Marbini, A.H. and Tavana, M. (2011) An Extension of the Linear Programming Method with Fuzzy Parameters. International Journal of Mathematics in Operational Research, 3, 44-55.

has been cited by the following article:

• TITLE: Goal Programming for Solving Fractional Programming Problem in Fuzzy Environment

  AUTHORS: Anil Kumar Nishad, Shiva Raj Singh

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

  JOURNAL NAME: Applied Mathematics, Vol.6 No.14, December 31, 2015

  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.