Document Type : Research Articles

Authors

• Narupon Tacha ¹
• Phongsakon Phayapsiang ¹
• Aiyared Iampan ²

¹ Department of Mathematics, School of Science, University of Phayao, Phayao 56000, Thailand

² Department of Mathematics, School of Science, University of Phayao, Thailand

Abstract

The aim of this paper is to introduce the notions of the length and the mean of a hyper structure in UP-algebras.
The notions of length fuzzy UP-subalgebras and mean fuzzy UP-subalgebras of UP-algebras are introduced, and related properties are investigated. Characterizations of length fuzzy UP-subalgebras and mean fuzzy UP-subalgebras are discussed.
Relations between length fuzzy UP-subalgebras (resp., mean fuzzy UP-subalgebras) and hyperfuzzy UP-subalgebras are established. Moreover, we discuss the relationships among length fuzzy UP-subalgebras (resp., mean fuzzy UP-subalgebras) and upper level subsets, lower level subsets, and equal level subsets of the length (resp., mean) of a fuzzy structure in UP-algebras.

Keywords

• UP-algebra
• length fuzzy UP-subalgebra
• mean fuzzy UP-subalgebra
• hyperfuzzy UP-subalgebra