Abstract
In this paper, an attempt has been taken to develop a method for solving fuzzy multi-objective linear fractional programming (FMOLFP) problem. Here, at first the FMOLFP problem is converted into (crisp) multi-objective linear fractional programming (MOLFP) problem using the graded mean integration representation (GMIR) method proposed by Chen and Hsieh. That is, all the fuzzy parameters of FMOLFP problem are converted into crisp values. Then the MOLFP problem is 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 regular simplex method which yields an efficient solution of the original FMOLFP problem. To show the efficiency of our proposed method, three numerical examples are illustrated and also for each example, a comparison is drawn between our proposed method and the respected existing method.
Highlights
Porchelvi et al (2014) presented procedures for solving both MOLFP problem and fuzzy multi-objective linear fractional programming (FMOLFP) problem using the complementary development method of Dheyab (2012), where the fractional linear programming is transformed into a linear programming problem
Later Guzel (2013) proposed a simplex type algorithm for finding an efficient solution of MOLFP problem based on a theorem studied in a work by Dinkelbach (1967), where he converted the main problem into a single objective linear programming (LP) problem
We have developed a method for solving FMOLFP problem by combining the methods proposed by Chen and Hsieh (1999) and Guzel (2013)
Summary
Making decisions is an essential part of our daily lives. Almost all decision problems we deal with have multiple, usually conflicting, criteria. Very often in real life situations, the values of coefficients of multi-objective linear fractional programming problems are only imprecisely available to the expert. To handle this type of situation, it would be preferable to interpret the coefficients as fuzzy numerical data. Porchelvi et al (2014) presented procedures for solving both MOLFP problem and FMOLFP problem using the complementary development method of Dheyab (2012), where the fractional linear programming is transformed into a linear programming problem. Later Guzel (2013) proposed a simplex type algorithm for finding an efficient solution of MOLFP problem based on a theorem studied in a work by Dinkelbach (1967), where he converted the main problem into a single objective LP problem. The membership function μà (x) associates with each point x ∈ X a real number in the interval [0, 1]
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