In this paper I will introduce the trapezoidal intuitionistic fuzzy numbers (IF numbers) and will prove some operations for them. Also I am going to propose a new ordering method for IF numbers in which I will consider two characteristic values of membership and non-membership functions for an IF number. These values are defined by the integral of the inverse fuzzy membership and non-membership...

In this study, we propose an approach to determine the shortest path length between a pair of specified nodes s and t on a network whose edge weights are represented by trapezoidal neutrosophic numbers. Finally, an illustrative example is provided to show the applicability and effectiveness of the proposed approach. Keywords—trapezoidal fuzzy neutrosophic sets; score function; Shortest path pro...

In the fuzzy arithmetic, the definitions of addition and multiplication of fuzzy numbers are based on Zadeh’s extension principle. From theoretical and practical points of view, this multiplication of fuzzy numbers owns several unnatural properties. Recently, to avoid this shortcoming, a new multiplicative operation of product type is introduced, the so-called cross-product of fuzzy numbers. Th...

Since the discovery of fuzzy sets, the arithmetic operations of fuzzy numbers (Zadeh [7, 8]) which may be viewed as a generalization of interval arithmetic (Moore [5]) have emerged as an important area of research within the theory of fuzzy sets (Mizumoto and Tanaka [4], Dubois and Prade [2]). The arithmetic operations of fuzzy numbers have been performed either by extension principle [7, 8] or...

logistics outsourcing has been at the top of the management agenda during recent decades. the selection of the proper service supplier is the key to success in logistic outsourcing firms could select the right supplier by applying appropriate methods and selection criteria. in this paper a new framework is proposed on the basis of weighted additive fuzzy programming approach and linear programm...