NEW IMPROVED METHOD FOR SOLVING THE FUZZY LINEAR PROGRAMMING PROBLEMS WITH VARIABLES GIVEN AS FUZZY NUMBERS

2021 ◽  
Vol 10 (12) ◽  
pp. 3699-3723
Author(s):  
L. Kané ◽  
M. Konaté ◽  
L. Diabaté ◽  
M. Diakité ◽  
H. Bado
Keyword(s):  
Linear Programming ◽  
Fuzzy Numbers ◽  
Optimal Solution ◽  
Fuzzy Linear Programming ◽  
Interval Linear Programming ◽  
Interval Numbers ◽  
Programming Technique ◽  
Solution Approach ◽  
Interval Linear ◽  
Linear Programming Problems

The present paper aims to propose an alternative solution approach in obtaining the fuzzy optimal solution to a fuzzy linear programming problem with variables given as fuzzy numbers with minimum uncertainty. In this paper, the fuzzy linear programming problems with variables given as fuzzy numbers is transformed into equivalent interval linear programming problems with variables given as interval numbers. The solutions to these interval linear programming problems with variables given as interval numbers are then obtained with the help of linear programming technique. A set of six random numerical examples has been solved using the proposed approach.

scholarly journals Mehar method for finding exact fuzzy optimal solution of fully fuzzy linear programming problems

2018 ◽  
Vol 1 (2) ◽  
Author(s):  
Gourav Gupta
Keyword(s):  
Linear Programming ◽  
Fuzzy Numbers ◽  
Optimal Solution ◽  
Triangular Fuzzy Number ◽  
Fuzzy Linear Programming ◽  
Decision Making Under Uncertainty ◽  
Triangular Fuzzy Numbers ◽  
Fuzzy Optimal Solution ◽  
Linear Programming Problems ◽  
Fuzzy Solutions

There are several methods in the literature to find the fuzzy optimal solution of fully fuzzy linear programming (FFLP) problems. However, in all these methods, it is assumed that the product of two trapezoidal (triangular) fuzzy numbers will also be a trapezoidal (triangular) fuzzy number. Fan et al. (“Generalized fuzzy linear programming for decision making under uncertainty: Feasibility of fuzzy solutions and solving approach”, Information Sciences, Vol. 241, pp. 12–27, 2013) proposed a method for finding the fuzzy optimal solution of FFLP problems without considering this assumption. In this paper, it is shown that the method proposed by Fan et al. (2013) suffer from errors and to overcome these errors, a new method (named as Mehar method) is proposed for solving FFLP problems by modifying the method proposed by Fan et al. (2013) . To illustrate the proposed method, some numerical problems are solved.

scholarly journals Linear Programming Problem with Interval Type 2 Fuzzy Coefficients and an Interpretation for Its Constraints

2016 ◽  
Vol 2016 ◽  
pp. 1-11 ◽  
Author(s):  
A. Srinivasan ◽  
G. Geetharamani
Keyword(s):  
Linear Programming ◽  
Fuzzy Numbers ◽  
Optimal Solution ◽  
Fuzzy Linear Programming ◽  
Trapezoidal Fuzzy Numbers ◽  
Degree Of Satisfaction ◽  
Linear Programming Problems ◽  
Interval Type ◽  
Perfectly Normal

Interval type 2 fuzzy numbers are a special kind of type 2 fuzzy numbers. These numbers can be described by triangular and trapezoidal shapes. In this paper, first, perfectly normal interval type 2 trapezoidal fuzzy numbers with their left-hand and right-hand spreads and their core have been introduced, which are normal and convex; then a new type of fuzzy arithmetic operations for perfectly normal interval type 2 trapezoidal fuzzy numbers has been proposed based on the extension principle of normal type 1 trapezoidal fuzzy numbers. Moreover, in this proposal, linear programming problems with resources and technology coefficients are perfectly normal interval type 2 fuzzy numbers. To solve this kind of fuzzy linear programming problems, a method based on the degree of satisfaction (or possibility degree) of the constraints has been introduced. In this method the fulfillment of the constraints can be measured with the help of ranking method of fuzzy numbers. Optimal solution is obtained at different degree of satisfaction by using Barnes algorithm with the help of MATLAB. Finally, the optimal solution procedure is illustrated with numerical example.

