A Study of Fully Fuzzy Linear Fractional Programming Problems by Signed Distance Ranking Technique

2018 ◽  
pp. 73-115 ◽  
Author(s):  
Moumita Deb
Keyword(s):  
Linear Programming ◽  
Fractional Programming ◽  
Optimal Solution ◽  
Fuzzy Linear Programming ◽  
Linear Fractional Programming ◽  
Signed Distance ◽  
Decision Variables ◽  
Ranking Technique ◽  
Crisp Linear Programming ◽  
Fuzzy Linear Fractional Programming

The aim of this chapter is to study fully fuzzy linear fractional programming (FFLFP) problems where all coefficients of the decision variables and parameters are characterized by triangular fuzzy numbers. To deal with this, the authors have first to transform FFLFP problems to fuzzy linear programming (FLP) problems by using Charnes and Cooper method and then use signed distance ranking to convert fuzzy linear programming (FLP) problems to crisp linear programming (LP) problems. The proposed method is solved by using the simplex method to find the optimal solution of the problem. The authors have studied sensitivity analysis to determine changes in the optimal solution of the fully fuzzy linear fractional programming (FFLFP) problems resulting from changes in the parameters. To demonstrate the proposed method, one numerical example is solved.

scholarly journals Solution of Fully Bipolar Fuzzy Linear Programming Models

2021 ◽  
Vol 2021 ◽  
pp. 1-31
Author(s):  
Muhammad Athar Mehmood ◽  
Muhammad Akram ◽  
Majed G. Alharbi ◽  
Shahida Bashir
Keyword(s):  
Linear Programming ◽  
Programming Problem ◽  
Linear Programming Problem ◽  
Fuzzy Numbers ◽  
Optimal Solution ◽  
Equality Constraints ◽  
Fuzzy Linear Programming ◽  
Mathematical Tool ◽  
Decision Variables ◽  
Crisp Linear Programming

The Yin-Yang bipolar fuzzy set is a powerful mathematical tool for depicting fuzziness and vagueness. We first extend the concept of crisp linear programming problem in a bipolar fuzzy environment based on bipolar fuzzy numbers. We first define arithmetic operations of unrestricted bipolar fuzzy numbers and multiplication of an unrestricted trapezoidal bipolar fuzzy number (TrBFN) with non-negative TrBFN. We then propose a method for solving fully bipolar fuzzy linear programming problems (FBFLPPs) with equality constraints in which the coefficients are unrestricted triangular bipolar fuzzy numbers and decision variables are nonnegative triangular bipolar fuzzy numbers. Furthermore, we present a method for solving FBFLPPs with equality constraints in which the coefficients and decision variables are unrestricted TrBFNs. The FBFLPP is transformed into a crisp linear programming problem, and then, it is solved to achieve the exact bipolar fuzzy optimal solution. We illustrate the proposed methodologies with several numerical examples.

Decision Making Approach to Fuzzy Linear Programming (FLP) Problems with Post Optimal Analysis

2015 ◽  
Vol 6 (4) ◽  
pp. 75-90 ◽  
Author(s):  
Monalisha Pattnaik
Keyword(s):  
Linear Programming ◽  
Fuzzy Numbers ◽  
Optimal Solution ◽  
Fuzzy Linear Programming ◽  
Fuzzy Decision ◽  
Optimal Analysis ◽  
Fuzzy Environment ◽  
Multi Objective Programming ◽  
Decision Variables ◽  
Ranking Technique

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 with MATLAB (R2009a) version software, the four dimensional slice diagram is represented to the application. Finally, numerical example is presented to illustrate the effectiveness of the theoretical results, and to gain additional managerial insights.

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 Application of linear fractional programming problem with fuzzy nature in industry sector

Filomat ◽  
2020 ◽  
Vol 34 (15) ◽  
pp. 5073-5084
Author(s):  
Sapan Das ◽  
S.A. Edalatpanah ◽  
T. Mandal
Keyword(s):  
Fractional Programming ◽  
Simple Structure ◽  
Fuzzy Numbers ◽  
Real Life ◽  
Optimal Solution ◽  
Linear Fractional Programming ◽  
Fuzzy Variables ◽  
Life Problems ◽  
Fuzzy Optimal Solution ◽  
Fuzzy Linear Fractional Programming

Several methods currently exist for solving fuzzy linear fractional programming problems under non negative fuzzy variables. However, due to the limitation of these methods, they cannot be applied for solving fully fuzzy linear fractional programming (FFLFP) problems where all the variables and parameters are fuzzy numbers. So, this paper is planning to fill in this gap and in order to obtain the fuzzy optimal solution we propose a new efficient method for FFLFP problems utilized in daily life circumstances. This proposed method is based on crisp linear fractional programming and has a simple structure. To show the efficiency of our proposed method some numerical and real life problems have been illustrated.

scholarly journals Solving fully fuzzy linear programming problems by controlling the variation range of variables

2021 ◽  
Vol 103 (3) ◽  
pp. 13-24
Author(s):  
S.M. Davoodi ◽  
◽  
N.A. Abdul Rahman ◽  
Keyword(s):  
Linear Programming ◽  
Optimal Solution ◽  
Fuzzy Linear Programming ◽  
Ranking Functions ◽  
Fuzzy Variables ◽  
Decision Variables ◽  
Proposed Model ◽  
Linear Programming Problems ◽  
Left And Right ◽  
The Right

This paper deals with a fully fuzzy linear programming problem (FFLP) in which the coefficients of decision variables, the right-hand coefficients and variables are characterized by fuzzy numbers. A method of obtaining optimal fuzzy solutions is proposed by controlling the left and right sides of the fuzzy variables according to the fuzzy parameters. By using fuzzy controlled solutions, we avoid unexpected answers. Finally, two numerical examples are solved to demonstrate how the proposed model can provide a better optimal solution than that of other methods using several ranking functions.

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