Group Decision Making Method Based On Hesitant Fuzzy Information And Its Application

With the rapid development of economy,many practical decision-making problems,such as supplier selection,medical diagnosis,and selection of factory site etc.,depend on experts' evaluation.However,such kinds of decision-making issues are becoming more and more complex.Things themselves are filled with uncertainty and ambiguity.The single expert seemly cannot handle with the situations.On the other hand,due to the limited knowledge level and experience of experts,some hesitations often appeal when experts give evaluation information.To solve these problems in decision-making activities,it is particularly important to study group decision-making(GDM)methods under hesitant fuzzy information.Based on hesitant fuzzy information,there are many GDM methods at present.However,there are still three shortcomings.Firstly,information measures of hesitant fuzzy elements(HFEs),including distance measures and entropy measures,fail to consider the hesitancy of HFEs and need to extend the length of HFEs,by which the original information of HFEs are easily changed.Secondly,most of the hesitant fuzzy decision-making methods are multi-crtiteria decision-making(MCDM).Single expert is unable to adapt to such complex decision-making environment.Some classic decision-making methods,such as qualitative flexible multiple criteria method(QUALIFLEX)are complex and time-consuming.Thirdly,when defining the consistency of hesitant fuzzy preference relationships(HFPRs),most of methods need to construct a completely consistent matrix,which is time-consuming and easily leads to the loss of original information.What's more,iterative algorithms are always used to adjust the consistency of the preference relationship and the consensus,which is time-consuming and depends on experts' high level,which is hard to perform.To make up the above shortcomings,this paper proposes a GDM method based on hesitant fuzzy information.The article is divided into three parts.(1)Firstly,a new hesitancy index of HFE is defined.Then,a generalized hesitant fuzzy Hausdorff distance is proposed considering the individual deviation of membership values and the hesitancy degree of HFEs simultaneously.Combined hesitant fuzzy entropy is presented integrating the defined fuzziness entropy and hesitancy entropy of HFEs.Based on the TOPSIS principle,the relative closeness of HFEs is proposed,which is used to sort the HFEs.(2)When the evaluation attribute set is easy to determine and the experts' knowledge level is high,an extended Preference Ranking Organization Method for Enrichment Evaluation(PROMETHEE)method is put forward for multi-criteria group decision-making(MCGDM)with HFSs.A linear programming model is constructed to determine DMs' weights objectively.To derive the criteria weights for each DM,a non-linear programming model is established through minimizing the relative entropy.Next,the PROMETHEE is employed to obtain individual ranking of alternatives for each DM.To obtain the collective order of alternatives,a multi-objective assignment model is established and transformed into a single objective assignment model for resolution.Thereby,an extended PROMETHEE method is put forward for MCGDM with HFSs.Finally,a green supplier selection example is demonstrated to verify the validity and feasibility of the proposed method.(3)When the evaluation attribute set is hard to determine and the experts' knowledge level is low,a new method for group decision making with HFPRs is proposed.A consensus index for the group is defined to measure the agreement among DMs.To improve the consistency and consensus simultaneously,a new goal program is established to obtain a group of HFPRs with acceptable consistency and consensus.Subsequently,an interval-valued hesitant fuzzy group decision matrix(IVHFGDM)is elicited from the individual HFPRs.A positive ideal matrix,a left negative ideal matrix and a right negative matrix are derived from the IVHFGDM.According to the relative closeness degrees,DMs' weights are determined objectively.Afterwards,the individual HFPRs are integrated into a normalized collective HFPR.It is proved that the normalized collective HFPR is acceptable consistent if all individual HFPRs are acceptable consistent.The final ranking is generated by the collective overall values of alternatives.Some examples are provided to validate effectiveness of the method.