A novel approach towards strongly fuzzy independent structure and its applications

Abstract

Open sets are regarded natural offshoots as they are the basic tool for structuring a topology in any environment and these are generating different generalizations whereas a few are stronger than the same and it is noteworthy that the open sets are lying in the center of the line of open like sets in any form. Fuzzy open set neither implies nor is implied by fuzzy \(\gamma ^*\)-open sets. Even more, the family of all fuzzy \(\gamma ^*\)-open sets generates a new fuzzy topology which is an independent structure that is beyond compare. In this treatise, it is claimed and established that there is a stronger form of fuzzy open set that contained in fuzzy open set as well as its associated independent fuzzy open set simultaneously for any given fuzzy topological space. Existence of strongly fuzzy independent topological space is shown in the light of fuzzy \(\delta ^*\)-open set. This study may be applicable in fuzzy bags connecting with relational database analysis.