Multi-criteria Decision Making Method Based On Interval-valued Picture Fuzzy Sets

Multi-attribute decision making is an important part of modern decision science.Its theory and method are widely used in many fields,such as investment,project location,project bidding and so on.So far,many scholars have used different fuzzy set measures and operators to solve the problem of multi-attribute decision making.As an extension of fuzzy set,intuitionistic fuzzy set.,interval-valued fuzzy set,interval-valued intuitionistic fuzzy set and picture fuzzy set,interval-valued picture fuzzy set can better deal with fuzzy information and inconsistent information.Therefore,this paper studies multi-attribute decision making in the fuzzy environment of interval-valued pictures.The main research contents and innovations of this paper are as follows:(1)Based on the three adjustable weight vectors,the reduced interval-valued picture fuzzy sets are given,and the Dice similarity measure between the reduced interval-valued picture fuzzy sets is further given,and its properties are studied.Based on the preference of decision-makers and the new Dice similarity measure,the algorithm of multi-attribute decision making is given from three angles of optimism,pessimism and neutrality respectively.(2)Based on Dombi t-norm and t-conorm,four new operators on interval-valued picture fuzzy sets are given,and their properties are studied.Based on four new operators,the algebraic aggregation operator and geometric aggregation operator on interval-valued picture fuzzy sets are constructed,which are Dombi weighted algebraic aggregation operator,Dombi order weighted algebraic aggregation operator,Dombi mixed weighted algebraic aggregation operator,Dombi weighted geometric aggregation operator,Dombi order weighted geometric aggregation operator and Dombi mixed weighted geometric aggregation operator.It is proved that the aggregation operator of Dombi weighted Algebra(or geometry)and the aggregation operator of Dombi order weighted Algebra(or geometry)are two special cases of the aggregation operator of Dombi mixed weighted Algebra(or geometry).Furthermore,the algorithm of multi-attribute decision making is given and used to solve practical problem.(3)A concrete example of economic investment is given,and the superiority of the proposed method is demonstrated through comparative study.