Methods for Solving $LR$-Type Pythagorean Fuzzy Linear Programming Problems with Mixed Constraints

Abstract

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.

Image Processing Based on Fuzzy Mathematics Theory

“…Image segmentation is an important pre-processing step of pattern recognition, machine vision, image understanding, and analysis. After decades of research, it still receives wide attention from many scholars [2]. ere are currently many methods for image segmentation, which can be broadly divided into four types: threshold-based segmentation methods, edge detection-based segmentation methods, region-based segmentation methods, and theory-based segmentation methods.…”

Extended Transportation Models Based on Picture Fuzzy Sets

“…Pérez-Cañedo et al [12] used lexicographical method and solved fully FLP problems having inequality constraints. Akram et al [13] proposed Pythagorean FLP problems with equality constraints. Akram et al [13] introduced LR-type Pythagorean fuzzy numbers and introduced a scheme to solve LR-type fully Pythagorean FLP problems with equality constraints.…”

“…Akram et al [13] proposed Pythagorean FLP problems with equality constraints. Akram et al [13] introduced LR-type Pythagorean fuzzy numbers and introduced a scheme to solve LR-type fully Pythagorean FLP problems with equality constraints. Mehmood et al [14,15] developed di erent techniques to nd optimal solutions of fully bipolar FLP problems.…”

A New Idea to Evaluate Networking Problem and MCGDM Problem in Parametric Interval Valued Pythagorean Arena

“…Apart from this literature survey, the concept of the Pythagorean set has also been fruitfully applied in several domains like operation research, graph theory, matrix evolution, etc. Luqman et al [43] incorporated the Pythagorean concept in risk management problems using Digraph and matrix concept; Akram et al [44] proposed LP model in the Pythagorean arena with equality constraints; Akram et al [44,45] manifested L-R type Pythagorean LP approaches with mixed and equality constraints; Enayattabar et al [46] introduced the concept of shortest path problem in IVPN environment; Di Caprio et al [47] focused on ant colony algorithm based on Pythagorean arena; Ebrahimnejad et al [48] developed advanced bee colony algorithm in IVPN domain; Akram et al [49] incorporated the concept of a planar graph in the Pythagorean environment which plays an essential role in graph theory problem.…”