Author(s)

Anil Kumar Nishad, Shiva Raj Singh^*

Department of Mathematics, Banaras Hindu University, Varanasi, India.

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.

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

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.