• Bulletin of the Korean Mathematical Society
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• v.40 no.1
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• pp.123-137
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• 2003

In this note first we define the notions of weak implicative and implicative hyper K-ideals of a hyper K-algebra H. Then we state and prove some theorems which determine the relationship between these notions and (weak) hyper K-ideals. Also we give some relations between these notions and all types of positive implicative hyper K-ideals. Finally we classify the implicative hyper K-ideals of a hyper K-algebra of order 3.

• Bulletin of the Korean Mathematical Society
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• v.53 no.5
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• pp.1483-1495
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• 2016

The notion of int-soft (implicative) filters in lattice implication algebras is introduced, and related properties are investigated. Characterizations of int-soft (implicative) filters are discussed. Conditions for an int-soft filter to be an int-soft implicative filter are provided. Extension property for int-soft implicative filters is established.

• Bulletin of the Korean Mathematical Society
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• v.35 no.1
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• pp.53-61
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• 1998

We introduce the concepts of a positive implicative filter and an associative filter in a lattice implication algebra. We prove that (i) every positive implicative filter is an implicative filter, and (ii) every associative filter is a filter. We provide equivalent conditions for both a positive implicative filter and an associative filter.

• Bulletin of the Korean Mathematical Society
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• v.43 no.1
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• pp.141-148
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• 2006

Fuzzy (weak) implicative hyper K-ideals are introduced, and relations among fuzzy weak implicative hyper K-ideals, fuzzy implicative hyper K-ideals and fuzzy hyper K-ideals are discussed.

• Communications of the Korean Mathematical Society
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• v.18 no.4
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• pp.621-628
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• 2003

We investigate some related properties of fuzzy filters and fuzzy implicative filters in lattice implication algebras. We find a characterization of fuzzy filters and fuzzy implicative filters, and we discuss a relation between fuzzy filters and fuzzy implicative filters in lattice implication algebras. Also we give an extension theorem of fuzzy implicative filters.

• Journal of applied mathematics & informatics
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• v.10 no.1_2
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• pp.51-62
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• 2002

The present paper gives a new construction of a quotient BCI(BCK)-algebra X/${\mu}$ by a fuzzy ideal ${\mu}$ in X and establishes the Fuzzy Homomorphism Fundamental Theorem. We show that if ${\mu}$ is a fuzzy ideal (closed fuzzy ideal) of X, then X/${\mu}$ is a commutative (resp. positive implicative, implicative) BCK(BCI)-algebra if and only if It is a fuzzy commutative (resp. positive implicative, implicative) ideal of X Moreover we prove that a fuzzy ideal of a BCI-algebra is closed if and only if it is a fuzzy subalgebra of X We show that if the period of every element in a BCI-algebra X is finite, then any fuzzy ideal of X is closed. Especiatly, in a well (resp. finite, associative, quasi-associative, simple) BCI-algebra, any fuzzy ideal must be closed.

• The Pure and Applied Mathematics
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• v.19 no.2
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• pp.127-136
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• 2012

In this paper, we introduce the notion of an implicative vague filter in BE-algebras, and investigate some properties of them. Also we give conditions for a vague set to be an implicative vague filter, and we characterize implicative vague filters in BE-algebras. We define the notion of $n$-fold implicative vague filters in BE-algebras and we give characterizations of $n$-fold implicative vague filters and $n$-fold implicative BE-algebras.

• Kyungpook Mathematical Journal
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• v.45 no.2
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• pp.177-189
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• 2005

We obtain characterizations of T-fuzzy (implicative) filters and some properties of T-product of fuzzy (implicative) filters in lattice implication algebras. We also establish the extension property for T-fuzzy implicative filters.

• Bulletin of the Korean Mathematical Society
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• v.34 no.2
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• pp.185-191
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• 1997

The notions of implicative semigroup and ordered filter were introduced by M. W. Chan and K. pp. Shum [3]. The first is a generalization of implicative semilattice (see W. C. Nemitz [6] and T. S. Blyth [2]) and has a close relation with the implication in mathematical logic and set theoretic difference (see G. Birkhoff [1] and H. B. Curry [4]). For the general development of implicative semilattice theory the ordered filters play an important role, which is shown by W. C. Nemitz [6].

• Bulletin of the Korean Mathematical Society
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• v.34 no.2
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• pp.193-198
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• 1997

In order to research the logical system whose propositional value is given in a lattice, Y. Xu [4] proposed the concept of lattice implication algebras, and discussed their some properties in [3] and [4]. Y. Xu and K. Qin [5] introduced the notions of filter and implicative filter in a lattice implication algebra, and investigated their properties. In this paper, in the first place, we give an equivalent condition of a filter, and provide some equivalent conditions that a filter is an implicative filter in a lattice implication algebra. By using these results, we construct an extension property for implicative filter.