Neutrosophic Cubic Set Theory Applied to UP-Algebras

Metawee Songsaeng, Aiyared Iampan

Abstract

Neutrosophic cubic sets which are the generalized form of fuzzy sets, cubic sets and neutrosophic sets and introduced by Jun et al. [Y.B. Jun, F. Smarandache, C.S. Kim, Neutrosophic cubic sets, New Math. Nat. Comput. 13 (1) (2017) 41--54].In this paper, we applied the concept of neutrosophic cubic sets to UP-algebras and we introduce the concepts of neutrosophic cubic UP-subalgebras, neutrosophic cubic near UP-filters, neutrosophic cubic UP-filters, neutrosophic cubic UP-ideals, and neutrosophic cubic strong UP-ideals of UP-algebras. Moreover, we discuss the relations between neutrosophic cubic UP-subalgebras (resp., neutrosophic cubic near UP-filters, neutrosophic cubic UP-filters, neutrosophic cubic UP-ideals and neutrosophic cubic strong UP-ideals) and their level subsets by means of interval-valued neutrosophic sets and neutrosophic sets.