Abstract
Two existing methods for solving a class of fuzzy linear programming (FLP) problems involving symmetric trapezoidal fuzzy numbers without converting them to crisp linear programming problems are the fuzzy primal simplex method proposed by Ganesan and Veeramani [1] and the fuzzy dual simplex method proposed by Ebrahimnejad and Nasseri [2]. The former method is not applicable when a primal basic feasible solution is not easily at hand and the later method needs to an initial dual basic feasible solution. In this paper, we develop a novel approach namely the primal-dual simplex algorithm to overcome mentioned shortcomings. A numerical example is given to illustrate the proposed approach.
Highlights
In optimizing real world systems, one usually ends up with a linear or nonlinear programming problem
Two existing methods for solving a class of fuzzy linear programming (FLP) problems involving symmetric trapezoidal fuzzy numbers without converting them to crisp linear programming problems are the fuzzy primal simplex method proposed by Ganesan and Veeramani [1] and the fuzzy dual simplex method proposed by Ebrahimnejad and Nasseri [2]
We describe a new method for solving linear programming problem with symmetric trapezoidal fuzzy numbers, called the primal-dual algorithm, similar to the dual simplex method, which begins with dual feasibility and proceeds to obtain primal feasibility while maintaining complementary slackness
Summary
In optimizing real world systems, one usually ends up with a linear or nonlinear programming problem. One important class of these methods that has been highlighted by many researches is based on comparing of fuzzy numbers using ranking functions Based on this idea, Maleki et al [13] proposed a simple method for solving fuzzy number linear programming (FNLP) problems. A. EBRAHIMNEJAD new method based on primal simplex algorithm for solving linear programming problem with symmetric trapezoidal fuzzy numbers without converting them to crisp linear programming problems. We describe a new method for solving linear programming problem with symmetric trapezoidal fuzzy numbers, called the primal-dual algorithm, similar to the dual simplex method, which begins with dual feasibility and proceeds to obtain primal feasibility while maintaining complementary slackness.
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