Unique Fuzzy Optimal Value of Fully Fuzzy Linear Programming Problems with Equality Constraints Having LR Flat Fuzzy Numbers

2016 ◽  
pp. 109-118
Author(s):  
Jagdeep Kaur ◽  
Amit Kumar
Keyword(s):  
Linear Programming ◽  
Fuzzy Numbers ◽  
Equality Constraints ◽  
Fuzzy Linear Programming ◽  
Optimal Value ◽  
Linear Programming Problems

scholarly journals Solving a Fully Fuzzy Linear Programming Problem through Compromise Programming

2013 ◽  
Vol 2013 ◽  
pp. 1-10 ◽  
Author(s):  
Haifang Cheng ◽  
Weilai Huang ◽  
Jianhu Cai
Keyword(s):  
Linear Programming ◽  
Programming Problem ◽  
Linear Programming Problem ◽  
Fuzzy Numbers ◽  
Equality Constraints ◽  
Compromise Programming ◽  
Fuzzy Linear Programming ◽  
Programming Approach ◽  
Optimal Value ◽  
Fuzzy Equality

In the current literatures, there are several models of fully fuzzy linear programming (FFLP) problems where all the parameters and variables were fuzzy numbers but the constraints were crisp equality or inequality. In this paper, an FFLP problem with fuzzy equality constraints is discussed, and a method for solving this FFLP problem is also proposed. We first transform the fuzzy equality constraints into the crisp inequality ones using the measure of the similarity, which is interpreted as the feasibility degree of constrains, and then transform the fuzzy objective into two crisp objectives by considering expected value and uncertainty of fuzzy objective. Since the feasibility degree of constrains is in conflict with the optimal value of objective function, we finally construct an auxiliary three-objective linear programming problem, which is solved through a compromise programming approach, to solve the initial FFLP problem. To illustrate the proposed method, two numerical examples are solved.

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.

LR-type fully pythagorean fuzzy linear programming problems with equality constraints

2021 ◽  
pp. 1-18
Author(s):  
Muhammad Akram ◽  
Inayat Ullah ◽  
Tofigh Allahviranloo ◽  
S.A. Edalatpanah
Keyword(s):  
Linear Programming ◽  
Fuzzy Numbers ◽  
Fuzzy Model ◽  
Equality Constraints ◽  
Fuzzy Linear Programming ◽  
Pythagorean Fuzzy Set ◽  
Research Article ◽  
Linear Programming Problems ◽  
Diet Problem ◽  
Pythagorean Fuzzy Numbers

A Pythagorean fuzzy set is a powerful model for depicting fuzziness and uncertainty. This model is more flexible and practical as compared to an intuitionistic fuzzy model. This research article presents a new model called LR-type fully Pythagorean fuzzy linear programming problem. We consider the notions of LR-type Pythagorean fuzzy number, ranking for LR-type Pythagorean fuzzy numbers and arithmetic operations for unrestricted LR-type Pythagorean fuzzy numbers. We propose a method to solve LR-type fully Pythagorean fuzzy linear programming problems with equality constraints. We describe our proposed method with numerical examples including diet problem.

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.

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