is the inherent characteristics of the solution itself, such as maximum output power, waveform distortion rate, and short-circuit current temperature coefficient when selecting equipment for an offshore photovoltaic power generation project; the other is the characteristics assigned by the decision-maker, such as the economic scale and commercial reputation of equipment suppliers for offshore photovoltaic power generation projects. Attributes can also be qualitative or quantitative.

[0040] Attributes that can be quantified with precise numbers are quantitative attributes, such as the payback period, internal rate of return, and current ratio of offshore photovoltaic power generation projects. Some attributes cannot be expressed with precise numbers and can only be described in words; these are called qualitative attributes, such as the harshness of the marine environment where the offshore photovoltaic power generation project is located, the sophistication of the technology, and the intensity of market competition. Qualitative attributes have significant uncertainty and require fuzzification using mathematical tools; this issue will be discussed in detail in the next subsection.

[0041] (4) Attribute weight

[0042] Attribute weights reflect a decision-maker's perception of the relative importance of attributes, typically represented by specific numerical values ​​between 0 and 1. Attributes possess both subjective and objective qualities because decision-makers need to judge their importance, a judgment often based on subjective evaluations calculated with precise numerical values. Weights describe the differences in the status of attributes in the decision-making process, encompassing three meanings: ① the reliability of individual attributes differs among alternatives; ② the importance of each attribute to the decision objective during the decision-making process.

[0043] The theoretical basis of fuzzy decision-making is fuzzy sets. Zadeh defines fuzzy sets as follows:

[0044] Let X be the universe of discourse, and A be a fuzzy set on X. The set of all fuzzy sets on X is defined as the fuzzy power set of X, denoted as F(A). Define μa(x) as a membership function on A, satisfying:

[0045] A={(x,μ A (x))|x∈X}

[0046] The general expression for the fuzzy number A can be written as:

[0047]

[0048] Where L(x) is a right-continuous increasing function and R(x) is a left-continuous decreasing function, and 0≤L(x)≤1, 0≤R(x)≤1.

[0049] It is understandable that fuzzy multi-attribute decision-making is a cross-application of multi-attribute decision-making and fuzzy theory. Based on fuzzy sets, and considering the weights of each attribute, it evaluates the evaluation object using single factors and then synthesizes the results to obtain a comprehensive evaluation. In practical comprehensive evaluation problems, there are usually many evaluation factors involved. On the one hand, the weights are difficult to determine; on the other hand, it is difficult to differentiate the weights. Therefore, classification and grading methods are often used to narrow the scope of each evaluation. Fuzzy multi-attribute decision-making problems under this framework are called multi-level evaluation problems, which require aggregation to obtain the overall evaluation result. The following content will discuss and analyze the fuzzy multi-attribute decision-making method adopted in this invention, namely, the hesitant fuzzy language terminology set and the fuzzy comprehensive evaluation method.

[0050] Investment risk assessment is widely defined by scholars both domestically and internationally as a typical fuzzy multi-attribute decision-making problem. The uncertainty of its decision information mainly stems from two aspects. First, project risk assessment is typically conducted during the planning and feasibility stages, making the assessment primarily based on pre-judgments of future situations, thus introducing uncertainty. Second, the judgment of decision information in investment risk assessment relies on the experience and knowledge of experts, a mindset that introduces a degree of fuzziness. Therefore, multi-attribute decision-making methods capable of handling incomplete and imprecise fuzzy information play a crucial role in ensuring the rationality and accuracy of investment risk assessment. Several multi-attribute decision-making methods for handling fuzzy information have been proposed, such as fuzzy logic and fuzzy set theory. However, these methods have significant drawbacks when two or more fuzzy information sources are present. To address this, many scholars have improved fuzzy sets, proposing various extended fuzzy sets, including type-2 fuzzy sets, intuitionistic fuzzy sets, and interval fuzzy sets. However, considering that experts participating in uncertain multi-attribute decision-making problems may not be able to express their opinions using a single language, hesitant fuzzy sets have been proposed to address situations where experts hesitate between multiple evaluation languages. The hesitant fuzzy language set was further improved and a hesitant fuzzy language term set was proposed, which enables experts to express evaluation information with richer statements over continuous intervals.

