Study on multi-objective linear fractional programming problem involving pentagonal intuitionistic fuzzy number

Abstract

In this paper, we have suggested an alternative approach to solve intuitionistic fuzzy multi objective linear fractional programming problems (IFMOLFPP). Here, the cost of the objective function, the resources and the technological coefficients are taken to be pentagonal intuitionistic fuzzy numbers. In the proposed method, we have transformed (IFMOLFPP) to intuitionistic fuzzy multi objective linear programming problem (IFMOLPP) and then the resultant (IFMOLPP) is converted into crisp multi objective linear programming problem (CMOLPP) under well defined accuracy function. We have established some theorems to show that the efficient solution of (CMOLPP) is also an efficient solution of (IFMOLPP) and (IFMOLFPP). Then by using Zimmermann’s technique under suitable non linear membership functions, we have reduced (CMOLPP) to a single objective LPP which can be easily solved by any LPP algorithm or software. We have illustrated the proposed approach by Numerical examples.