Decision Making And Application Of Multiple Criteria Based On Type II Triangular Fuzzy Numbers

Membership degrees reflect the decision maker’s confidence in a fuzzy decision making problem. This degree of an element in a certain fuzzy set is hard to be expressed with a real number. Using fuzzy sets to express these membership values is reasonable. The existing studies mostly focus on the type-2fuzzy set (number) whose membership is discrete or denoted by intervals. Such membership often cannot reflect the decision makers’confidence well. Using a group of triangular fuzzy numbers to denote continuous fuzzy memberships is more adequate. We call such type-2fuzzy numbers as triangular type-2fuzzy numbers.This paper studies triangular type-2fuzzy numbers and its application in multi-criteria decision-making:(1) The operational laws, score function, possibility degree and distance are defined. For aggregating the triangular type-2fuzzy information, some aggregation operators are also introduced. For the problem of the multi-criteria decision making which the uncertainty of the criteria values is difficult to give with an accurate number, triangular type-2fuzzy number is used to show the decision information. And multi-criteria decision-making method based on different triangular type-2operators is proposed.(2) Methods of criteria weights problems are developed. And three methods are proposed to handle multi-criteria decision-making problems:Firstly, cluster method calculates the overall benefit value and the individual regret value. Then the maximum value and the minimum value of them will be found. Take them as the ideal and negative ideal solutions, and add them into the solution set. Thirdly, calculate the similarity of each solution in the new solution set. Finally, in order to find the best solution, similarity matrix will be clustered.In regret theory method, the regret utility matrix is attained by using the regret function and utility function. Then the regret utility values come out. Not only is the utility of the selected alternatives but also the regret degree to the unselected ones taken into account. And the ranking of alternatives is gotten by using the outranking net flow.Ideal point methods firstly calculate the attitude index. Then, by finding the ideal and negative ideal solutions and distances of them, the comprehensive attribute values and the rank of the alternatives can be obtained.(3) An example of green supplier selection is provided to demonstrate the feasibility and effectiveness of the proposed method. Firstly, the influencing factor of the green supplier selection is analysed, and the criteria are obtained. The linguistic information is transformed into triangular type-2fuzzy information. Then two fuzzy multi-criteria decision making methods are used. Finally, their results are compared and discussed with weighted average method and the information.