A new method for fuzzy numbers ranking on the basis of hypotenuse set (Q2204291)

Summary: The fuzzy numbers ranking plays a significant role in many fuzzy application systems. This paper presents a new approach for fuzzy numbers ranking and six definitions are introduced for comparing fuzzy numbers. The purpose of paper is to rank the trapezoidal/triangular fuzzy numbers based on the hypotenuse set for each fuzzy number. Each member (hypotenuse) of the set (L-R) is resulted from a certain level (\({\lambda}\)-cut) of membership degree. The hypotenuse length is calculated for each level based on the distance of each fuzzy number with fuzzy number indicator. The fuzzy number indicator is affected by all the fuzzy numbers for ranking. Therefore, the relative preference is measured in each level (\({\lambda}\)-cut) and the absolute preference is totally represented in terms of all levels. Additionally, the proposed method is compared with the available methods. Several examples are studies for expressing the advantages of the reasonable performance of proposed method.