• Honam Mathematical Journal
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• v.29 no.2
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• pp.279-288
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• 2007

The notion of fuzzy n-fold implicative ordered filters in implicative semigroups is introduced, and related properties are investigated. Relations between fuzzy ordered filters and fuzzy n-fold implicative ordered filters are provided. Characterizations of a fuzzy n-fold implicative ordered filter are given, and an extension property for a fuzzy n-fold implicative ordered filter is obtained.

• Journal of the Korean Institute of Intelligent Systems
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• v.13 no.2
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• pp.243-246
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• 2003

In this paper we define a weak positive implicative hyperBCK-ideal of hyperBCK-algebra. Also we investigate that every positive implicative hyperBCK-algebra is a positive implicative hyperK-algebra and then we prove that every positive implicative hyperK-algebra is a weak positive implicative hyperk-algebra.

• Bulletin of the Korean Mathematical Society
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• v.39 no.2
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• pp.185-198
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• 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.

• Communications of the Korean Mathematical Society
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• v.26 no.2
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• pp.183-196
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• 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.

• Journal of applied mathematics & informatics
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• v.35 no.5_6
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• pp.513-528
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• 2017

The concept of weak implicative filters is introduced in BE-algebras. Some characterizations of weak implicative filters are derived in terms of filters of a BE-algebra. Fuzzification is applied to the class of weak implicative filters. Some properties of fuzzy weak implicative filters are studied with respect to fuzzy relations and homomorphisms. The notion of triangular normed fuzzy weak implicative filters is introduced in BE-algebras and their properties are studied.

• Communications of the Korean Mathematical Society
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• v.14 no.1
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• pp.47-55
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• 1999

This paper continues the investigations of implicative semigroups and of their ordered filters which were started in general case by M.W. Chan and K. P. Shum [3]. In particular, the notion of an implicative ordered filter of an implicative semigroup is introduced. We state some equivalent conditions for an ordered filter to be an implicative ordered filter and obtain the so called extension property for implicative ordered filters.

• Honam Mathematical Journal
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• v.25 no.1
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• pp.43-52
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• 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.

• Journal of the Chungcheong Mathematical Society
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• v.27 no.3
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• pp.419-426
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• 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.

• Bulletin of the Korean Mathematical Society
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• v.36 no.1
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• pp.109-117
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• 1999

We introduce the notion of a fuzzy topological implicative algebras and apply some of Foster's results [2] to homomorphic images and inverse images of fuzzy topological implicative algebras.

• Honam Mathematical Journal
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• v.34 no.2
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• pp.171-181
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• 2012

The notion of implicative vague ideals of BCK-algebras is defined, and several properties of it are investigated. Relations between a vague ideal and an implicative vague ideal is discussed. Characterizations of an implicative vague ideal are considered.