Approaches To Multiple Attribute Group Decision Making Based On Several Hesitant Fuzzy Information

As the world grows more prosperous,people get richer and the standard of living improves accordingly,and the real-life decision environment that decision makers(DMs)are facing is also becoming more and more complicated.Considering the lack of their own knowledge,complexity for objective things and disturbances from internal or external uncertainty and ambiguity,it is almost impossible for DMs to access information by exact values,while they may be hesitant when they evaluate the real-life complex problems.In this situation,hesitant fuzzy evaluations are powerful tools for representing uncertainty and solving this type of problem,so far,several studies have utilized the hesitant fuzzy information for many real-world applications.The primary goal of this paper is to deeply study and explore the multiple attribute group decision making(MAGDM)problems with several hesitant fuzzy information.The structure of this paper is arranged as follows:Chapter 1 mainly introduces the research background and significant of this paper,and analyses the current research situations at home and abroad,and further proposes the main research problems of this paper.Chapter 2 introduces the linguistic term set,numerical scale,hesitant fuzzy set,Pythagorean fuzzy sets,and the Archimedean t-norms and s-norms?In Chapter 3,because linguistic words mean different things to different people,first,a specific linguistic scale function with the purpose of making transformations between linguistic terms and numerical values is developed.The proposed method represents a wide range of existing linguistic scale functions,and can quantitatively reflect the linguistic behaviors of DMs.On the basis of the lowest common multi-ple principle in number theory,an improved supplementary regulation for hesitant fuzzy linguistic term sets(HFLTS)with different lengths is proposed to reserve the fidelity of original information,some new distance measures for HFLTS are present-ed further.Next,a novel hesitant fuzzy linguistic TOPSIS method based on the maximizing deviation model is developed to solve the MADM problems in which the attribute values take the form of HFLTS and the weights of attributes are com-pletely unknown.Finally,a numerical example is elaborated on the performance of our approach.Comparative analysis is also provided and discussed to show the effectiveness and advantages of the proposed method.In Chapter 4,based on the improved supplementary regulation for HFLTS and the Archimedean t-norms and s-norms,an approach to MAGDM with hesitant fuzzy linguistic aggregation operators is developed.Considering that some existing operational laws of HFLTS still have some limitations,some deficiencies of them are analyzed.Then,some novel operational laws for HFLTSs on the basis of the improved supplementary regulation and the Archimedean t-norms and s-normsis are developed,some essential properties are discussed in detail.As a hot and key research topic for information fusion,some Archimedean t-norms and s-norms based hesitant fuzzy linguistic aggregation operators are proposed to aggregate HFLTSs.The entropy and cross-entropy of HFLTSs are proposed and applied to deriving the attribute weights.Finally,a numerical example related to assessment of health-care waste disposal methods is provided to show the utility and effectiveness of method,which are then compared to the existing methods.In Chapter 5,in view of the effectiveness of hesitant fuzzy sets(HFSs)for ex-pressing the hesitant situation,and the powerfulness of Pythagorean fuzzy sets(PF-Ss)in handling vagueness and uncertainty,this chapter develops some novel hesitant Pythagorean fuzzy sets(HPFSs)based methods in enhancing fuzzy related prob-lems flexibility.First,some existing basic properties and operators are extended and improved in detail.For the sake of application,on the basis of lowest common mul-tiple principle in number theory,an improved normalization algorithm is proposed to reserve the fidelity of original information.Then,a flexible and multipurpose generalized distance measure for HPFSs is presented,and a MAGDM method based on the extended hesitant Pythagorean fuzzy VIKOR is developed.Finally,three numerical examples,one from the bidirectional approximate reasoning system and other from the medical diagnosis and selection model of health management center,are presented to elaborate on the performance of our approach.In the end,the conclusion chapter summarizes the research results and makes expectation of future research.