Linear Programming Problems in Fuzzy Decision Space (original) (raw)
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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...
From ranking fuzzy numbers to solving fuzzy linear programming: a comprehensive review
International Journal of Computing Science and Mathematics, 2014
Solving fuzzy linear programming (FLP) requires the employment of a consistent ranking of fuzzy numbers. Ineffective fuzzy number ranking would lead to a flawed and erroneous solving approach. This paper presents a comprehensive and extensive review on fuzzy number ranking methods. Ranking techniques are categorised into six classes based on their characteristics. They include centroid methods, distance methods, area methods, lexicographical methods, methods based on decision maker's viewpoint, and methods based on left and right spreads. A survey on solving approaches to FLP is also reported. We then point out errors in several existing methods that are relevant to the ranking of fuzzy numbers and thence suggest an effective method to solve FLP. Consequently, FLP problems are converted into non-fuzzy single (or multiple) objective linear programming based on a consistent centroid-based ranking of fuzzy numbers. Solutions of FLP are then obtained by solving corresponding crisp single (or multiple) objective programming problems by conventional methods.. He has published a number of peer-reviewed papers in the field of operational research, optimisation and soft computing techniques. His current research interest includes expert systems, applications of intelligent systems for optimisation, classification and forecasting.
Fuzzy number linear programming: A probabilistic approach (3)
Journal of Applied Mathematics and Computing, 2004
In the real world there are many linear programming problems where all decision parameters are fuzzy numbers. Several approaches exist which use different ranking functions for solving these problems. Unfortunately when there exist alternative optimal solutions, usually with different fuzzy value of the objective function for these solutions, these methods can not specify a clear approach for choosing a solution. In this paper we propose a method to remove the above shortcoming in solving fuzzy number linear programming problems using the concept of expectation and variance as ranking functions
Fuzzy Number Linear Programming: A Probabilistic Approach
2002
In real world there are many problems which have linear programming models where all decision parameters are fuzzy numbers. There are some approaches which are using different ranking functions for solving these problems. Unfortunately all these methods when there exist alternative optimal solutions, usually with different fuzzy value of the objective function for these solutions, can not specify a clear approach for choosing a solution. In this paper using the concept of expectation and variance as ranking functions, we propose a method to remove the above shortcomings in solving fuzzy number linear programming problems.
A managerial decision-making approach to fuzzy linear programming problems
International Journal of Management Science and Engineering Management, 2014
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. In this paper, using the concept of fuzzy numbers comparison, we introduce a very effective method for solving these problems. Then we propose a new method for solving linear programming problems with fuzzy variables. This paper extends linear programming based problem into a fuzzy environment. With the problem assumptions, the optimal solution can still be theoretically solved using the simplex based method. To handle fuzzy decision variables can be generated initially, then solved and improved sequentially using the fuzzy decision approach by introducing a robust ranking technique. The proposed procedure was programmed. The model is illustrated with a numerical example and a sensitivity analysis is of the optimal solution is studied with respect changes in parameter which incorporates all concepts of a fuzzy arithmetic approach to draw managerial insights.
2010
In this paper the shortcomings of an existing method for comparing the generalized fuzzy numbers are pointed out and a new method is proposed for same. Also using the proposed ranking method, a generalized simplex algorithm is proposed for solving a special type of fuzzy linear programming (FLP) problems. To illustrate the proposed algorithm a numerical example is solved and the advantages of the proposed algorithm are discussed. Since the proposed algorithm is a direct extension of classical algorithm so it is very easy to understand and apply the proposed algorithm to find the fuzzy optimal solution of FLP problems occurring in the real life situations.
Decision Making Approach to Fuzzy Linear Programming (FLP) Problems with Post Optimal Analysis
International Journal of Operations Research and Information Systems, 2015
This paper finds solutions to the fuzzy linear program where some parameters are fuzzy numbers. 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, the author introduces a very effective method for solving these problems. This paper extends linear programming based problem in fuzzy environment. With the problem assumptions, the optimal solution can still be theoretically solved using the simplex based method. To handle the fuzzy decision variables can be initially generated and then solved and improved sequentially using the fuzzy decision approach by introducing robust ranking technique. The model is illustrated with an application and a post optimal analysis approach is obtained. The proposed procedure was programmed wi...
New ranking function for fuzzy linear programming problem and system of linear equations
Journal of Information and Optimization Sciences, 2018
Linear Programming problems and System of Linear equations have many applications in various science and engineering problems like network analysis, operations research etc. In general Linear Programming Problem (LPP) and the system of linear equations contain crisp parameters that is real numbers or complex numbers as their coefficients and constants, but in real life applications, LPP and system of equations may contain the constrains or the parameters as uncertain. These uncertain values are not the exact real numbers but vary within some range of values, the values may vary within an interval or can be considered as fuzzy number. In this paper, we have developed a new Ranking function (which converts the fuzzy number into crisp) to solve a fully fuzzy LPP and System of equations. Unlike the previous ranking functions, the proposed ranking function uses fuzzy number itself improving the accuracy of the solution. The ranking function is derived by replacing the non-parallel sides of the trapezoidal fuzzy number with non-linear functions. Various numerical examples are included and compared with the pre-existing methods.
Ibn AL-Haitham Journal For Pure and Applied Sciences
Fuzzy numbers are used in various fields such as fuzzy process methods, decision control theory, problems involving decision making, and systematic reasoning. Fuzzy systems, including fuzzy set theory. In this paper, pentagonal fuzzy variables (PFV) are used to formulate linear programming problems (LPP). Here, we will concentrate on an approach to addressing these issues that uses the simplex technique (SM). Linear programming problems (LPP) and linear programming problems (LPP) with pentagonal fuzzy numbers (PFN) are the two basic categories into which we divide these issues. The focus of this paper is to find the optimal solution (OS) for LPP with PFN on the objective function (OF) and right-hand side. New ranking function (RF) approaches for solving fuzzy linear programming problems (FLPP) with a pentagonal fuzzy number (PFN) have been proposed, based on new ranking functions (N RF). The simplex method (SM) is very easy to understand. Finally, numerical examples (NE) are use...
Different strategies to solve fuzzy linear programming problems
2012
Fuzzy linear programming problems have an essential role in fuzzy modeling, which can formulate uncertainty in actual environment In this paper we present methods to solve (i) the fuzzy linear programming problem in which the coefficients of objective function are trapezoidal fuzzy numbers, the coefficients of the constraints, right hand side of the constraints are triangular fuzzy numbers, and (ii) the fuzzy linear programming problem in which the variables are trapezoidal fuzzy variables, the coefficients of objective function and right hand side of the constraints are trapezoidal fuzzy numbers, (iii) the fuzzy linear programming problem in which the coefficients of objective function, the coefficients of the constraints, right hand side of the constraints are triangular fuzzy numbers. Here we use α –cut and ranking functions for ordering the triangular fuzzy numbers and trapezoidal fuzzy numbers. Finally numerical examples are provided to illustrate the various methods of the fuz...