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In this paper, the notions of ideals in NBCK-algebras are presented and some properties of such ideals are analyzed. Essentially, our approach is to define NBCK-algebras of all cosets by considering an operation on the set of all cosets defined via ideals. Afterwards, our aim is to study ideal theorems on NBCK-algebras. [ABSTRACT FROM AUTHOR]

Using the notion of bipolar-valued fuzzy soft set, the concepts of bipolar-valued fuzzy soft (weak, s -weak, strong) hyper BCK ideal are introduced, and related properties and relations are investigated. Characterizations of bipolar-valued fuzzy soft (weak) hyper BCK ideal are considered. Conditions for a bipolar-valued fuzzy soft weak hyper BCK ideal to be a bipolar-valued fuzzy soft s -weak hyper BCK ideal are provided. Conditions for a bipolar-valued fuzzy soft set to be a bipolar-valued fuzzy soft strong hyper BCK ideal are displayed. [ABSTRACT FROM AUTHOR]

In the present paper, we introduce the concept of neutrosophic implicative 𝒩 -ideal in B C K -algebras, and investigate several properties. Also, we provide characterizations of the neutrosophic implicative 𝒩 -ideal. Furthermore, we discuss relations between neutrosophic positive implicative 𝒩 -ideal, neutrosophic commutative 𝒩 -ideal and neutrosophic implicative 𝒩 -ideal. Finally, we characterize implicative B C K -algebra by using neutrosophic implicative 𝒩 -ideal. [ABSTRACT FROM AUTHOR]

The concept and properties of cubic sets were first introduced and investigated by Jun et al. in 2011. In this paper, we first introduce the concept of cubic sets in UP-subalgebras and consider the UP-ideals of a UP-algebra. Relationships between the cubic UP-subalgebras and the cubic UP-ideals of a UP-algebra are investigated. In addition, the homomorphic images and the inverse images of the cubic UP-subalgebras and the cubic UP-ideals are also studied. Related properties of UP -algebras and their UP-ideals are explored and discussed. Finally, the Cartesian product of cubic UP-algebras are investigated. [ABSTRACT FROM AUTHOR]