An Innovative Unique Factorization Approach of Fuzzy Fractional Ideals in Dedekind Domains

A solid mathematical technique for handling uncertainty is offered by the Zadeh-conceived notion of fuzzy sets, provides a convenient point of departure for the construction of a conceptual framework. In this paper, we explore the advantages of applying techniques from fuzzy set theory, paving the way for innovative approaches in the study of fuzzy multiplicative ideal theory. This study investigates that every nonzero fuzzy fractional ideal in a Dedekind domain has a unique factorization into fuzzy prime ideals. We demonstrate a few intermediate findings about the localization of a noetherian domain at its fuzzy fractional ideals. Introducing the new concepts and provide some examples via discrete valuation ring illustrates that a discrete valuation ring is the localization of a noetherian domain at its fuzzy fractional ideals.