• Journal of applied mathematics & informatics
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• 제33권5_6호
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• pp.739-748
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• 2015

The notion of quasi-lattice implication algebras is a generalization of lattice implication algebras. In this paper, we give an optimized definition of quasi-lattice implication algebra and show that this algebra is a distributive lattice and that this algebra is a lattice implication algebra. Also, we define a congruence relation Φ_F induced by a filter F and show that every congruence relation on a quasi-lattice implication algebra is a congruence relation Φ_F induced by a filter F.

• Kyungpook Mathematical Journal
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• 제43권4호
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• pp.539-545
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• 2003

We present a set of equations that axiomatizes the class of all lattice implication algebras. The construction is different from the one given in [7], and the proof is direct: i.e., it does not rely on results from outside the realm of the lattice implication algebras, such as the theory of BCK-algebras. Then we show that the lattice H implication algebras are nothing more than the familiar Boolean algebras. Finally we obtain some negative results for the embedding of lattice implication algebras into Boolean algebras.

• 대한수학회논문집
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• 제18권4호
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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.

• 대한수학회보
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• 제38권1호
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• pp.191-195
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• 2001

In this paper, a simple axiom system of lattice implication algebras is presented, it is convenient for verifying whether an algebra of type (2,2,2,1,0,0) becomes a lattice implication algebra.

• 대한수학회보
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• 제34권2호
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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.

• 호남수학학술지
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• 제31권3호
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• pp.323-333
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• 2009

We introduce the concepts of a fuzzifying filter and a fuzzifying implicative filter in lattice implication algebras.

• Journal of applied mathematics & informatics
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• 제13권1_2호
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• pp.385-392
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• 2003

Using a fuzzy filter, a new congruence relation induced by the fuzzy filter is given in lattice implication algebras, and some of their properties are investigated.

• Kyungpook Mathematical Journal
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• 제45권2호
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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.

• 대한수학회논문집
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• 제19권1호
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• pp.11-21
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• 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.

• Journal of applied mathematics & informatics
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• 제32권3_4호
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• pp.323-330
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• 2014

The notion of transitive filters is introduced in lattice implication algebras. A necessary and sufficient condition is derived for every filter to become a transitive filter. Some sufficient conditions are also derived for a filter to become a transitive filter. The concept of absorbent filters is introduced and their properties are studied. A set of equivalent conditions is obtained for a filter to become an absorbent filter.