Networking model based on fuzzy graphs of almost primary fuzzy ideals of near-rings

Abstract

Sometimes traditional mathematical methods do not work properly to find the solutions of the problems with uncertainties in different field of sciences. The reason is that there are lot of complexities and ambiguities which occur in real-world problems. Researchers from all across the world have created new theories such as fuzzy set theory, rough set theory, etc., to overcome such circumstances. Over the past few decades numerous fuzzy algebraic structures and substructures have been studied, like fuzzy rings, fuzzy near-rings, fuzzy ideals of near-rings, and so on. In this study, we present the notion of almost primary fuzzy ideals (almost primary f-ideals) of near-rings and provide their application through the fuzzy graphs associated with them. Firstly, we provide numerous characterizations of almost primary f-ideals in near-rings. We observe that every almost primary f-ideal is not a primary fuzzy ideal (PFI) in near-rings, and show when a primary fuzzy ideal is an almost primary f-ideals in near-rings. Some interrelationships between a classical almost primary ideal (API) and almost primary f-ideals of near-rings are also established. Finally, we introduce the fuzzy graph structure related to APFIs of near-rings and present a model of general networks.