Research On Multi-attribute Decision-making Methods Based On Fuzzy Evaluation Information

With the continuous development of economy and society,decision-making issues in the field of economic management have become more and more complex.To help the decision makers make best choices,more and more scholars have devoted themselves to the research of multi-attribute decision making methods,and many effective and novel methods have been put forward.In the real world,the multi-attribute decision-making(MADM)problems are usually very complicated.On one hand,the decision-making problems themselves are usually complicated,bring troubles to decision makers from the perspective of technologies,and making it difficult to make crisp decisions.On the other hand,because that decision makers are usually from different fields and limited by their background and prior knowledge,it is often difficult for decision-makers to express their evaluation information with crisp numbers.At present,scholars at home and abroad usually utilize fuzzy set theory to depict decision makers' evaluation values and study MADM methods from fuzzy set theory.The classical fuzzy set theory was proposed in 1965 and has been widely used in the field of MADM problems since then.As the decision-making problems in the real world become more and more complex,more and more scholars have realized the drawbacks of the classic fuzzy set theory and they proposed quite a few extensions of the classic fuzzy set theory,facing different decision-making context,such as the intuitionistic fuzzy sets,type-2 fuzzy sets,Pythagorean fuzzy sets,hesitating fuzzy sets,etc.,which have been widely used in the field of MADM problems.Recently,some new fuzzy set theories have been proposed,which have significant advantages in describing the evaluation information of decision-makers when compared with the existing fuzzy theories.However,there are few studies on the applications of these novel fuzzy set theories to MADM problems.Aiming at several new types of fuzzy set theories(q-rung dual hesitant fuzzy sets,Pythagorean uncertain linguistic sets,q-rung orthopair uncertain linguistic sets,and cubic q-rung orthopair fuzzy sets),this article investigated novel MADM methods under these fuzzy environments from the perspectives of information aggregation operators and traditional decision-making methods,and applied the new MADM methods in realistic MADM problems.The main work and innovations of this dissertation are:(1)A multi-attribute decision making method based on q-rung dual hesitation fuzzy sets is studied.Considering that the unduly high or low evaluation values provided by decision makers maybe have negative impact on the final decision-making results,and the interrelationship among attributes,this work extends the classical power Bonferroni mean(PBM)into q-rung dual hesitant fuzzy sets and proposes a series of novel q-rung dual hesitant fuzzy compound aggregation operators.Compared with the existing operators,these newly proposed operators have some significant advantages and priorities.Then,based on these newly proposed operators,a new MADM method is developed.Finally,a case study and comparative analysis are carried out to demonstrate the effectiveness and superiority of the new method.(2)The information fusion operators and MADM methods of Pythagorean uncertain linguistic information and the q-rung orthopair uncertain linguistic information are studied.To solve the MADM problems with the evaluation information expressed by Pythagorean fuzzy uncertain linguistic variables,we combine the power average operator with the Muirhead mean operator,and propose the power Muirhead mean(PMM)operator.After that,we further expand the PMM operator into the Pythagorean fuzzy uncertain linguistic sets and introduce some novel compound operators.Based on which,a new MADM method is put forward.This dissertation further studies the MADM problem with the evaluation values given by q-rung orthopair uncertain linguistic information.Moreover,several fusion operators of q-rung orthopair uncertain linguistic sets are given,and the properties and some special cases are systematically discussed.A novel MADM method for unknown attribute weights is presented,and the effectiveness and superiority of the new method are verified by computational power analysis and comparative analysis.(3)A MADM method based on cubic q-rung orthopair fuzzy sets is studied.As an extension of cubic intuitionistic fuzzy sets and cubic Pythagorean fuzzy sets,cubic q-rung orthopair fuzzy sets have some obvious advantages in describing uncertain information.Focus on the MADM problems expressed by cubic q-rung orthopair fuzzy information,this work introduces the classic TOPSIS method into the field of cubic orthopair fuzzy sets and proposes a new Cq-ROF-TOPSIS method to solve MADM problems.The effectiveness of the new method is verified by a numerical example.