Research On Multiple Attribute Group Decision Making Methods Based On Spherical Fuzzy Sets

As a new extension form of fuzzy sets,spherical fuzzy sets(SFSs)can express the decision makers’ preference information more comprehensively and deeply,which are an effective tool to deal with fuzzy decision problems at present.This thesis studies and explores multiple attribute group decision making(MAGDM)problems whose decision data is spherical fuzzy information in depth.The main work and achievements are as follows:(1)From the perspective of prospect theory,the classical MABAC method,GRA method,TODIM method and ELECTRE I method are improved under spherical fuzzy environment and four kinds of spherical fuzzy MAGDM methodological frameworks in considering decision makers’ mental behavior are proposed.Further,entropy weight method,D-CRITIC method,MEREC method and correlation coefficient method are extended under SFSs to calculate the objective weights of attributes,so as to enhance the rationality of weight information.Finally,the practicability of the proposed four kinds of spherical fuzzy MAGDM methods based on prospect theory is illustrated by numerical examples respectively.In addition,the effectiveness and superiority of the proposed methods are further verified by sensitivity test of parameter and comparison with some existing methods under SFSs.(2)Spherical fuzzy MAGDM methods based on SFDPWHM operator and SFDPWGHM operator are proposed.In order to improve the flexibility of decision process and reflect the interrelationships between attributes,HM operator and GHM operator are first extended under SFSs based on spherical fuzzy Dombi algorithm to propose SFDHM operator,SFDGHM operator and their weighted forms successively.Meanwhile,some ideal properties of these operators such as idempotence,monotonicity and boundedness are discussed.Considering the influence of some extreme data from decision makers on the evaluation results,SFDHM operator and SFDGHM operator are combined with power average operator to present SFDPHM operator,SFDPWHM operator,SFDPGHM operator and SFDPWGHM operator.Accordingly,some properties of these operators are studied and some special cases are discussed.Subsequently,two new spherical fuzzy MAGDM methods are established based on the proposed aggregation operators.Finally,the practicability of the proposed methods is illustrated by a numerical example of enterprise resource planning system evaluation,and the effectiveness and superiority of the proposed methods are further verified by sensitivity test of parameters and comparison with some existing methods under SFSs.(3)Spherical fuzzy MAGDM method based on SFPWPMSM operator is proposed.In order to reflect the partitioned relationship among attributes and deal with the interrelationships among multiple attributes in the same partition,SFPMSM operator and SFWPMSM operator are first developed by extending PMSM operator under SFSs.At the same time,some ideal properties of the proposed operators,such as idempotence,monotonicity as well as boundedness are discussed and some special values of parameters are given.Considering that power average operator can reduce the influence of extreme data from decision makers on the evaluation results,SFPMSM operator and SFWPMSM operator are combined with power average operator to further propose SFPPMSM operator and SFPWPMSM operator,and some properties and special cases of these two operators are discussed.Subsequently,a new spherical fuzzy MAGDM method is proposed based on the above research.Meanwhile,a new spherical fuzzy entropy measure is introduced to obtain attribute weight information when attribute weights are completely unknown.Finally,the practicability of the proposed method is illustrated by a numerical example of hydraulic power plant project evaluation,and the effectiveness and superiority of the proposed method are further verified by sensitivity test of parameters and comparison with some existing methods under SFSs.(4)Spherical fuzzy MAGDM methods based on SFAPWMM operator and SFAPWGMM operator are proposed.In order to improve the versatility and flexibility of the decision process and reflect the interrelationships among any attributes,Archimedean algorithm based on SFSs is first proposed and some of its properties,such as commutative law,distributive law and associative law are discussed.Secondly,based on the proposed Archimedean algorithm,MM operator and GMM operator are extended in SFSs to propose SFAMM operator,SFAGMM operator and their weighted forms successively.At the same time,some ideal properties of these operators such as commutativity,idempotence,monotonicity as well as boundedness are discussed and some special cases of these operators are investigated.Considering that there is always a certain preference relationship among attributes in some practical decisions,SFAMM operator and SFAGMM operator are combined with prioritized average operator to further propose SFAPMM operator,SFAPWMM operator,SFAPGMM operator and SFAPWGMM operator.In addition,some properties of these operators and some special values of parameters are discussed.Subsequently,two new spherical fuzzy MAGDM methods are proposed based on the above research.Finally,the practicability of the proposed methods is illustrated by a numerical example for the evaluation of financial manager candidates,and the effectiveness as well as superiority of the proposed methods are further verified by sensitivity test of parameters and comparison with some existing methods under SFSs.The proposed methods in this thesis not only make up for the shortcomings of existing spherical fuzzy MAGDM methods in dealing with uncertain problems,but also enrich and develop theories and methods of spherical fuzzy MAGDM.In addition,the proposed methods provide more choices for decision makers to deal with other uncertain problems and also offer a theoretical reference for improving decision making methods in other complex fuzzy environments.