Sun Shin Ahn

Fuzzy subinclines (ideals) of incline algebras

The fuzzification of subinclines (ideals) in inclines are considered, and some related properties are investigated. We also state the product of fuzzy subinclines (ideals), and the projections of fuzzy subinclines (ideals). We discuss fuzzy relations, fuzzy characteristic subinclines (ideals).

Double-Framed Soft Sets with Applications in BCK/BCI-Algebras

In order to lay a foundation for providing a soft algebraic tool in considering many problems that contain uncertainties, the notion of double-framed soft sets is introduced, and applications in BCK/BCI-algebras are discussed. The notions of double-framed soft algebras in BCK/BCI-algebras are introduced, and related properties are investigated. Characterizations of double-framed soft algebras are considered. Product and int-uni structure of double-framed soft algebras are discussed, and several examples are provided.

Quotient structures of some implicative algebras via fuzzy implicative filters

In this paper we discuss quotient implicative algebras induced by fuzzy implicative filters, and establish the fuzzy fundamental homomorphism theorem for some implicative algebras.

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 (closed) hesitant fuzzy soft ideals are introduced, and related properties are investigated. Relations between a hesitant fuzzy soft subalgebra and a (closed) hesitant fuzzy soft ideal are discussed. Conditions for a hesitant fuzzy soft set to be a hesitant fuzzy soft subalgebra are given, and conditions for a hesitant fuzzy soft subalgebra to be a hesitant fuzzy soft ideal are provided. Characterizations of a (closed) hesitant fuzzy soft ideal are considered.

Intersection-Soft Filters in -Algebras

The notions of (strong) intersection-soft filters in -algebras are introduced, and related properties are investigated. Characterizations of a (strong) intersection-soft filter are established, and a new intersection-soft filter from old one is constructed. A condition for an intersection-soft filter to be strong is given, and an extension property of a strong intersection-soft filter is established.

Applications of Soft Sets in BE-Algebras

The notion of intersectional soft subalgebras of a BE-algebra is introduced, and related properties are investigated. Characterization of an intersectional soft subalgebra is discussed. The problem of classifying intersectional soft subalgebras by their inclusive subalgebras will be solved.

Falling -Ideals in -Algebras

Based on the theory of a falling shadow which was first formulated by Wang (1985), a theoretical approach of the ideal structure in 𝑑-algebras is established. The notions of a falling 𝑑-subalgebra, a falling 𝑑-ideal, a falling 𝐵𝐶𝐾-ideal, and a falling 𝑑♯-ideal of a 𝑑-algebra are introduced. Some fundamental properties are investigated. Relations among a falling 𝑑-subalgebra, a falling 𝑑-ideal, a falling 𝐵𝐶𝐾-ideal, and a falling 𝑑♯-ideal are stated. Characterizations of falling 𝑑-ideals and falling 𝑑♯-ideals are discussed. A relation between a fuzzy 𝑑-subalgebra and a falling 𝑑-subalgebra is provided.

Structures of Pseudo Ideal and Pseudo Atom in a Pseudo Q-Algebra

As a generalization of Q-algebra, the notion of pseudo Q-algebra is introduced, and some of their properties are investigated. The notions of pseudo subalgebra, pseudo ideal, and pseudo atom in a pseudo Q-algebra are introduced. Characterizations of their properties are provided.

Classes of Int-Soft Filters in Residuated Lattices

The notions of int-soft filters, int-soft G-filters, regular int-soft filters, and MV-int-soft filters in residuated lattices are introduced, and their relations, properties, and characterizations are investigated. Conditions for an int-soft filter to be an int-soft G-filter, a regular int-soft filter, or an MV-int-soft filter are provided. The extension property for an int-soft G-filter is discussed. Finally, it is shown that the notion of an MV-int-soft filter coincides with the notion of a regular int-soft filter in BL-algebras.

The Theory of Falling Shadows Applied to -Ideals in -Algebras

On the basis of the theory of a falling shadow which was first formulated by Wang (1985), the notion of falling 𝑑∗-ideals in 𝑑-algebras is introduced, and related properties are investigated. Characterizations of a falling 𝑑∗-ideal are established. Relations among falling 𝑑∗-ideals, falling 𝑑-ideals, falling 𝑑#-ideals, falling 𝑑-subalgebras, and falling BCK-ideals are discussed.