Hesitant Triangular Fuzzy Set Theory And Its Applications In Decision Making

Hesitant fuzzy set is a very practical fuzzy information processing tool,which has been successfully applied in the fields of clustering,decision making,pattern recognition,and image processing.In order to highlight the uncertainty and ambiguity of decision values,and to some extent make up for the shortcomings and disadvantages of hesitant fuzzy sets,theory of the hesitant triangular fuzzy set and its application are studied.Aiming at the hesitation ambiguity of decision makers and the complexity of decision values in practical decision-making problems,this paper proposes three types of fuzzy distance measures and decision-making methods under hesitant triangular fuzzy environment.The rationality and feasibility of those methods are verified through case analysis.The main research contents are as follows:1.For the decision-making problem where the decision value is hesitant triangular fuzzy element,the distance formula of hesitant triangular fuzzy set and decision-making method based on hesitant triangular fuzzy distance measure are studied.Through the case analysis of multi-attribute decision-making and group decision-making under hesitant triangular fuzzy environment,it is stated that the distance measure of the hesitant triangular fuzzy set is rationality and feasibility in decision making.2.Different importance which different elements in hesitant triangular fuzzy elements as membership,the concepts of weighted hesitant triangular fuzzy sets are proposed,the group decision problem with decision value as weighted hesitant triangular fuzzy element is studied.First,formula of weighted hesitant triangular fuzzy distance is given.Secondly,based on the convenience of calculation and without change the importance of triangular fuzzy numbers as membership,a method of adding elements to weighted hesitant triangular fuzzy elements is proposed.Finally,a group decision-making method based on weighted hesitant triangular fuzzy distance measurement is proposed and applied to group decision-making under hesitant triangular fuzzy environment.Numerical examples show that the weighted hesitant triangular fuzzy distance metric has rationality and feasibility in group decision making.3.Based on difference of set elements and the objectivity of decision results,a hesitant triangular vector fuzzy set concept and algorithms are proposed,the distance formula of the hesitant triangular vector fuzzy set and the group decision-making method based on the hesitant triangular vector fuzzy distance measure are studied,and applied to group decision-making under hesitant triangular fuzzy environment.Numerical examples show that the hesitant triangular vector fuzzy distance metric has rationality and feasibility.