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.

scholarly journals Methods for Solving L R -Type Pythagorean Fuzzy Linear Programming Problems with Mixed Constraints

2021 ◽  
Vol 2021 ◽  
pp. 1-29
Author(s):  
Muhammad Akram ◽  
Inayat Ullah ◽  
Majed G. Alharbi
Keyword(s):  
Linear Programming ◽  
Fuzzy Sets ◽  
Fuzzy Linear Programming ◽  
Pythagorean Fuzzy Set ◽  
New Techniques ◽  
Mixed Constraints ◽  
Linear Programming Problems ◽  
Practical Model ◽  
Pythagorean Fuzzy Numbers ◽  
Formula Type

A Pythagorean fuzzy set is the superset of fuzzy and intuitionistic fuzzy sets, respectively. Yager proposed the concept of Pythagorean fuzzy sets in which he relaxed the condition that sum of square of both membership degree and nonmembership degree of an element of a set must not be greater than 1. This paper introduces two new techniques to solve L R -type fully Pythagorean fuzzy linear programming problems with mixed constraints having unrestricted L R -type Pythagorean fuzzy numbers as variables and parameters by introducing unknown variables and using a ranking function. Furthermore, we show the equivalence of both the proposed methods and compare the solutions obtained by the two techniques. Besides this, we solve an already existing practical model using proposed techniques and compare the result.

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.

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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