Chul Hwan Park

Soft set theory applied to ideals in d-algebras

The notions of (transitive) soft d-algebras, soft edge d-algebras, soft d^*-algebras, soft d-ideals, soft d^@?-ideals, soft d^*-ideals, and d-idealistic (d^@?-idealistic, or d^*-idealistic) soft d-algebras are introduced. Also, their related properties are surveyed.

Fuzzy soft set theory applied to BCK/BCI-algebras

Abstract In the paper [P.K. Maji, R. Biswas, A.R. Roy, Fuzzy soft sets, J. Fuzzy Math. 9 (3) (2001) 589–602], Maji et al. introduced the concept of fuzzy soft sets as a generalization of the standard soft sets, and presented an application of fuzzy soft sets in a decision making problem. The aim of this manuscript is to apply fuzzy soft set for dealing with several kinds of theories in BCK/BCI-algebras. The notions of fuzzy soft BCK/BCI-algebras, (closed) fuzzy soft ideals and fuzzy soft p -ideals are introduced, and related properties are investigated.

Intuitionistic nil radicals of intuitionistic fuzzy ideals and Euclidean intuitionistic fuzzy ideals in rings

The notion of intuitionistic nil radicals of intuitionistic fuzzy ideals in rings is introduced, and related properties are investigated. The notion of semiprime intuitionistic fuzzy ideals is provided, and its characterization is established. The concept of Euclidean intuitionistic fuzzy ideals is also introduced, and its characterization is established.

Coderivations of Ranked Bigroupoids

The notion of (co)derivations of ranked bigroupoids is discussed by Alshehri et al. (in press), and their generalized version is studied by Jun et al. (under review press). In particular, Jun et al. (under review press) studied coderivations of ranked bigroupoids. In this paper, the generalization of coderivations of ranked bigroupoids is discussed. The notion of generalized coderivations in ranked bigroupoids is introduced, and new generalized coderivations of ranked bigroupoids are obtained by combining a generalized self-coderivation with a rankomorphism. From the notion of (𝑋,∗,a)-derivation, the existence of a rankomorphism of ranked bigroupoids is established.

FALLING SHADOWS APPLIED TO SUBALGEBRAS AND IDEALS OF BCK/BCI-ALGEBRAS

Abstract. falling subalgebra/ideal of a BCK/BCI-algebra is intro-duced. Relations between falling subalgebras and falling ideals aregiven. Relations between fuzzy subalgebras/ideals and falling sub-algebras/ideals are provided. A characterization of a falling ideal isestablished. 1. Introduction and Preliminaries1.1. IntroductionIn the study of a uni ed treatment of uncertainty modelled by meansof combining probability and fuzzy set theory, Goodman [2] pointed outthe equivalence of a fuzzy set and a class of random sets. Wang andSanchez [8] introduced the theory of falling shadows which directly re-lates probability concepts with the membership function of fuzzy sets.The mathematical structure of the theory of falling shadows is formu-lated in [7]. Tan et al. [5, 6] established a theoretical approach to de nea fuzzy inference relation and fuzzy set operations based on the theory offalling shadows. Yuan and Lee [9] considered a fuzzy subgroup (subring,ideal) as the falling shadow of the cloud of the subgroup (subring, ideal).In this article, we introduce the notion of falling subalgebras/ideals inBCK/BCI-algebras based on the theory of falling shadows. We give rela-tions between falling subalgebras and falling ideals. We also provide re-lations between fuzzy subalgebras/ideals and falling subalgebras/ideals.We establish a characterization of a falling ideal. We show that everyfalling subalgebra/ideal is a T

Implicative Ideals of BCK-Algebras Based on the Fuzzy Sets and the Theory of Falling Shadows

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 among falling fuzzy ideals, falling fuzzy implicative ideals, falling fuzzy positive implicative ideals, and falling fuzzy commutative ideals are given. Relations between fuzzy implicative ideals and falling fuzzy implicative ideals are provided.

IMPLICATIVE SOFT IDEALS AND IMPLICATIVE IDEALISTIC SOFT BCK-ALGEBRAS

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 BCK- algebras and implicative idealistic soft BCK-algebras is introduced, and related properties are investigated. Relations between implicative soft ideals and commutative (resp. positive implicative) soft ideals are dis- cussed. Also, relations between implicative idealistic soft BCK-algebras and commutative (resp. positive implicative) idealistic soft BCK-algebras are provided.

Hypervector Spaces Based on Intersectional Soft Sets

The notion of int-soft subfields, int-soft algebras over int-soft subfields, and int-soft hypervector spaces are introduced, and their properties and characterizations are considered. In connection with linear transformations, int-soft hypervector spaces are discussed.

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

The notion of -subalgebras of several types is introduced, and related properties are investigated. Conditions for an -structure to be an -subalgebra of type are provided, and a characterization of an -subalgebra of type is considered.

A METHOD TO MAKE BCK-ALGEBRAS

Using the notion of posets, a method to make BCK-algebras is considered. We show that if a poset has the least element, then the induced BCK-algebra is bounded.