A cubic set theory approach to UP-algebras. Issue 8 (16th November 2020) - Taboon, Korawit; Butsri, Phatchara; Iampan, Aiyared
Abstract: The concepts of cubic UP-subalgebras and cubic UP-ideals of UP-algebras were first introduced by Senapati et al. [Cubic set structure applied in UP-algebras, 2018]. In this paper, we first introduce the concepts of cubic near UP-filters, cubic UP-filters, and cubic strong UP-ideals of UP-algebras. Relationships between cubic UP-subalgebras (resp., cubic near UP-filters, cubic UP-filters, cubic UP-ideals, and cubic strong UP-ideals) and their level subsets of a cubic set in UP-algebra are discussed. Moreover, we introduce the concept of cubic sets of anti type in UP-algebras, and study the properties as well as previous concepts.