Research On Multi-Attribute Decision-Making Method Of Fuzzy Language

The purpose of studying multiple attribute decision making methods related to fuzzy language is to solve many complex problems in real life,such as environmental assessment,financial investment,medical diagnosis,and so on.In these problems,the values or weights of attributes are often not clear,and there is a certain degree of ambiguity or uncertainty.Therefore,it is necessary to use fuzzy logic and fuzzy mathematics methods for analysis and decision-making.This paper proposes four methods for multi attribute decision making in fuzzy language.The first method is a triangular fuzzy number ranking method based on probability density function and probability formula.Firstly,using the relationship between probability density and membership function,the probability density function under three different risk attitudes is constructed;Secondly,the size comparison between triangular fuzzy numbers is transformed into the size relationship comparison between random variables,and the corresponding probability calculation formula is defined;Then,it is proved that the possibility formula satisfies the axioms of normalization,intuition,complementarity,reflexivity,transitivity and superiority;Finally,a triangular fuzzy number ranking algorithm based on probability density function and probability degree formula is given,and its feasibility and effectiveness are verified by an example,and the impact of different risk attitudes on the ranking results is analyzed.The second method is to propose a group decision making method combining Bayesian formula and reliability theory for the case that the attribute value in the multi-attribute decision making problem is a probabilistic language term set.The method mainly includes the following steps: firstly,the Bayesian formula proposed in this paper is used to synthesize the subjective weight and objective weight to obtain the combined weight of each attribute;Secondly,the probabilistic language term set is transformed into trapezoidal fuzzy numbers to avoid introducing new elements in the standardization process;Then,the WA operator is used to aggregate multiple decision matrices and calculate the comprehensive trapezoidal fuzzy number of each scheme;Finally,the ranking method of reliability theory is used to rank the schemes.This paper verifies the feasibility of the proposed method through an example,and compares it with other relevant methods.The third method is based on grey correlation analysis and projection method.This method mainly includes the following steps: firstly,a new probability normalization method is proposed,which normalizes the probability part of the probability language term set and standardizes it according to different situations;Secondly,the grey correlation analysis method is introduced to calculate the correlation degree between each scheme and each attribute,and the weighted correlation matrix is obtained according to the attribute weight;Then the positive and negative ideal solutions are determined in the weighted incidence matrix,and the closeness of each scheme to the positive ideal solution in the distance and direction is calculated by the projection method;Finally,the schemes are sorted according to the degree of proximity.This method is compared with other relevant methods,which verifies the feasibility and effectiveness of the proposed method.The fourth method is a risk-based multi-attribute decision-making method based on regret theory,which is applicable to the case where the attribute value is a probabilistic language term set and the natural state probability is an interval number.The method mainly includes the following steps: firstly,the probabilistic language term set is transformed into interval grey number,and the decision matrix is simplified into interval grey number matrix;Secondly,the utility value and regret value of each scheme under each attribute are calculated to obtain the perceived utility of the decision maker to the scheme;Then an optimization model is built to maximize the comprehensive perceived utility of the scheme,and the interval probability is converted into point probability;Finally,the schemes are sorted according to the comprehensive perceived utility.Compared with other methods,this paper verifies the feasibility and effectiveness of the proposed method.Studying the multi-attribute decision-making of fuzzy language can help us better understand and solve the complex problems in real life,improve the accuracy and reliability of decision-making,and is of great significance for promoting social and economic development and improving people’s living standards.