Uncertainty Measures Of Probabilistic Linguistic Term Sets And Its Application In Group Decision Making

The probabilistic linguistic term sets(PLTSs)can reflect the qualitative decision information flexibly and comprehensively,and has been widely used in the field of supply chain management,risk assessment of investment projects and medical diagnosis.It has become a research hotspot in fuzzy decision theory.The entropy is used to measure the uncertainty of PLTSs,and is also an important part of the research on fuzzy set theory.This paper proposes the axiomatic definitions and specific entropy formulas of fuzzy entropy,hesitant entropy and comprehensive entropy of PLTSs;The cross entropy of PLTSs and its relationship with fuzzy entropy are studied.Finally,the method of reasonably selecting different entropy formulas to determine criterion weights and expert weights is proposed,so as to establish a group decision making method based on criterion weights and expert weights.The structure of this paper is as follows.In the first chapter,we introduce the research background,development status and related preparatory knowledge of PLTSs and its entropy theory.In the second chapter,we research the entropy and cross entropy of PLTSs.Firstly,the axiomatic definitions of fuzzy entropy,hesitant entropy and comprehensive entropy of PLTSs are defined;the fuzzy entropy formula is constructed by considering the relationship between fuzzy entropy and distance;the hesitant entropy formula considers the deviation of each linguistic term and the deviation of each linguistic term from the average value to construct the specific entropy formula of hesitant entropy;a comprehensive entropy formula is given,which can comprehensively reflects the characteristics of fuzziness and hesitation.Then,it defines the cross entropy of PLTSs,and derives the fuzzy entropy formula based on the relationship between cross entropy and fuzzy entropy.Finally,the proposed entropy formula is compared with the existing entropy formula by combining specific data.In the third chapter,we study the determination method of criterion weights,expert weights and group decision making method under probabilistic hesitant fuzzy information.It is emphasized that different aspects of the uncertainty of PLTSs should be considered in different decision problems to determine criterion weights and expert weights.In the multi-criteria group decision making environment,only the hesitant entropy is considered to calculate the criterion weights,and then the optimal solution is obtained by comparing the relationship between the cross entropy and the ideal solution.When determining the weight of experts in priority relation group decision making problem,the fuzziness and hesitation of probabilistic hesitant fuzzy linguistic information are considered at the same time,and then the group probabilistic linguistic priority relationship is obtained by aggregation.Finally,the comprehensive evaluation value is calculated to rank the alternatives.