Neutrosophic Set Theory Applied to UP-Algebras

Abstract

The notions of neutrosophic UP-subalgebras, neutrosophic near UP-filters, neutrosophic UP-filters, neutrosophic UP-ideals, and neutrosophic strongly UP-ideals of UP-algebras are introduced, and several properties are investigated. Conditions for neutrosophic sets to be neutrosophic UP-subalgebras, neutrosophic near UP-filters, neutrosophic UP-filters, neutrosophic UP-ideals, and neutrosophic strongly UP-ideals of UP-algebras are provided. Relations between neutrosophic UP-subalgebras (resp., neutrosophic near UP-filters, neutrosophic UP-filters, neutrosophic UP-ideals, neutrosophic strongly UP-ideals) and their level subsets are considered.

A novel approach to neutrosophic sets in UP-algebras

“…. A NS Λ in X is called a neutrosophic UP-subalgebra of X if it satisfies the following conditions: Songsaeng and Iampan [23] proved that the notion of neutrosophic UP-subalgebras is a generalization of neutrosophic near UP-filters, neutrosophic near UP-filters is a generalization of neutrosophic UP-filters, neutrosophic UP-filters is a generalization of neutrosophic UP-ideals, and neutrosophic UP-ideals is a generalization of neutrosophic strong UP-ideals. Now, we introduce the notions of special neutrosophic UP-subalgebras, special neutrosophic near UPfilters, special neutrosophic UP-filters, special neutrosophic UP-ideals, and special neutrosophic strong UP-ideals of UP-algebras, provide the necessary examples, investigate their properties, and prove their generalizations.…”

“…Songsaeng and Iampan [23] introduced the notions of neutrosophic UP-subalgebras, neutrosophic near UP-filters, neutrosophic UP-filters, neutrosophic UP-ideals, and neutrosophic strong UP-ideals of UPalgebras in UP-algebras.…”

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

“…Jun et al 14 applied the concept of a neutrosophic N -structure to a BCK/BCI-algebra in 2017. Songsaeng and Iampan [31][32][33] applied the concept of a neutrosophic set to a UP-algebra. Ibrahim et.…”

“…Iqbal et al 11 introduced the concept of a neutrosophic cubic subalgebra and a neutrosophic cubic closed ideal of a B-algebra in 2016. Songsaeng and Iampan 30 introduced the concept of a neutrosophic cubic set in a UP-algebra in 2020. Khalid et.…”

“…In 2020, the concepts of a neutrosophic cubic UP-subalgebra, a neutrosophic cubic near UP-filter, a neutrosophic cubic UP-filter, a neutrosophic cubic UP-ideal, and a neutrosophic cubic strong UP-ideal of a UPalgebra were introduced by Songsaeng and Iampan 30 with the following definition.…”