[0051] The definition of the hesitant and ambiguous language terminology set of this invention is as follows:

[0052] Define S = {s0, ..., s} t-1 Given a set of linguistic terms S, an ordered continuous subset Hs of S is called a hesitant and fuzzy linguistic term set (HFLTS).

[0053] For example, let the set of linguistic terms S = {very poor, poor, slightly poor, average, slightly good, better, very good}, then Hs = {average, slightly good, very good} is a hesitant and fuzzy set of linguistic terms containing seven consecutive ordered linguistic elements from “very poor” to “very good”.

[0054] Let Hs be a set of hesitant and fuzzy language terms, then Hs is called + and Hs - Let Hs be the upper and lower bounds, respectively, where:

[0055]

[0056] Let Hs be a set of hesitant and fuzzy language terms, then... The complement of Hs, where:

[0057]

[0058] set up and If two sets of hesitant and ambiguous linguistic terms are given, then their union is:

[0059]

[0060] set up and If two sets of hesitant and ambiguous linguistic terms are given, then their intersection is:

[0061]

[0062] Specifically, fuzzy comprehensive evaluation is a comprehensive evaluation method based on fuzzy set theory. It applies the principle of fuzzy relation synthesis to comprehensively evaluate the object of evaluation from multiple attributes. Fuzzy comprehensive evaluation uses the concept of membership degree to divide the range of change of the evaluated object. On the one hand, it takes into account the hierarchical nature of the object division, reflecting the fuzziness of evaluation standards and influencing factors; on the other hand, it can fully utilize the knowledge and experience of decision-makers, making the evaluation results more consistent with reality. In conducting fuzzy comprehensive evaluation, it is first necessary to determine the set of influencing factors of the evaluated object, the evaluation set; secondly, the weights of each factor and the corresponding membership degree vectors are determined using a certain method to obtain the fuzzy evaluation matrix; finally, the fuzzy evaluation matrix and the weight vectors of the factors are fuzzily synthesized to obtain the fuzzy comprehensive evaluation result. The basic steps of fuzzy comprehensive evaluation can be summarized as follows:

[0063] 1) Establish the factor set: Evaluation factor set U = {u1, u2, ..., u} n} is a classic set. Since multi-level, multi-attribute decision problems often contain sub-indicators, the factor set contains a sub-factor set U. i ={u i1 u i2 , ..., u in};

[0064] 2) Establish a comment set: Comment set V = {v1, v2, ..., v}m}, where element v j This represents the j-th evaluation result.

[0065] 3) Single-factor fuzzy evaluation: If the membership degree of the i-th element in the factor set U to the 1-th element in the comment set V is r i1 The result of the single-factor evaluation of the i-th element is represented by fuzzy set R. i =[r i1 ,r i2 ...,r in [Using m single-factor evaluation sets R1, R2, ..., R] m Forming matrix R m×n This is called the fuzzy comprehensive evaluation matrix.

[0066]

[0067] 4) Determine the factor weight vector: Construct the weight vector by forming a pairwise comparison matrix using the analytic hierarchy process, obtaining W = {w1, w2, ..., w...} m}

[0068] 5) Fuzzy synthesis operation: After determining the single-factor evaluation matrix R and the factor weight vector W, the fuzzy vector A on U is transformed into the fuzzy vector B on V through fuzzy transformation, as shown in the following formula:

[0069]

[0070] In this context, "·" represents a composition operator. Common composition operators include single-factor deterministic models, principal-factor emphasizing models, and weighted average models. This invention selects the weighted average model.

