Research On Measures And Decision Making Methods Based On Hesitant Information

As new extensions of fuzzy sets,hesitant fuzzy sets(HFSs),dual hesitant fuzzy sets(DHFSs)and hesitant fuzzy linguistic term sets(HFLTSs)have a better ability of modelling uncertainty.They can reflect the real opinions and ideas of decision makers by describing their hesitant decision information objectively and accurately.This paper is to deeply investigate and explore the measures and decision making methods in the context of the hesitant information(including hesitant fuzzy information,dual hesitant fuzzy information and hesitant fuzzy linguistic information).The main work is summarized as follows:(1)The entropy measures of hesitant fuzzy information are investigated.The fact that the uncertainty of hesitant fuzzy information includes two aspects:fuzziness and non-specificity is first pointed out.Then the entropy of hesitant fuzzy information by a two-tuple entropy model is defined,and some methods are proposed for constructing the entropy formulas of hesitant fuzzy information.Besides,based on the entropy measures of hesitant fuzzy information,a new comparison method of hesitant fuzzy elements is put forward.(2)The distance measures of hesitant fuzzy linguistic information and their applications in multiple attribute decision making(MADM)are studied.With some simple fuctions,various methods are proposed for constructing distance measures of HFLTSs,and a comprehensive and in-depth analysis and comparison of fine properties of distance measures derived from different construction methods is conducted.Then the signed distance of HFLTSs is defined and a signed distance-based hesitant fuzzy linguistic decision making method is proposed for solving the MADM problems in which the attribute values are HFLTSs and the weights of attributes are completely unknown or expressed by HFLTSs.(3)The aggregation techniques for hesitant fuzzy decision information are studied when the attributes are in different priority levels and in each priority level there exist several attributes,and their applications in hesitant fuzzy MADM are discussed.Motivated by the concepts of classical t-norms and t-conorms,hesitant fuzzy t-norms and t-conorms are defined,and their relationships with classical t-norms and t-conorms are investigated.Then after discussing the flaw of existing hesitant fuzzy prioritized aggregation operators,the hesitant fuzzy prioritized "or" operator is developed to fuse the hesitant fuzzy decision information when the attributes are in different priority levels and in each priority level there exist several attributes.Additionally,a decision making method is proposed to solve the MADM problems in which the attributes are in different priority levels and the attribute values are hesitant fuzzy elements.(4)The aggregation techniques for dual hesitant fuzzy decision information when there exists a prioritization relationship over attributes are investigated,and their applications in dual hesitant fuzzy MADM are explored.The concepts of dual hesitant fuzzy t-norms and t-conorms are defined,and a special class of dual hesitant fuzzy t-norms and t-conorms are constructed by using classical t-norms and t-conorms.With dual hesitant fuzzy t-norms and t-conorms,the dual hesitant fuzzy prioritized weighted triangular operator is developed for fusing the dual hesitant fuzzy decision information of alternatives with regard to the prioritized attributes.Besides,a decision making method is proposed to tackle the MADM problems in which there exists a prioritization relationship over attributes and the attribute values take the form of dual hesitant fuzzy elements.(5)The methods for group decision making with dual hesitant fuzzy preference relations are explored.In the decision making process,to embody the principle of fair competition,some symmetric aggregation operators for dual hesitant fuzzy information are proposed,and to give full play to the advantages of DHFSs,dual hesitant fuzzy preference relations are established for depicting all preference and non-preference information of decision makers over alternatives comprehensively and detailedly.Considering that compatibility is a very effective tool to measure the consensus of opinions within a group,two formulas for computing the compatibility degree between dual hesitant fuzzy preference relations are developed.Additionally,the symmetric dual hesitant fuzzy aggregation operators and compatibility measures are applied to group decision making with dual hesitant fuzzy preference relations and two group decision making methods are proposed.(6)Based upon the possibility degree formulas for comparing HFLTSs,some procedures are given to determine the real-valued relative weights of attributes with the provided weight information of attributes expressed by HFLTSs,and an algorithm is developed to model the prioritization among attributes by revising the real-valued weights of attributes according to the decision maker's requirements.Meanwhile,a hesitant fuzzy linguistic SIR method is proposed to solve the MADM problems in which the attributes are in different priority levels,and the weights of attributes and the attribute values are expressed by HFLTSs.