• 대한수학회보
• /
• 제39권2호
• /
• pp.185-198
• /
• 2002

We Consider the fuzzification of sub-implicative ideals in BCI-algebras, and investigate some related properties. We give conditions for a fuzzy ideal to be a fuzzy sub-implicative ideal. we show that (1) every fuzzy sub-implicative ideal is a fuzzy ideal, but the converse is not true, (2) every fuzzy sub-implicative ideal is a fuzzy positive implicative ideal, but the converse is not true, and (3) every fuzzy p-ideal is a fuzzy sub-implicative ideal, but the converse is not true. Using a family of sub-implicative ideals of a BCI-algebra, we establish a fuzzy sub-implicative ideal, and using a level set of a fuzzy set in a BCI-algebra, we give a characterization of a fuzzy sub-implicative ideal.

• 대한수학회논문집
• /
• 제26권2호
• /
• pp.183-196
• /
• 2011

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 discussed. Also, relations between implicative idealistic soft BCK-algebras and commutative (resp. positive implicative) idealistic soft BCK-algebras are provided.

• 대한수학회논문집
• /
• 제12권3호
• /
• pp.499-505
• /
• 1997

This paper is a continuation of [3]. We prove that if A is quasi-associative (resp. an implicative) ideal of a BCI-algebra X then the k-nil radical of A is a quasi-associative (resp. an implicative) ideal of X. We also construct the quotient algebra $X/[Z;k]$ of a BCI-algebra X by the k-nhil radical [A;k], and show that if A and B are closed ideals of BCI-algebras X and Y respectively, then

• Journal of applied mathematics & informatics
• /
• 제12권1_2호
• /
• pp.243-250
• /
• 2003

The fuzzification of (Positive implicative) pseudo-ideals in a pseudo-BCK algebra is discussed, and several properties are investigated. Characterizations of a fuzzy pseudo-ideal are displayed.

• 대한수학회보
• /
• 제46권1호
• /
• pp.147-153
• /
• 2009

In this paper, we give some constructions of implicative/commutative d-algebras which are not BCK-algebras. This demonstrate that the notion of implicative/commutative d-algebras are indeed generalizations of the same in BCK-algebras.

• 호남수학학술지
• /
• 제25권1호
• /
• pp.43-52
• /
• 2003

The fuzzification of positive implicative hyper K-ideals in hyper K-algebras is considered, Relations between fuzzy positive implicative hyper K-ideal and fuzzy hyper K-ideal are given. Characterizations of fuzzy positive implicative hyper K-ideals are provided. Using a family of positive implicative hyper K-ideals we make a fuzzy positive implicative hyper K-ideal. Using the notion of a fuzzy positive implicative hyper K-ideal, a weak hyper K-ideal is established.

• 충청수학회지
• /
• 제27권3호
• /
• pp.419-426
• /
• 2014

In this paper, we introduce the notion of a positive implicative filter in BE-algebras. We show that every positive implicative filter is a filter in BE-algebras. We give some examples that a filter may not be a positive implicative filter and also a positive implicative filter may be not an implicative filter in BE-algebras. We also give some equivalent conditions of a positive implicative filter in BE-algebras.

• 호남수학학술지
• /
• 제44권2호
• /
• pp.209-218
• /
• 2022

The notion of positive implicative MBJ-neutosophic ideal of BCK-algebras is defined and some properties of it are investigated. Relations between positive implicative MBJ-neutrosophic ideal and positive implicative ideal are discussed. In a BCK-algebra, the extension property for positive implicative MBJ-neutrosophic ideal is established.

• Journal of applied mathematics & informatics
• /
• 제13권1_2호
• /
• pp.153-163
• /
• 2003

The fuzzification of a positive implicative filter is considered, and some of properties are investigated. The relation among fussy filter, fuzzy n-fold implicative filter, and fuzzy n-fold positive implication filter is discussed.

• 대한수학회논문집
• /
• 제19권1호
• /
• pp.11-21
• /
• 2004

We discuss the n-fold implicative/fantastic filters in lattice implication algebras, which are extended notions of implicative/fantastic filters. Characterizations of n-fold implicative/fantastic filters are given. Conditions for a filter to be n-fold implicative are provided. Extension property for an n-fold fantastic filter is established.