Soft subalgebras and ideals of BCK/BCI-algebras based on $${{\mathcal {N}}}$$-structures

Hesitant Fuzzy Soft Subalgebras and Ideals in BCK/BCI-Algebras

As a link between classical soft sets and hesitant fuzzy sets, the notion of hesitant fuzzy soft sets is introduced and applied to a decision making problem in the papers by Babitha and John (2013) and Wang et al. (2014). The aim of this paper is to apply hesitant fuzzy soft set for dealing with several kinds of theories in BCK/BCI-algebras. The notions of hesitant fuzzy soft subalgebras and (c...

Soft subalgebras and soft ideals of BCK/BCI-algebras related to fuzzy set theory

The notion of ∈-soft set and q-soft set based on a fuzzy set is introduced, and characterizations for an ∈-soft set and a q-soft set to be (idealistic) soft BCK/BCIalgebras are provided. Using the notion of (∈,∈∨ q)-fuzzy BCK/BCI subalgebras/ideals, characterizations for an ∈-soft set and a q-soft set to be (idealistic) soft BCK/BCI-algebras are established. AMS subject classifications: 06D72, ...

Generalizations of N-Subalgebras in BCK/BCI-Algebras Based on Point N-Structures

The aim of this article is to obtain more general forms than the papers of Jun et al. 2010 ; Jun et al. in press . The notions of N-subalgebras of types ∈, qk , ∈,∈ ∨qk , and q,∈ ∨qk are introduced, and the concepts of qk-support and ∈ ∨qk-support are also introduced. Several related properties are investigated. Characterizations of N-subalgebra of type ∈,∈ ∨qk are discussed, and conditions for...

Subalgebras of BCK/BCI-Algebras Based on Cubic Soft Sets

Operations of cubic soft sets including "AND" operation and "OR" operation based on P-orders and R-orders are introduced and some related properties are investigated. An example is presented to show that the R-union of two internal cubic soft sets might not be internal. A sufficient condition is provided, which ensure that the R-union of two internal cubic soft sets is also internal. Moreover, ...

N-Subalgebras in BCK/BCI-Algebras Based on Point N-Structures