Study On Methods For Hesitant Fuzzy Decision Making

As the development of science and technology,modern decision making prob-lems are becoming more and more complex.It is difficult for decision makers to ex-press uncertain decision information effectively.Therefore,various hesitant fuzzy sets and hesitant fuzzy preference relations have been proposed to reflect the uncertainty of decision makers,which have been widely used in many fields such as society,eco-nomic management,engineering management and military.Based on the theories of hesitant fuzzy sets(HFSs),interval-valued dual hesitant fuzzy sets(IVDHFSs),prob-abilistic hesitant multiplicative sets(PHMSs)and probabilistic hesitant multiplicative preference relations(PHMPRs),this thesis study methods of decision making,the main work is summarized as follows:(1)A new hesitant fuzzy multiple attribute decision making method with un-known weight information.Some new generalized hesitant fuzzy hybrid weighted aggregation operators are proposed,such as the new generalized hesitant fuzzy hybrid weighted averag-ing(NGHFHWA)operator and the new generalized hesitant fuzzy hybrid weighted geometric(NGHFHWG)operator.Their desirable properties and the relationships are discussed.Then,based on the proposed aggregation operators,a new approach for hesitant fuzzy multiple attribute decision making(HF-MADM)problems with unknown weight information is introduced.Further,a practical example is used to illustrate the detailed implementation process of the proposed approach.A sensitivity analysis of the decision results is analyzed with different parameters.Finally,com-parative studies are given to verify the advantages of our method.(2)Multiple attribute group decision making methods based on interval-valued dual hesitant fuzzy power Heronian aggregation operators.The interval-valued dual hesitant fuzzy 2nd-order central polymerization degree(IVDHFCP₂)function is introduced,for the case that score values of different interval-valued dual hesitant fuzzy elements(IVDHFEs)are identical.This function can fur-ther compare different IVDHFEs.Then,we develop a series of interval-valued dual hesitant fuzzy power Heronian aggregation(IVDHFPHA)operators,i.e.,the interval-valued dual hesitant fuzzy power Heronian mean(IVDHFPHM)operator,the interval-valued dual hesitant fuzzy power geometric Heronian mean(IVDHFPGHM)operator and their weighted forms.Some desirable properties and their special cases are dis-cussed.These proposed operators can simultaneously reflect the interrelationship of aggregated arguments and reduce the influence of unreasonable evaluation values.Fi-nally,two approaches for interval-valued dual hesitant fuzzy multiple attribute group decision making(IVDHF-MAGDM)with known or unknown weight information are presented.An illustrative example and comparative studies are given to verify the advantages of our methods.A sensitivity analysis of the decision results is analyzed with different parameters.(3)Group decision making based on probabilistic hesitant multiplicative infor-mation.On the basis of the concept of PHMSs,we define the Hausdorff distance be-tween probabilistic hesitant multiplicative elements(PHMEs),and study its proper-ties.The generalized Archimedean t-norm and t-conorm can generalize most of the existing generalized t-norms and t-conorms,including generalized Algebraic,Ein-stein,Hammer and Frank.Then,we define the generalized Archimedean operations of PHMEs,and discuss the relationships.Further,a series of extended Archimedean probabilistic hesitant multiplicative aggregation operators are given,such as extend-ed Archimedean probabilistic hesitant multiplicative weighted aggregation operators,extended Archimedean probabilistic hesitant multiplicative Choquet integral opera-tors and extended Archimedean probabilistic hesitant multiplicative power aggrega-tion operators.Some properties and special cases are discussed.Finally,based on the proposed operators,we propose an approach to probabilistic hesitant multiplica-tive multiple attribute group decision making.An illustrative example is given to verify the effectiveness and practicability of our method.By comparing with the cor-responding hesitant multiplicative group decision making method,the advantages of our method are verified.(4)Group decision making method of probabilistic hesitant multiplicative pref-erence relation based on expected consistency.For the probabilistic hesitant multiplicative preference relation(PHMPR)which has incomplete probabilistic information,we construct the probability calculation model of PHMPRs based on the expected consistency.Then,the expected consis-tency index of the incomplete PHMPRs is defined,and the inconsistent optimization algorithm is given.Finally,we propose the group decision making method based on the expected consistency of incomplete PHMPRs,which is applicable to both the decision making problems with partially known information and completely known information.The unknown information is obtained by the model,which can reduce the subjective or objective error.