The Prominentness of Fuzzy GE-Filters in GE-Algebras

Abstract

Based on the concept of fuzzy points, the notion of a prominent fuzzy GE-filter is defined, and the various properties involved are investigated. The relationship between a fuzzy GE-filter and a prominent fuzzy GE-filter is discussed, and the characterization of a prominent fuzzy GE-filter is considered. The conditions under which a fuzzy GE-filter can be a prominent fuzzy GE-filter are explored, and conditions for the trivial fuzzy GE-filter to be a prominent fuzzy GE-filter are provided. The conditions under which the ∈t-set and Qt-set can be prominent GE-filters are explored. Finally, the extension property for the prominent fuzzy GE-filter is discussed.