Goal Programming for Solving Fractional Programming Problem in Fuzzy Environment

Abstract

This paper is comprised of the modeling and optimization of a multi objective linear programming problem in fuzzy environment in which some goals are fractional and some are linear. Here, we present a new approach for its solution by using α-cut of fuzzy numbers. In this proposed method, we first define membership function for goals by introducing non-deviational variables for each of objective functions with effective use of α-cut intervals to deal with uncertain parameters being represented by fuzzy numbers. In the optimization process the under deviational variables are minimized for finding a most satisfactory solution. The developed method has also been implemented on a problem for illustration and comparison.

This paper is comprised of the modeling and optimization of a multi objective linear programming problem in fuzzy environment in which some goals are fractional and some are linear. Here, we present a new approach for its solution by using α-cut of fuzzy numbers. In this proposed method, we first define membership function for goals by introducing non-deviational variables for each of objective functions with effective use of α-cut intervals to deal with uncertain parameters being represented by fuzzy numbers. In the optimization process the under deviational variables are minimized for finding a most satisfactory solution. The developed method has also been implemented on a problem for illustration and comparison.

Keywords

Fuzzy Sets, Trapezoidal Fuzzy Number (TFN), Multi-Objective Linear Programming Problem (MOLPP), Multi-Objective Linear Fractional Programming Problem (MOLFPP)

Fuzzy Sets, Trapezoidal Fuzzy Number (TFN), Multi-Objective Linear Programming Problem (MOLPP), Multi-Objective Linear Fractional Programming Problem (MOLFPP)

Cite this paper

Nishad, A. and Singh, S. (2015) Goal Programming for Solving Fractional Programming Problem in Fuzzy Environment.*Applied Mathematics*, **6**, 2360-2374. doi: 10.4236/am.2015.614208.

Nishad, A. and Singh, S. (2015) Goal Programming for Solving Fractional Programming Problem in Fuzzy Environment.

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