scholarly journals A New Approach for Solving Fully Fuzzy Linear Programming by Using the Lexicography Method

2016 ◽  
Vol 2016 ◽  
pp. 1-6 ◽  
Author(s):  
A. Hosseinzadeh ◽  
S. A. Edalatpanah
Keyword(s):  
Linear Programming ◽  
Fuzzy Numbers ◽  
Point Of View ◽  
Fuzzy Linear Programming ◽  
New Approach ◽  
New Model ◽  
New Methods ◽  
Remarkable Agreement ◽  
Crisp Linear Programming

The fully fuzzy linear programming (FFLP) problem has many different applications in sciences and engineering, and various methods have been proposed for solving this problem. Recently, some scholars presented two new methods to solve FFLP. In this paper, by considering theL-Rfuzzy numbers and the lexicography method in conjunction with crisp linear programming, we design a new model for solving FFLP. The proposed scheme presented promising results from the aspects of performance and computing efficiency. Moreover, comparison between the new model and two mentioned methods for the studied problem shows a remarkable agreement and reveals that the new model is more reliable in the point of view of optimality.

BOUNDED LINEAR PROGRAMS WITH TRAPEZOIDAL FUZZY NUMBERS

2010 ◽  
Vol 18 (03) ◽  
pp. 269-286 ◽  
Author(s):  
ALI EBRAHIMNEJAD ◽  
SEYED HADI NASSERI ◽  
FARHAD HOSSEINZADEH LOTFI
Keyword(s):  
Linear Programming ◽  
Fuzzy Numbers ◽  
Natural Extension ◽  
Upper Bounds ◽  
Linear Programs ◽  
Bounded Linear ◽  
New Approach ◽  
Trapezoidal Fuzzy Numbers ◽  
Linear Programming Problems ◽  
Crisp Linear Programming

Recently Ganesan and Veeramani introduced a new approach for solving a kind of linear programming problems involving symmetric trapezoidal fuzzy numbers without converting them to the crisp linear programming problems. But their approach is not efficient for situations in which some or all variables are restricted to lie within fuzzy lower and fuzzy upper bounds. In this paper, by a natural extension of their approach we obtain some new results leading to a new method to overcome this shortcoming.

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.

scholarly journals Optimization of LR -Type Fully Bipolar Fuzzy Linear Programming Problems

2021 ◽  
Vol 2021 ◽  
pp. 1-36
Author(s):  
Muhammad Athar Mehmood ◽  
Muhammad Akram ◽  
Majed G. Alharbi ◽  
Shahida Bashir
Keyword(s):  
Linear Programming ◽  
Programming Problem ◽  
Linear Programming Problem ◽  
Fuzzy Numbers ◽  
Equality Constraints ◽  
Fuzzy Linear Programming ◽  
Numerical Examples ◽  
Linear Programming Problems ◽  
Formula Type ◽  
Crisp Linear Programming

In this study, we present a technique to solve LR -type fully bipolar fuzzy linear programming problems (FBFLPPs) with equality constraints. We define LR -type bipolar fuzzy numbers and their arithmetic operations. We discuss multiplication of LR -type bipolar fuzzy numbers. Furthermore, we develop a method to solve LR -type FBFLPPs with equality constraints involving LR -type bipolar fuzzy numbers as parameters and variables. Moreover, we define ranking for LR -type bipolar fuzzy numbers which transform the LR -type FBFLPP into a crisp linear programming problem. Finally, we consider numerical examples to illustrate the proposed method.

A Fast Approach to Solve Matrix Games with Payoffs of Trapezoidal Fuzzy Numbers

2016 ◽  
Vol 33 (06) ◽  
pp. 1650047 ◽  
Author(s):  
Sanjiv Kumar ◽  
Ritika Chopra ◽  
Ratnesh R. Saxena
Keyword(s):  
Linear Programming ◽  
Linear Programming Problem ◽  
Fuzzy Numbers ◽  
Optimization Problems ◽  
Fuzzy Linear Programming ◽  
Matrix Game ◽  
Matrix Games ◽  
Trapezoidal Fuzzy Numbers ◽  
Fast Approach ◽  
The Matrix

The aim of this paper is to develop an effective method for solving matrix game with payoffs of trapezoidal fuzzy numbers (TrFNs). The method always assures that players’ gain-floor and loss-ceiling have a common TrFN-type fuzzy value and hereby any matrix game with payoffs of TrFNs has a TrFN-type fuzzy value. The matrix game is first converted to a fuzzy linear programming problem, which is converted to three different optimization problems, which are then solved to get the optimum value of the game. The proposed method has an edge over other method as this focuses only on matrix games with payoff element as symmetric trapezoidal fuzzy number, which might not always be the case. A numerical example is given to illustrate the method.

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.

Sign in / Sign up

Export Citation Format

Share Document