A duality approach for solving bounded linear programming problems with fuzzy variables based on ranking functions and its application in bounded transportation problems

There are several methods, in the literature, for solving fuzzy variable linear programming problems (fuzzy linear programming in which the right-hand-side vectors and decision variables are represented by trapezoidal fuzzy numbers). In this paper, the shortcomings of some existing methods are point...

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Published in:International journal of systems science Vol. 46; no. 11; pp. 2048 - 2060
Main Author: Ebrahimnejad, Ali
Format: Journal Article
Language:English
Published: Taylor & Francis 18.08.2015
Subjects:
bounded dual simplex method
Fuzzy
fuzzy linear programming problem
Fuzzy logic
Fuzzy set theory
Linear programming
linear ranking functions
Mathematical analysis
Optimization
Supply and demand
Transportation problem
ISSN:0020-7721, 1464-5319
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Abstract There are several methods, in the literature, for solving fuzzy variable linear programming problems (fuzzy linear programming in which the right-hand-side vectors and decision variables are represented by trapezoidal fuzzy numbers). In this paper, the shortcomings of some existing methods are pointed out and to overcome these shortcomings a new method based on the bounded dual simplex method is proposed to determine the fuzzy optimal solution of that kind of fuzzy variable linear programming problems in which some or all variables are restricted to lie within lower and upper bounds. To illustrate the proposed method, an application example is solved and the obtained results are given. The advantages of the proposed method over existing methods are discussed. Also, one application of this algorithm in solving bounded transportation problems with fuzzy supplies and demands is dealt with. The proposed method is easy to understand and to apply for determining the fuzzy optimal solution of bounded fuzzy variable linear programming problems occurring in real-life situations.
AbstractList There are several methods, in the literature, for solving fuzzy variable linear programming problems (fuzzy linear programming in which the right-hand-side vectors and decision variables are represented by trapezoidal fuzzy numbers). In this paper, the shortcomings of some existing methods are pointed out and to overcome these shortcomings a new method based on the bounded dual simplex method is proposed to determine the fuzzy optimal solution of that kind of fuzzy variable linear programming problems in which some or all variables are restricted to lie within lower and upper bounds. To illustrate the proposed method, an application example is solved and the obtained results are given. The advantages of the proposed method over existing methods are discussed. Also, one application of this algorithm in solving bounded transportation problems with fuzzy supplies and demands is dealt with. The proposed method is easy to understand and to apply for determining the fuzzy optimal solution of bounded fuzzy variable linear programming problems occurring in real-life situations.
Author Ebrahimnejad, Ali
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  organization: Department of Mathematics, Qaemshahr Branch, Islamic Azad University
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SubjectTerms bounded dual simplex method
Fuzzy
fuzzy linear programming problem
Fuzzy logic
Fuzzy set theory
Linear programming
linear ranking functions
Mathematical analysis
Optimization
Supply and demand
Transportation problem
Title A duality approach for solving bounded linear programming problems with fuzzy variables based on ranking functions and its application in bounded transportation problems
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