A parametric approach to fuzzy multi-objective linear fractional program: An alpha cut based method

In the multi-objective programming problem (MOPP), finding an efficient solution is challenging and partially encompasses some difficulties in practice. This paper presents an approach to address the multi-objective linear fractional programing problem with fuzzy coefficients (FMOLFPP). In the method, at first, the concept of α - cuts is used to change the fuzzy numbers into intervals. Therefore, the fuzzy problem is further changed into an interval-valued linear fractional programming problem (IVLFPP). Afterward, this problem is transformed into a linear programming problem (LPP) using a parametric approach and the weighted sum method. It is proven that the solution resulted from the LPP is at least a weakly ɛ - efficient solution. Two examples are given to illustrate the method.

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

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.

An Efficient Branch-and-Bound Algorithm for Globally Solving Minimax Linear Fractional Programming Problem

This paper presents an efficient outer space branch-and-bound algorithm for globally solving a minimax linear fractional programming problem (MLFP), which has a wide range of applications in data envelopment analysis, engineering optimization, management optimization, and so on. In this algorithm, by introducing auxiliary variables, we first equivalently transform the problem (MLFP) into the problem (EP). By using a new linear relaxation technique, the problem (EP) is reduced to a sequence of linear relaxation problems over the outer space rectangle, which provides the valid lower bound for the optimal value of the problem (EP). Based on the outer space branch-and-bound search and the linear relaxation problem, an outer space branch-and-bound algorithm is constructed for globally solving the problem (MLFP). In addition, the convergence and complexity of the presented algorithm are given. Finally, numerical experimental results demonstrate the feasibility and efficiency of the proposed algorithm.

An Approach for Solving Multi-Objective Linear Fractional Programming Problem with fully Rough Interval Coefficients

In this paper, a multi-objective linear fractional programming (MOLFP) problem is considered where all of its coefficients in the objective function and constraints are rough intervals (RIs). At first, to solve this problem, we will construct two MOLFP problems with interval coefficients. One of these problems is a MOLFP where all of its coefficients are upper approximations of RIs and the other is a MOLFP where all of its coefficients are lower approximations of RIs. Second, the MOLFP problems are transformed into a single objective linear programming (LP) problem using a proposal given by Nuran Guzel. Finally, the single objective LP problem is solved by a regular simplex method which yields an efficient solution of the original MOLFP problem. A numerical example is given to demonstrate the results.