Image and Inverse Image of Neutrosophic Cubic Sets in UP-Algebras under UP-Homomorphisms

Abstract

The concept of a neutrosophic cubic set in a UP-algebra was introduced by Songsaeng and Iampan [Neu-trosophic cubic set theory applied to UP-algebras, 2019]. In this paper, we define the image and inverse image of a neutrosophic cubic set in a non-empty set under any function and study the image and inverse image of a neutrosophic cubic UP-subalgebra (resp., neutrosophic cubic near UP-filter, neutrosophic cubic UP-filter, neutrosophic cubic UP-ideal, neutrosophic cubic strong UP-ideal) of a UP-algebra under some UP-homomorphisms.

Bipolar Fuzzy Shift UP-Filters

“…For simplicity, we denote the NS {(t, α(t), β(t), γ(t)) | t ∈ G} by α, β, γ . Songsaeng et al [19,20] applied neutrosophic set theory to UP-algebras, introduced many concepts of neutrosophic UPsubstructures, and investigated their properties. A neutrosophic shift of the UP-filter of a UP-algebra is an interesting and important concept of neutrosophic UP-substructures and is defined as follows:…”