A novel method for solving linear programming problems with symmetric trapezoidal fuzzy numbers (original) (raw)
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Applied Mathematics, 2011
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 . 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.
FUZZY (TRAPEZOIDAL) LINEAR PROGRAMMING PROBLEMS A COMPUTERIZED SOLUTION
Journal of Engineering for Development, 2021
This paper considers a Rectangular (trapezoidal) fuzzy linear programming problem and develops computerized solutions to these problems. The computerized process which is known as the software was programmed using the Microsoft visual basic.Net programming language. The method used is the simplex method which is normally used for solving linear programming problems in crisp environment. In conducting the analysis, the rectangular fuzzy linear programming problems involving fully rectangular (trapezoidal) fuzzy linear programming problem, or just when its objective function variables are fuzzy, or when just its right-hand side constants are fuzzy were considered. Then the results of the manual and software solution were compared on the some bench mark questions. The software shows robustness and accurate.
A Generalized Model for Fuzzy Linear Programs with Trapezoidal Fuzzy Numbers
2017
In this paper, we generalize a linear programming problem with symmetric trapezoidal fuzzy number which is introduced by Ganesan and et al. in [3] to a general kind of trapezoidal fuzzy number. In this way, we first establish a new arithmetic operation for multiplication of two trapezoidal fuzzy numbers. Then in order to preparing a method for solving the fuzzy linear programming as well as the primal simplex algorithm, we use a general linear ranking function as a convenient approach in the literature. In fact, our main contribution in this work is based on 3 items: 1) Extending the current fuzzy linear program to a general kind which is not essentially including the symmetric trapezoidal fuzzy numbers , 2) Defining a new multiplication role of two trapezoidal fuzzy numbers, 3) Establishing a fuzzy primal simplex algorithm for solving the generalized model. We in particular emphasize that this study can be used for establishing fuzzy dual simplex algorithm, fuzzy prima...
Fuzzy linear programs with trapezoidal fuzzy numbers
2006
The objective of this paper is to deal with a kind of fuzzy linear programming problem involving symmetric trapezoidal fuzzy numbers. Some important and interesting results are obtained which in turn lead to a solution of fuzzy linear programming problems without converting them to crisp linear programming problems.
Soft Computing
Linear programming (LP) has long proved its merit as the most flexible and most widely used technique for resource allocation problems in various fields. To solve an LP problem, we have traditionally considered crisp values for the parameters, which are unrealistic in real-world decision-making under uncertainty. The fuzzy set theory has been used to model the imprecise parameter values in LP problems to overcome this shortcoming, resulting in a fuzzy LP (FLP) problem. This paper proposes a new method for solving fuzzy variable linear programming (FVLP) problems in which the decision variables and resource vectors are fuzzy numbers. We show how to use the standard simplex algorithm to solve this problem by converting the fuzzy problem into a crisp one once a linear ranking function is chosen. The novelty of the proposed model resides in that it requires less effort on fuzzy computations as opposed to the existing fuzzy methods. Furthermore, to solve the FVLP problem using the existing methods, fuzzy arithmetic operations and the solution to fuzzy systems of equations are required. By contrast, only arithmetic operations of real numbers and the solution to crisp systems of equations are required to solve the same problem with the method proposed in this study. Finally, a transportation case study in the coal industry is presented to demonstrate the applicability of the proposed algorithm.
A method for solving linear programming with interval-valued trapezoidal fuzzy variables
RAIRO - Operations Research
An efficient method to handle the uncertain parameters of a linear programming (LP) problem is to express the uncertain parameters by fuzzy numbers which are more realistic, and create a conceptual and theoretical framework for dealing with imprecision and vagueness. The fuzzy LP (FLP) models in the literature generally either incorporate the imprecisions related to the coefficients of the objective function, the values of the right-hand side, and/or the elements of the coefficient matrix. The aim of this article is to introduce a formulation of FLP problems involving interval-valued trapezoidal fuzzy numbers for the decision variables and the right-hand-side of the constraints. We propose a new method for solving this kind of FLP problems based on comparison of interval-valued fuzzy numbers by the help of signed distance ranking. To do this, we first define an auxiliary problem, having only interval-valued trapezoidal fuzzy cost coefficients, and then study the relationships betwee...
Revised simplex method and its application for solving fuzzy linear programming problems
2012
Linear programming models play an important role in management, economic, data envelopment analysis, operations research and many industrial applications. In many practical situations there is a kind of ambiguity in the parameters of these models which can be expressed by means of fuzzy numbers. In the literature of fuzzy mathematical programming there are many types of the fuzzy linear programming problems. But in this paper, we deal with a kind of linear programming which includes the triangular fuzzy numbers in its parameters. For finding the solution of these problems, we propose a revised simplex algorithm for an extended linear programming problem which is equivalent to the original fuzzy linear programming problem. An illustrative example is presented to clarify the proposed approach. A fuzzy DEA model has been also considered as a practical application to illustrate the effectiveness of the proposed approach.
Proposed Simplex Method For Fuzzy Linear Programming With Fuzziness at the Right Hand Side
Linear programming (LP) is one of the frequently applied tools in operations research, it plays a vital role for solving real-life problem because of its efficiency and simplicity. However, managers and decision makers may lack information about exact values of most of the parameters used in any of the optimization models, the flexible approach of fuzzy linear programming (FLP) comes up with a powerful tool to deal with such situations. In this paper, the simplex method for imprecise resources has been proposed to solve the parametrized LP. GAMS software can always be use to solve the FLP with fuzziness at the RHS in a simplest way.
Linear Programming Problems in Fuzzy Environment : The Post Optimal Analyses
2015
This paper proposes a new method of Robust ranking technique, which is used for defuzzifying the trapezoidal fuzzy number into a crisp number to represent the fuzzy set. In practice, there are many problems in which all decision parameters are fuzzy numbers, and such problems are usually solved by either probabilistic programming or multi objective programming methods. Unfortunately all these methods have shortcomings. In this paper, using the concept of comparison of fuzzy numbers, a very effective method is introduced for solving these problems. The model is illustrated with numerical application to generate a good solution and post optimal analyses are obtained. Investigation of the properties of an optimal solution allows developing a simplex algorithm in fuzzy environment. Furthermore, the proposed technique allows the significant ways to help the decision-maker for formulating their decisions and drawing managerial insights efficiently. © 2015 World Academic Press, UK. All rig...