𝒩‐Structures Applied to Closed Ideals in BCH‐Algebras

Abstract

The notions of𝒩-subalgebras and𝒩-closed ideals in BCH-algebras are introduced, and the relation between𝒩-subalgebras and𝒩-closed ideals is considered. Characterizations of𝒩-subalgebras and𝒩-closed ideals are provided. Using special subsets,𝒩-subalgebras and𝒩-closed ideals are constructed. A condition for an𝒩-subalgebra to be an𝒩-closed ideal is discussed. Given an𝒩-structure, the greatest𝒩-closed ideal which is contained in the𝒩-structure is established.

N-SUBALGEBRAS OF TYPE (∈, ∈ ∨ q) BASED ON POINT N-STRUCTURES IN BCK/BCI-ALGEBRAS

“…Using the similar method to the transfer principle in fuzzy theory (see [3,7]), Jun et al [6] considered transfer principle in N -structures as follows.…”

“…Theorem 2.2 (N -transfer principle, See [6]). An N -structure (X, f ) satisfies the property P if and only if for all α ∈ [−1, 0],…”

“…They applied N -structures to BCK/BCI-algebras, and discussed N -subalgebras and N -ideals in BCK/BCI-algebras. Jun et al [6] considered closed ideals in BCH-algebras based on N -structures. Also, using N -structures, Jun and Lee introduced the notion of an N -essence in a subtraction algebra, and investigated related properties.…”

N-Hyper Sets

“…To attain such object, Jun et al [2] introduced a new function, which is called negative-valued function, and constructed N -structures. Since then, N -structures are applied to rings (see [3]), BCH-algebras (see [4]), (ordered) semigroups (see [5][6][7][8]). The combination of soft sets and N -structures is dealt with in [9,10] and [11].…”

The Combination of Soft Sets and -Structures with Applications

“…They applied N-structures to BCK/BCI-algebras, and discussed N-subalgebras and N-ideals in BCK/BCIalgebras. Jun et al [12] considered closed ideals in BCHalgebras based on N-structures.…”