The aim of this paper is to apply the concept of interval-valued intuitionistic fuzzy set to implicative ideals and commutative ideals in BCK-algebras and introduced the new notion of interval-valued intuitionistic fuzzy implicative ideals in BCK-algebras and interval-valued intuitionistic fuzzy commutative ideals in BCK-algebras and related properties are investigated.

In this paper, we introduce a new of BH-algebra and pseudo BH-algebra. We call covid-19 Also, give the concepts ( BH-algebra, ). And study some relationships between them.

Copyright q 2010 Young Bae Jun et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. Based on the theory of falling shadows and fuzzy sets, the notion of a falling fuzzy implicative ideal of a BCK-algebra is introduced. Relations...

In 1982, Pawlak introduced the concept of a rough set (see [6]). This concept is fundamental for the examination of granularity in knowledge. It is a concept which has many applications in data analysis (see [7]). Rough set theory is applied to semigroups and groups (see [4, 5]), and BCK-algebras (see [3]). In this paper, we apply the rough set theory to BCC-algebras, and we discuss the notion ...

Given Φ,Ψ ∈ {∈, q,∈ ∨ q}, the notion of (Φ, Ψ)neutrosophic subalgebras of a BCK/BCI-algebra are introduced, and related properties are investigated. Characterizations of an (∈,∈)neutrosophic subalgebra and an (∈,∈∨ q)-neutrosophic subalgebra are provided. Given special sets, so called neutrosophic ∈-subsets, neutrosophic q-subsets and neutrosophic ∈∨ q-subsets, conditions for the neutrosophic ∈...

In this paper, we investigate the ideal theory in BCK-algebras and we define the notions of primary and P -primary ideals. Then we show that in bounded implicative BCK-algebras, if an ideal has a primary decomposition, then it has a reduced primary decomposition. In the follow, we extend the above concepts to X-modules (Extended BCK-modules) and we introduce the notions of primary and P -primar...

Molodtsov [5] introduced the concept of soft set as a new mathematical tool for dealing with uncertainties that is free from the difficulties that have troubled the usual theoretical approaches. In this paper we apply the notion of soft sets by Molodtsov to an implicative ideal of BCK-algebras. The notion of implicative soft ideals in BCKalgebras and implicative idealistic soft BCK-algebras is ...

The intuitionistic fuzzification of (strong, weak, s-weak) hyperBCK-ideals is introduced, and related properties are investigated. Characterizationsof an intuitionistic fuzzy hyper BCK-ideal are established. Using acollection of hyper BCK-ideals with some conditions, an intuitionistic fuzzyhyper BCK-ideal is built.

In this paper, by considering the notion of ∧-closed set in BCK-algebras, we construct the fractions of BCK-algebras and we get some related results.