The Research On Multi-attribute Group Decision Making Based On Probabilistic Linguistic Term Sets

Due to the uncertainty and complexity of decision-making environment and the ambiguity of human cognitive thinking,it is sometimes difficult for decision makers to describe and evaluate realistic decision-making problems with crisp numbers.Moreover,compared with the crisp number,the qualitative description of decision-making problems are more in line with human thinking and cognitive habits.As a result,the research of multi-attribute decision making methods based on linguistic variables has developed rapidly.Since linguistic variables only allow decision makers to express assessment information in a single linguistic term,they can not meet the decision maker’s need to provide multiple linguistic assessment information.The hesitant fuzzy linguistic term set can satisfy the decision makers’ need to express information in multiple linguistic terms,but it cannot describe the different importance or weight of linguistic terms.Based on this,the concept of probabilistic linguistic term set has been proposed,which not only can reflect all possible linguistic variables but also express their respective importance or weight,and it can express information more completely and accurately.Therefore,they can provide more help for solving practical decision-making problems.In multi-attribute decision-making method,information integration operator is an important tool for information integration.As a simple operator in information integration operator,power average operator can get the relevant weight by fusing the support degree between data to eliminate the influence of too small or too large evaluation value,so as to solve the situation that experts have subjective bias and wrong score.At present,the research on the combination of probabilistic linguistic term set and power average operator is still insufficient,so this paper further studies the multi-attribute decision-making method of probabilistic linguistic power average operator based on improved operation rules.At the same time,this paper discusses the bidirectional projection method based on approximating ideal solution,PROMETHEE method based on hierarchical priority relation and TODIM method based on considering decision maker’s bounded rationality,and extends it to the environment of probabilistic linguistic term set.Therefore,this paper establishes a multi-attribute decision-making method based on the information integration operator of probabilistic linguistic term set and three decision-making methods,which can solve practical decision-making problems more accurately and effectively.The main innovations of this paper include the following aspects:(1)Based on the improved operation rules,this paper combines the probabilistic linguistic term set with the power average operator,proposes the probabilistic linguistic power average operator and the probabilistic linguistic weighted power average operator,and studies its relevant properties.(2)This paper defines the related formulas of projection measure and the improved possibility formula of probabilistic linguistic term set.Based on this,the bidirectional projection method and the PROMETHEE method based on probabilistic linguistic term set are proposed,and also the TODIM method based on hybrid normalized Euclidean distance formula of probabilistic linguistic term set is proposed.(3)This paper establishes a multi-attribute group decision-making method based on the above-mentioned information integration operators and decision-making methods,and verifies their applicability,effectiveness and superiority through specific practical application examples,so as to further enrich and develop the basic theory of multi-attribute decision-making based on probabilistic linguistic term set.