Topological numbers in uniform intuitionistic fuzzy environment and their application in neural network

Abstract

Intuitionistic Fuzzy sets combine the ideas of uniformity, membership, and non-membership grades of the elements. Similarly, Intuitionistic Fuzzy Graphs are the generalization of simple fuzzy graphs. Depending on the uniformity of the fuzzy graphs (USIF) they can be categorized in different ways via membership values. From the idea of uniform fuzzy topological indices, we have developed the concepts of uniform intuitionistic fuzzy topological indices for uniform intuitionistic fuzzy graphs. This idea provides a more adaptable and nuanced representation of structural properties in graphs or networks. According to the theory of fuzzy topological indices, the importance of topological indices changes depending on the circumstance and the specific problem at hand. When the interactions between nodes are uncertain but not always hesitant, fuzzy graph theory and its adjusted topological indices are sufficient to capture and assess the underlying structure. In such cases where uncertainty is more complicated and hesitation is a major problem then there are better ways to address by intuitionistic fuzzy graph theory and the topological indices that go along with it. This article, developed the concept of uniform intuitionistic fuzzy graphs afresh and proposed Intuitionistic Fuzzy Topological Indices. We determine these indices using the topological indices and labeling of crisp graphs, rather than relying on the degrees of intuitionistic fuzzy graphs and edge portions. This approach is then applied to find intuitionistic fuzzy topological indices. Also, we have provided the MATLAB algorithm to illustrate the concept of IF labeling of cellular neural networks of any order. An example is given to explain the idea and approach towards one kind of uniform intuitionistic fuzzy graph represented by Cellular Neural Networks and graphical plots of the indices involved are also made.