[0071] The fuzzy multi-attribute decision evaluation method according to embodiments of the present invention addresses uncertainty: Fuzzy comprehensive evaluation can handle uncertainty and fuzziness in the evaluation process, especially when evaluation criteria are unclear or difficult to quantify. It considers multiple factors comprehensively: This method allows for the simultaneous consideration of multiple influencing factors, synthesizing these factors through the concept of membership degree to obtain a comprehensive evaluation result. It offers flexibility and adaptability: The fuzzy comprehensive evaluation method has excellent flexibility and can adapt to various evaluation scenarios and needs, especially when evaluation factors are complex or evaluation criteria are variable. It provides decision support: This method can fully leverage the knowledge and experience of decision-makers, and the results obtained through fuzzy synthesis operations are more consistent with reality, providing strong support for decision-makers. It improves the scientific rigor of the evaluation: Through the application of mathematical models and fuzzy set theory, fuzzy comprehensive evaluation improves the scientific rigor and systematic nature of the evaluation process. It simplifies the decision-making process: Fuzzy comprehensive evaluation simplifies complex decision-making processes through fuzzy mathematics, enabling decision-makers to understand and process evaluation results more intuitively. It provides interpretability of results: The results of fuzzy comprehensive evaluation are generally more intuitive and easier to interpret, helping decision-makers and relevant stakeholders understand and accept the evaluation results. Optimizing resource allocation: In resource allocation and project selection, fuzzy comprehensive evaluation can help decision-makers optimize resource allocation and improve resource utilization efficiency based on evaluation results. Risk assessment: In risk management and assessment, fuzzy comprehensive evaluation can provide fuzzy boundaries for potential risks, helping decision-makers identify and address risks.

[0072] like Figure 2 As shown, to achieve the above objectives, the present invention proposes a fuzzy multi-attribute decision evaluation system 10, comprising:

[0073] Terminology set definition module 100 is used to define the terminology set of hesitant and ambiguous language;

[0074] The membership function determination module 200 is used to determine the evaluation object and its influencing factors based on the hesitant fuzzy language term set to form a factor set, and to assign weights to each influencing factor to determine the membership function of each factor;

[0075] The membership value calculation module 300 is used to perform fuzzy synthesis operation on the membership function of each factor and the corresponding weight, so as to obtain a comprehensive membership value through fuzzy synthesis.

[0076] The fuzzy evaluation module 400 is used to perform fuzzy evaluation on the evaluation object based on the comprehensive membership value to obtain the fuzzy comprehensive evaluation result of the evaluation object.

[0077] Furthermore, the terminology set definition module 100 is also used for:

[0078] Define S = {s0,...,s} t-1Let S be a given set of linguistic terms, where an ordered, continuous subset Hs of S is called a hesitant, fuzzy linguistic term set;

[0079] Let the set of linguistic terms S = {very poor, poor, slightly poor, average, slightly good, better, very good}, then Hs = {average, slightly good, very good} is a hesitant and fuzzy set of linguistic terms containing seven consecutive ordered linguistic elements from very poor to very good.

[0080] Furthermore, the terminology set definition module is also used for:

[0081] Let Hs be a set of hesitant and fuzzy language terms, then Hs is called + and Hs - Let Hs be the upper and lower bounds, respectively, where:

[0082]

[0083] Let Hs be a set of hesitant and fuzzy language terms, then... The complement of Hs, where:

[0084]

[0085] set up and If two sets of hesitant and ambiguous linguistic terms are given, then their union is:

[0086]

[0087] set up and If two sets of hesitant and ambiguous linguistic terms are given, then their intersection is:

[0088]

[0089] Furthermore, it also includes:

[0090] Establish a factor set: Evaluation factor set U = {u1, u2, ..., u} n Multi-level, multi-attribute decision problems contain sub-indicators; therefore, the factor set contains a sub-factor set U. i ={u i1 u i2 , ..., u in};

[0091] Establish a comment set: Comment set V = {v1, v2, ..., v} m}, where element v j This represents the j-th evaluation result.

[0092] Furthermore, it also includes:

[0093] Single-factor fuzzy evaluation: If the membership degree of the i-th element in the factor set U to the 1-th element in the comment set V is r i1 The result of the single-factor evaluation of the i-th element is represented by fuzzy set R. i =[r i1 r i2 ..., r in Given m single-factor evaluation sets R1, R2, ..., R... m Forming matrix R m×n This is called the fuzzy comprehensive evaluation matrix:

[0094]

[0095] Determine the factor weight vector: Construct the weight vector by forming a pairwise comparison matrix using the analytic hierarchy process, obtaining W = {w1, w2, ..., w...} m};

[0096] Fuzzy synthesis operation: After determining the single-factor evaluation matrix R and the factor weight vector W, the fuzzy vector A on U is transformed into the fuzzy vector B on V through fuzzy transformation, as shown in the following formula:

[0097]

[0098] In this context, "·" represents a composition operator.

