A uniform interval-valued intuitionistic fuzzy environment: topological descriptors and their application in neural networks

Abstract

The concept of being uniform strong interval-valued intuitionistic fuzzy (also termed as USIVIF) is an integration of two ideologies, which are called "uniformity" and "strong interval-valued intuitionistic fuzzy sets". Inspired by the study on uniform fuzzy topological indices, it is natural to introduce uniform IVIFTIs. Originally, topological indices were generalized for the fuzzy sets However, the utilization of the interval-valued intuitionistic fuzzy topological indices provides a finer approach, especially if there are multiple uncertainties based on intervals. Consequently, both theories imply that topological indices are not fixed and depend on certain situations or problems in the question. In this article, the generalized results for the uniform degree of the fuzzy sets associated with individual vertices/edges of strong interval-valued intuitionistic fuzzy graphs were presented and results for the total uniform degree of such graphs were also included. In addition, the nature of the implemented methods and models was discussed based on the cellular neural interval-valued intuitionistic fuzzy graphs of sets of membership and non-membership values.

Keywords

• strong interval-valued intuitionistic fuzzy graph
• uniform interval-valued intuitionistic fuzzy environment
• cellular neural interval-valued intuitionistic fuzzy network
• zagreb index
• general randić index
• harmonic index