Graph of Pythagorean neutrosophic fuzzy ideal of M Gamma groups in near rings

Abstract

Fuzzy sets have shown themselves to be a dependable subject of study in numerous domains. They are an excellent option for the simplification and extension of classical sets due to their simplicity and flexibility. This study aims to draw a connection between the ideal algebraic structure of a near ring in M$\Gamma$ group and neutrosophic fuzzy (NF) theory, graph theory, and neutrosophic fuzzy graph theory. The concept of a neutrosophic fuzzy (NF) ideal's graph, its regular graph, and their isomorphism in the M$\Gamma$ group of near rings are examined. Additionally, a couple of their qualities are examined here as theorems. To indicate membership, non-membership, and indeterminacy in any information, the neutrosophic set is thrown off. Additionally, some of their characteristics are listed here as theorems. A generalization of the Pythagorean fuzzy set with condition \(0 \leq {\alpha_A}(a)^2 + {\beta_A}(a)^2 + {\gamma_A}(a)^2 \leq 2\) and neutrosophic set with dependent neutrosophic components is the Pythagorean neutrosophic set (PNS). Therefore, we provide a few examples and enhance some of the fundamental features for this Pythagorean Neutrosophic Fuzzy Graph (PNFG).