[0099] The fuzzy multi-attribute decision evaluation system according to embodiments of the present invention addresses uncertainty by handling the uncertainty and fuzziness in the evaluation process, especially when evaluation criteria are unclear or difficult to quantify. It considers multiple factors simultaneously, integrating these factors through the concept of membership degrees to obtain a comprehensive evaluation result. The fuzzy comprehensive evaluation method offers excellent flexibility, adapting to various evaluation scenarios and needs, particularly when evaluation factors are complex or evaluation criteria are variable. It provides decision support by fully leveraging the knowledge and experience of decision-makers, and the results obtained through fuzzy synthesis operations are more consistent with reality, providing strong support for decision-makers. It enhances the scientific rigor of the evaluation by applying mathematical models and fuzzy set theory, improving the scientific and systematic nature of the evaluation process. It simplifies the decision-making process by simplifying complex decisions through fuzzy mathematics, enabling decision-makers to understand and process evaluation results more intuitively. Finally, it ensures the interpretability of the results, as the results of fuzzy comprehensive evaluation are generally more intuitive and easier to interpret, helping decision-makers and stakeholders understand and accept the evaluation results. Optimizing resource allocation: In resource allocation and project selection, fuzzy comprehensive evaluation can help decision-makers optimize resource allocation and improve resource utilization efficiency based on evaluation results. Risk assessment: In risk management and assessment, fuzzy comprehensive evaluation can provide fuzzy boundaries for potential risks, helping decision-makers identify and address risks.

[0100] In the description of this specification, the references to terms such as "one embodiment," "some embodiments," "example," "specific example," or "some examples," etc., indicate that a specific feature, structure, material, or characteristic described in connection with that embodiment or example is included in at least one embodiment or example of the present invention. In this specification, the illustrative expressions of the above terms do not necessarily refer to the same embodiment or example. Furthermore, the specific features, structures, materials, or characteristics described may be combined in any suitable manner in one or more embodiments or examples. Moreover, without contradiction, those skilled in the art can combine and integrate the different embodiments or examples described in this specification, as well as the features of different embodiments or examples.

[0101] Furthermore, the terms "first" and "second" are used for descriptive purposes only and should not be construed as indicating or implying relative importance or implicitly specifying the number of technical features indicated. Thus, a feature defined as "first" or "second" may explicitly or implicitly include at least one of that feature. In the description of this invention, "a plurality of" means at least two, such as two, three, etc., unless otherwise explicitly specified.

Claims

1. A fuzzy multi-attribute decision evaluation method, characterized in that, include: Define a set of hesitant and ambiguous language terms; Based on the hesitant fuzzy language terminology set, the evaluation object and its influencing factors are determined to form a factor set, and a weight is assigned to each influencing factor to determine the membership function of each factor; The membership function of each factor and its corresponding weight are combined using fuzzy synthesis to obtain a comprehensive membership value. Based on the comprehensive membership value, a fuzzy evaluation is performed on the evaluation object to obtain the fuzzy comprehensive evaluation result of the evaluation object.

2. The method according to claim 1, characterized in that, Define a set of hesitant and ambiguous language terms, including: Define S = {s0, ..., s} t-1 Let S be a given set of linguistic terms, where an ordered, continuous subset Hs of S is called a hesitant, fuzzy linguistic term set; Let the set of linguistic terms S = {very poor, poor, slightly poor, average, slightly good, better, very good}, then Hs = {average, slightly good, very good} is a hesitant and fuzzy set of linguistic terms containing seven consecutive ordered linguistic elements from very poor to very good.

3. The method according to claim 2, characterized in that, The definition of a hesitant and ambiguous language terminology set also includes: Let Hs be a set of hesitant and fuzzy language terms, then Hs is called + and Hs _ Let Hs be the upper and lower bounds, respectively, where: Let Hs be a set of hesitant and fuzzy language terms, then... The complement of Hs, where: set up and If two sets of hesitant and ambiguous linguistic terms are given, then their union is: set up and If two sets of hesitant and ambiguous linguistic terms are given, then their intersection is:

4. The method according to claim 1, characterized in that, The method further includes: Establish a factor set: Evaluation factor set U = {u1, u2, ..., u...} n Multi-level, multi-attribute decision problems contain sub-indicators, and the factor set contains a sub-factor set U. i ={u i1 u i2 , ..., u in }; Establish a comment set: Comment set V = {v1, v2, ..., v} m }, where element v j This represents the j-th evaluation result.

