Research On Multiple Attribute Decision Making Methods Based On Hesitant Decision Information

Multiple attribute decision making(MADM),as an important part of modern decision science,is widely used in various fields such as military,economic,engineering,management,and so on.With the development of social economy and information technology,decision environments and decision problems are becoming more and more uncertain and complicated.Thus,it is difficult for decision makers(DMs)to effectively depict decision information by using precise values.As high-order extensions of fuzzy set theory,the theories of hesitant fuzzy sets(HFSs),dual hesitant fuzzy sets(DHFSs)and distributed hesitant linguistic term sets(DHLTs)are becoming useful tools for DMs to portray uncertain decision information because of their promising performance in reflecting the mental process of human beings' thinking and understanding.MADM mainly involves two key issues,namely decision information fusion and attribute weight determination.Aiming at the above key issues,this thesis focuses on the development of MADM methods with hesitant decision information to perfect the theories in such decision-making fields,which further provides more theoretical foundations for supporting real-world MADM.Therefore,this work is interesting and significant from both the theoretical and practical perspectives.After reviewing some existing domestic and foreign studies concerning imformation measure-based and information aggregation-based MADM methods,and the ones concerning preference relation-based attribute weight determination techniques,the objective of this thesis is to study MADM problems with hesitant decision information represented by HFSs,DHFSs,and DHLTs.Distance and correlation measures of hesitant fuzzy information,as well as aggregation functions of hesitant decision information are deeply investigated.Meanwhile,consistency definions of distribution linguistic preference relations(DLPRs)are also presented.On the basis of the foregoing theoretical results,MADM methods with hesitant decision information are developed by addressing the two key issues as outlined above.The main research contents and innovations of this thesis are summarized below:(1)Based on the improved distance measures of hesitant fuzzy information,a hesitant fuzzy MADM method with unknown attribute weights is proposed.After analyzing the limitations of the existing hesitant fuzzy distance measures,a few improved hesitant fuzzy distance measures and the corresponding weighted forms that do not need to consider the lengths of hesitant fuzzy elements(HFEs)as well as the arrangement of their possible values are developed.Then to deal with the situations where DLPRs with complete symbolic proportions are used to express the relative importances of attributes,definitions of expected consistency for such type of DLPRs are presented and some consistency-based goal programming models are proposed to derive attribute priority weights.Moreover,a hesitant fuzzy distance measure-based method is put forward to address the MADM problems where the attribute values are expressed as HFSs and the relative importances of attributes are represented by DLPRs with complete symbolic proportions.Numerical examples are solved by the proposed method to demonstrate its applicability and validity.(2)Based on the improved correlation measures of hesitant fuzzy information,a hesitant fuzzy MADM method with unknown attribute weights is proposed.After analyzing the limitations of the existing hesitant fuzzy correlation measures,an improved hesitant fuzzy correlation measure and its weighted form which do not need to consider the lengths of HFEs as well as the sequence of their possible values are proposed.Then to handle the situations where DLPRs with incomplete symbolic proportions are employed to describe the relative importances of attributes,definitions of expected consistency for such type of DLPRs are presented and some consistency-based goal programming models are proposed to derive attribute priority weights.Finally,a hesitant fuzzy correlation measure-based method is put forward to deal with the MADM problems where the attribute values are provided in terms of HFSs and the relative importances of attributes are expressed by DLPRs with incomplete symbolic proportions.Numerical examples are solved by the proposed method to demonstrate its applicability and validity.(3)Based on the original score function of hesitant fuzzy information and the hesitant fuzzy Frank aggregation operators,a hesitant fuzzy MADM approach which takes the risk attitudes of DMs into consideration is presented.Inspired by the concepts of mean and variance in statistics,an original score function of HFE is developed to compare different HFEs.Then based on Frank operational rules of HFEs,hesitant fuzzy hybrid averaging and geometric aggregation operators which consider the risk attitudes of DMs are presented.The relationships between the proposed aggregation operators and some existing operators are analyzed.The monotonicity of arithmetic and geometric aggregated HFEs with respect to a parameter in Frank t-norm and t-conorm and their relationship are also demonstrated.In particular,the monotonicity is employed to associate the parameter with the risk attitude of a DM,by which the meaning of the parameter in MADM is explained and a method is designed to determine the value of the parameter.(4)Based on the new comparison rule of dual desitant fuzzy information and the dual hesitant fuzzy Frank aggregation operators,a dual hesitant fuzzy MADM approach which considers the risk attitudes of DMs is presented.Motivated by the concepts of mean and variance in statistics,original score and accuracy functions of dual hesitant fuzzy element(DHFE)are developed to construct a new comparison rule of DHFEs.Then the operational rules of DHFEs based on Frank t-norm and t-conorm are investigated,by which a family of dual hesitant fuzzy Frank aggregation operators are built.The monotonicity of arithmetic and geometric aggregated DHFEs with respect to a parameter in Frank t-norm and t-conorm and their relationship are also demonstrated.In particular,the monotonicity is employed to associate the parameter with the risk attitude of a decision maker,by which a model is designed to determine the parameter.Furthermore,an investment evaluation problem is discussed by the proposed MADM approach,which shows that the dynamic decision results can provide more choices for DMs.This work studies the MADM method based on hesitant decision information from the following two aspects: decision information fusion and attribute weight determination.In general,a few research results in hesitant decision information fusion and attribute weight determination have been achieved,which provide some theoretical foundations for supporting practical MADM.However,as an important part of management science,the research about MADM will continue with the development of human activities.There are still many problems in the future that need to be studied and explored.How to characterize multi-source heterogeneous decision information in a more standardized form is the next step research direction;with the expansion of decision information representation,the research on fusion methods of extended decision information is a hot topic in the future;how to derive attribute weights directly from DLPRs with incomplete symbolic proportions rather than based on their related numerical preference relations is the focus of future research.