scholarly journals Mehar Methods for Fuzzy Optimal Solution and Sensitivity Analysis of Fuzzy Linear Programming with Symmetric Trapezoidal Fuzzy Numbers

2014 ◽  
Vol 2014 ◽  
pp. 1-8 ◽  
Author(s):  
Sukhpreet Kaur Sidhu ◽  
Amit Kumar ◽  
S. S. Appadoo
Keyword(s):  
Sensitivity Analysis ◽  
Linear Programming ◽  
Fuzzy Numbers ◽  
Optimal Solution ◽  
Fuzzy Linear Programming ◽  
New Method ◽  
Real Numbers ◽  
Trapezoidal Fuzzy Numbers ◽  
Fuzzy Optimal Solution ◽  
Linear Programming Problems

The drawbacks of the existing methods to obtain the fuzzy optimal solution of such linear programming problems, in which coefficients of the constraints are represented by real numbers and all the other parameters as well as variables are represented by symmetric trapezoidal fuzzy numbers, are pointed out, and to resolve these drawbacks, a new method (named as Mehar method) is proposed for the same linear programming problems. Also, with the help of proposed Mehar method, a new method, much easy as compared to the existing methods, is proposed to deal with the sensitivity analysis of the same type of linear programming problems.

scholarly journals Ranking Function Application for Optimal Solution of Fractional programming problem

2020 ◽  
Vol 25 (1) ◽  
Author(s):  
Rasha Jalal
Keyword(s):  
Linear Programming ◽  
Programming Problem ◽  
Fractional Programming ◽  
Linear Programming Problem ◽  
Fuzzy Numbers ◽  
Optimal Solution ◽  
Ranking Function ◽  
Linear Fractional Programming ◽  
Fractional Programming Problem ◽  
Linear Programming Problems

The aim of this paper is to suggest a solution procedure to fractional programming problem based on new ranking function (RF) with triangular fuzzy number (TFN) based on alpha cuts sets of fuzzy numbers. In the present procedure the linear fractional programming (LFP) problems is converted into linear programming problems. We concentrate on linear programming problem problems in which the coefficients of objective function are fuzzy numbers, the right- hand side are fuzzy numbers too, then solving these linear programming problems by using a new ranking function. The obtained linear programming problem can be solved using win QSB program (simplex method) which yields an optimal solution of the linear fractional programming problem. Illustrated examples and comparisons with previous approaches are included to evince the feasibility of the proposed approach.

scholarly journals A Simplified Novel Technique for Solving Linear Programming Problems with Triangular Fuzzy Variables via Interval Linear Programming Problems

2021 ◽  
pp. 82-93
Author(s):  
Ladji Kané ◽  
Lassina Diabaté ◽  
Daouda Diawara ◽  
Moussa Konaté ◽  
Souleymane Kané
Keyword(s):  
Linear Programming ◽  
Simplex Method ◽  
Real Problem ◽  
Interval Linear Programming ◽  
Numerical Examples ◽  
Fuzzy Variables ◽  
Novel Technique ◽  
Interval Linear ◽  
Linear Programming Problems

This study proposes a novel technique for solving Linear Programming Problems with triangular fuzzy variables. A modified version of the well-known simplex method and the Existing Method for Solving Interval Linear Programming problems are used for solving linear programming problems with triangular fuzzy variables. Furthermore, for illustration, some numerical examples and one real problem are used to demonstrate the correctness and usefulness of the proposed method. The proposed algorithm is flexible, easy, and reasonable.

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