Fuzzy Sets in UP-algebras with Respect to A Triangular Norm

Authors : Pakpimon BURANDATE, Sawittree THONGARSA, Aiyared IAMPAN

Pages : 410-432

View : 18 | Download : 14

Publication Date : 2019-10-15

Article Type : Research Paper

Abstract :In this paper, we apply the notion of fuzzy sets with respect to a triangular norm to UP-algebras. We introduce the notions of $T$-fuzzy UP-subalgebras, $T$-fuzzy near UP-filters, $T$-fuzzy UP-filters, $T$-fuzzy UP-ideals, and $T$-fuzzy strongly UP-ideals, their properties are investigated and some useful examples are discussed. We discuss the relations between $T$-fuzzy UP-subalgebras insert ignore into journalissuearticles values(resp., $T$-fuzzy near UP-filters, $T$-fuzzy UP-filters, $T$-fuzzy UP-ideals, and $T$-fuzzy strongly UP-ideals); and a notion of UP-subalgebras insert ignore into journalissuearticles values(resp., near UP-filters, UP-filters, UP-ideals, strongly UP-ideals);, and their level subsets and UP-homomorphisms are studied. Moreover, we have introduced the notion of fuzzy sets with respect to a triangular norm of anti-type in UP-algebras, and studied the properties as well as previous notions.
Keywords : UP algebra, T fuzzy UP subalgebra, T fuzzy near UP filter, T fuzzy UP filter, T fuzzy UP ideal, T fuzzy strongly UP ideal