A New Method for Ranking Fuzzy Numbers Using the Circumcenter and its Application in Performance Evaluation of Supply Chain Management

Since much of human reasoning is based on imprecise, vague and subjective values, most of decision-making processing, in reality, requires handling and evaluation of fuzzy numbers. Ranking fuzzy numbers is one of very important research topics in fuzzy set theory because it is a base of decision-making in applications. Although so far, many methods for ranking of fuzzy numbers have been discussed broadly, most of them contained some shortcomings, such as requirement of complicated calculations, inconstancy with human intuition and indiscrimination. In this paper, we introduce a new method by using of the affine combination on the circumcenter. This method ranks various types of fuzzy numbers which include normal, generalized trapezoidal, and triangular fuzzy numbers along with crisp numbers with the particularity that crisp numbers are to be considered particular cases of fuzzy numbers. The advantages of the new proposed are that it can be applied for most of the defuzzification and the calculation is far simple and easy than previous methods. The effectiveness of the proposed method and its advantages is demonstrated by numerical examples, comprehensive comparing different ranking method with this method and also its benefits will be illustrated by the numerical example, as well as a case study on supply chain management.