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

• Journal of the Chungcheong Mathematical Society
• /
• v.32 no.2
• /
• pp.179-189
• /
• 2019

In this paper, we introduce the notion of symmetric bi-generalized derivation of lattice implication algebra L and investigated some related properties. Also, we prove that a map $F:L{\times}L{\rightarrow}L$ is a symmetric bi-generalized derivation associated with symmetric bi-derivation D on L if and only if F is a symmetric map and it satisfies $F(x{\rightarrow}y,z)=x{\rightarrow}F(y,z)$ for all $x,y,z{\in}L$.

• Honam Mathematical Journal
• /
• v.31 no.3
• /
• pp.323-333
• /
• 2009

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

• Journal of applied mathematics & informatics
• /
• v.13 no.1_2
• /
• pp.385-392
• /
• 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.

• Journal of applied mathematics & informatics
• /
• v.13 no.1_2
• /
• 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.

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

• Communications of the Korean Mathematical Society
• /
• v.19 no.1
• /
• 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.

• Journal of applied mathematics & informatics
• /
• v.32 no.3_4
• /
• pp.323-330
• /
• 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.

• Journal of applied mathematics & informatics
• /
• v.14 no.1_2
• /
• pp.137-155
• /
• 2004

Fuzzification of a fantastic filter in a lattice implication algebra is considered. Relations among a fuzzy filter, a fuzzy fantastic filter, and fuzzy positive implicative filter are stated. Conditions for a fuzzy filter to be a fuzzy fantastic filter are given. Using the notion of level set, a characterization of a fuzzy fantastic filter is considered. Extension property for fuzzy fantastic filters is established. The notion of normal/maximal fuzzy fantastic filters and complete fuzzy fantastic filters is introduced, and some related properties are investigated.

• Journal of the Korean Mathematical Society
• /
• v.36 no.2
• /
• pp.369-380
• /
• 1999

As a continuation of the paper [3], in this paper we investigate the further properties on LI-ideals, and show that how to generate an LI-ideal by both and LI-ideal and an element. We define a prime LI-ideal, and give an equivalent condition for a proper LI-ideal to be prime. Using this result, we establish the extension property and prime LI-ideal theorem.