A revisit of a mathematical model for solving fully fuzzy linear programming problem with trapezoidal fuzzy numbers

Subject Areas : Statistics

A.  Ebrahimnejad ¹ (Department of Mathematics, Qaemshahr Branch, Islamic Azad University, Qaemshahr, Iran.)

Received: 2019-03-02 Accepted : 2019-06-25 Published : 2019-05-01

Keywords: اعداد فازی ذوزنقه‌ای, مقایسه الفبایی, برنامه‌ریزی خطی تماماً فازی, برنامه‌ریزی خطی چندهدفه,

Abstract :

In this paper fully fuzzy linear programming (FFLP) problem with both equality and inequality constraints is considered where all the parameters and decision variables are represented by non-negative trapezoidal fuzzy numbers. According to the current approach, the FFLP problem with equality constraints first is converted into a multi–objective linear programming (MOLP) problem with crisp constraints and then a lexicographic ordering method is used for solving the resulting MOLP problem. However, this approach cannot be used for finding the fuzzy optimal solution of FFLP problems with inequality constraints. The aim of this study is to point out and correct some errors in the definitions, notations operations and fuzzy ordering of the current approach for solving FFLP problems with fuzzy inequality constraints. Hence, a modified approach to obtain the fuzzy optimal solution of the FFLP problems with inequality constraints is proposed. Finally, several numerical examples are presented to illustrate the proposed approach.