Theory Of Probabilistic Linguistic Term Set And Its Application In Multi-attribute Decision Making

The probabilistic linguistic term set,as a new tool for describing uncertain decision information,can better reflect the degree of hesitation of decision makers,linguistic variables,and the relative importance of each linguistic variable in actual decision making problems,and its theory and its applications in the fields of modern medicine,cluster analysis,and edge computing have attracted extensive attention from scholars at home and abroad.This article is driven by practical decision making problems and studies related theories of probabilistic linguistic term sets and their applications in multi-attribute decision making problems,including the normalization of incomplete probabilistic linguistic term sets,operations of the probabilistic linguistic term sets,the probabilistic linguistic E-VIKOR method,the probabilistic linguistic two-step method and the probabilistic linguistic double interactive alternative reduction approach proposed based on the actual decision making problems.The specific work is divided into the following four parts:The first part studies the normalization method of incomplete probabilistic linguistic term sets.Through the equivalent expression form of probabilistic linguistic term sets,construct an equivalent transformation function that can map probabilistic linguistic term sets to high-dimensional space to obtain the vector representation forms of the probabilistic linguistic term sets which have the same dimension,then the conversion between the probabilistic linguistic term set and its vector form can realize.According to the difference between the number of decision makers and the linguistic term set in the actual decision making process,the projection-based normalization methods are constructed separately.The deviation degree formula verifies the rationality and feasibility of this method.The second part studies the operations of the probabilistic linguistic term set.By analyzing the operations of the probabilistic linguistic term set in the existing kinds of literature,there may be unreasonable calculation results due to the direct multiplication of probabilities,based on the equivalent transformation function between linguistic variable and numerical value and the adjustment method of probabilistic linguistic term set,redefine the new operations of probabilistic linguistic term set,and deeply study the idempotency of the operations.The results show that the operation results in this article are more in line with the actual decision process,and the operations are also simpler.The third part studies the E-VIKOR method for the probabilistic linguistic multi-attribute decision making problems.Based on the operations of the probabilistic linguistic term set given in the second part,an improved probabilistic linguistic E-VIKOR method is proposed.By analyzing the probabilistic linguistic E-VIKOR method only considers the distance between each alternative and the positive ideal solution may cause unreasonable results,the improved probabilistic linguistic E-VIKOR method is proposed to deal with the multi-attribute decision making problems which can consider the distance between each alternative and the positive and negative ideal solutions.Some comparative analyses among the improved probabilistic linguistic E-VIKOR method,the probabilistic linguistic VIKOR method,and the extended TOPSIS method are carried out to illustrate the merits of the improved probabilistic linguistic E-VIKOR method.The fourth part studies the probabilistic linguistic multi-attribute decision making method of interval attribute weight information.It mainly discusses the incomplete evaluation information,interval attribute weight,and probabilistic linguistic multi-attribute decision making problems involving multiple decision makers.For the incomplete probabilistic linguistic term set,use the projection-based normalization method given in the first part to normalize it.For the interval attribute weights in multi-attribute decision making problems and whether the decision process is interactive,the probabilistic linguistic two-step method and the probabilistic linguistic double interactive alternative reduction approach are given to solve the actual problems in the decision making process.The example verifies the application of the above two methods in the probabilistic linguistic multi-attribute decision making problems of interval attribute weight information.