5. The method according to claim 4, characterized in that, The method further includes: Single-factor fuzzy evaluation: If the membership degree of the i-th element in the factor set U to the 1-th element in the comment set V is r i1 The result of the single-factor evaluation of the i-th element is represented by fuzzy set R. i =[r i1 r i2 …, r in Given m single-factor evaluation sets R1, R2, ..., R... m Forming matrix R m×n This is called the fuzzy comprehensive evaluation matrix: Determine the factor weight vector: Construct the weight vector by forming a pairwise comparison matrix using the analytic hierarchy process, obtaining W = {w1, w2, ..., w...} m }; Fuzzy synthesis operation: After determining the single-factor evaluation matrix R and the factor weight vector W, the fuzzy vector A on U is transformed into the fuzzy vector B on V through fuzzy transformation, as shown in the following formula: Here, "·" represents a composition operator.

6. A fuzzy multi-attribute decision evaluation system, characterized in that, include: The terminology set definition module is used to define the terminology set for hesitant and ambiguous language. The membership function determination module is used to determine the evaluation object and its influencing factors based on the hesitant fuzzy language terminology set to form a factor set, and to assign weights to each influencing factor to determine the membership function of each factor; The membership value calculation module is used to perform fuzzy synthesis operation on the membership function of each factor and the corresponding weight to obtain a comprehensive membership value through fuzzy synthesis. The fuzzy evaluation module is used to perform fuzzy evaluation on the evaluation object based on the comprehensive membership value to obtain the fuzzy comprehensive evaluation result of the evaluation object.

7. The system according to claim 6, characterized in that, The terminology set definition module is also used for: Define S = {s0, ..., s} t-1 Let S be a given set of linguistic terms, where an ordered, continuous subset Hs of S is called a hesitant, fuzzy linguistic term set; Let the set of linguistic terms S = {very poor, poor, slightly poor, average, slightly good, better, very good}, then Hs = {average, slightly good, very good} is a hesitant and fuzzy set of linguistic terms containing seven consecutive ordered linguistic elements from very poor to very good.

8. The system according to claim 7, characterized in that, The terminology set definition module is also used for: Let Hs be a set of hesitant and fuzzy language terms, then Hs is called + and Hs - Let Hs be the upper and lower bounds, respectively, where: Let Hs be a set of hesitant and fuzzy language terms, then... The complement of Hs, where: set up and If two sets of hesitant and ambiguous linguistic terms are given, then their union is: set up and If two sets of hesitant and ambiguous linguistic terms are given, then their intersection is:

9. The system according to claim 6, characterized in that, Also includes: Establish a factor set: Evaluation factor set U = {u1, u2, ..., u...} n Multi-level, multi-attribute decision problems contain sub-indicators; therefore, the factor set contains a sub-factor set U. i ={u i1 u i2 , ..., u in }; Establish a comment set: Comment set V = {v1, v2, ..., v} m }, where element v j This represents the j-th evaluation result.

10. The system according to claim 9, characterized in that, Also includes: Single-factor fuzzy evaluation: If the membership degree of the i-th element in the factor set U to the 1-th element in the comment set V is r i1 The result of the single-factor evaluation of the i-th element is represented by fuzzy set R. i =[r i1 r i2 …, r in Given m single-factor evaluation sets R1, R2, ..., R... m Forming matrix R m×n This is called the fuzzy comprehensive evaluation matrix: Determine the factor weight vector: Construct the weight vector by forming a pairwise comparison matrix using the analytic hierarchy process, obtaining W = {w1, w2, ..., w...} m }; Fuzzy synthesis operation: After determining the single-factor evaluation matrix R and the factor weight vector W, the fuzzy vector A on U is transformed into the fuzzy vector B on V through fuzzy transformation, as shown in the following formula: Here, "·" represents a composition operator.

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