From finitely many independent fuzzy sets to possibility-based fuzzy linear programming problems

2007 ◽  
Vol 10 (6) ◽  
pp. 757-766 ◽  
Author(s):  
Kakuzo Iwamura ◽  
Masayuki Kageyama
Keyword(s):  
Linear Programming ◽  
Fuzzy Sets ◽  
Fuzzy Linear Programming ◽  
Linear Programming Problems

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.

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