Multi-criteria Group Decision Making Models Based On Probabilistic Linguistic Z-number And Their Applications

Decision-making exists widely in daily life.In the decision-making process,experts often use linguistic variables in approximate reasoning.The use of linguistic variables makes researches on linguistic decision making in full swing.Linguistic decision making and group decision making theory have become indispensable parts of modern decision making theory.Probabilistic linguistic Z-number extends the fuzzy restrict of Z-number into probabilistic linguistic term sets,it can more flexibly reflect the evaluation information of experts and the importance of each linguistic term.Meanwhile,it can also reflect the hesitation degree of experts.In this thesis,the uncertainty measure of probabilistic linguistic Z-number and the multi-criteria group decision making problem based on probabilistic linguistic Z-number are discussed.The main works are as follows:1.The uncertainty measure of probabilistic linguistic Z-number is studied.Firstly,according to the type of classical fuzzy sets corresponding to the linguistic term,the discrete and continuous probabilistic linguistic Z-number are defined.Then,the uncertainty of probabilistic linguistic Z-number is measured from three aspects respectively:hesitation degree,fuzziness degree and inherent uncertainty.Based on the above three angles,discrete and continuous entropy formulas are constructed,and their properties are proved.Finally,the entropy of discrete probabilistic linguistic Z-number is taken as an example to show the process of entropy calculation.2.The TOPSIS for multi-criteria group decision making method based on probabilistic linguistic Z-number is discussed.The original decision information of the multi-criteria group decision making problem discussed in this chapter is linguistic Z-number,so the model of merging linguistic Z-number into probabilistic linguistic Z-number is firstly introduced.The positive and negative ideal solutions in the probabilistic linguistic Z-number environment are illustrated.Considering the fuzzy restriction and reliability restriction in Z-number theory,the distance formula of probabilistic linguistic Z-number is proposed and its properties are proved.The TOPSIS multi-criteria group decision making model based on the probabilistic linguistic Z-number is given,and the effectiveness of the model is verified by taking the enterprise choosing investment project as an example.3.The multi-criteria group decision making method based on ranking value under probabilistic linguistic Z-number environment is proposed.Normalization,preprocessing and aggregation formulas of the probabilistic linguistic Z-number are given firstly.Secondly,considering the characteristics of the two parts—fuzzy restriction and reliability restriction of probabilistic linguistic Z-number,the ranking value formula is established.Then,after constructing a weight determination model considering risk preference,the procedures of multi-criteria group decision making based on ranking value are given.Lastly,an example of selection of water shortage areas is given to verify the effectiveness and feasibility of the proposed method.