Internally Stable Set in Intuitionistic Fuzzy Graph

In this paper, the idea of maximum intuitionistic internally stable vertex subset of graph with fuzzy intuitionistic stability degree is considered. The notion of an internally stable set is introduced as some invariant of an intuitionistic fuzzy graph. Here an intuitionistic fuzzy graph is considered as a pair consisting of a crisp set of vertices and an intuitionistic fuzzy set of undirected edges. The paper considers an approach for finding all maximal intuitionistic internally stable subsets of vertices, as a method extension for calculating all maximal internally stable subsets in a crisp graph. The method that allows estimating all maximal internally stable subsets in a fuzzy graph with the highest degree of stability is considered. An example illustrating the operation of the method for finding the internally stable set of the intuitionistic fuzzy graph is also represented in this article.

Automated summary

This paper discusses the concept of maximum intuitionistic internally stable vertex subset in a graph with fuzzy intuitionistic stability degree. The notion of an internally stable set is introduced as an invariant of an intuitionistic fuzzy graph. The paper proposes an approach for finding all maximal intuitionistic internally stable subsets of vertices, as an extension of the method for calculating all maximal internally stable subsets in a crisp graph. The method that allows estimating all maximal internally stable subsets in a fuzzy graph with the highest degree of stability is considered. An example illustrating the operation of the method for finding the internally stable set of the intuitionistic fuzzy graph is also presented in this article.