Fuzzy solution of fully fuzzy multi-objective linear fractional programming problems

T Loganathan T Loganathan,Ganesan Kandasamy

doi:10.18187/pjsor.v17i4.3368

Abstract

In this study, we present a novel method for solving fully fuzzy multi-objective linear fractional programming problems without transforming to equivalent crisp problems. First, we calculate the fuzzy optimal value for each fractional objective function and then we convert the fully fuzzy multi-objective linear fractional programming problem to a single objective fuzzy linear fractional programming problem and ﬁnd its fuzzy optimal solution which inturn yields a fuzzy Pareto optimal solution for the given fully fuzzy multi-objective linear fractional programming problem. To demonstrate the proposed strategy, a numerical example is provided.

Highlights

Multi-objective linear fractional programming problems(MOLFPP) occurs when there are several ratios of quantities to be optimized simultaneously
A new algorithm is proposed for the solution of FFMOLFPP without transforming to equivalent crisp problem
This contradicts the fact that y∗ is a fuzzy pareto optimal solution of PI

Summary

Introduction

Multi-objective linear fractional programming problems(MOLFPP) occurs when there are several ratios of quantities to be optimized simultaneously. Nuran Guzel(Guzel, 2013) introduced a new solution procedure to solve MOLFPP by reducing it to linear programming problem(LPP). Farhana Akond Pramy (Pramy, 2020) introduced graded mean integration method to solve the fuzzy multi objective linear fractional programming problem (FMOLFPP). Loganathan and Ganesan (Loganathan and Ganesan, 2019) presented a solution for fully fuzzy linear fractional programming problem(FFLFPP) with a new approach. 2020)proposed a pair of piece-wise linear membership functions to solve FMOLFPP. We consider FFMOLFPP that included triangular fuzzy numbers and proposed a new method for its solution. The proposed method facilitate the decision maker to solve FFMOLFPP without transforming it to an equivalent crisp problem.

Ranking of Triangular Fuzzy Numbers

Arithmetic Operations of Triangular Fuzzy Numbers

Algorithm

Numerical Example

Concluding Remarks