• 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.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.

• Journal of applied mathematics & informatics
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• v.13 no.1_2
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• pp.153-163
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• 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.

• Journal of applied mathematics & informatics
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• v.33 no.3_4
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• pp.459-467
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• 2015

The notion of int-soft implicative filters of a BE-algebra is introduced, and related properties are investigated. The problem of clas- sifying int-soft positive implicative by their γ-inclusive filter is solved. We provide conditions for a soft set to be an int-soft filter. We make a new int-soft implicative filter from old one.

• Journal of applied mathematics & informatics
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• v.34 no.5_6
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• pp.527-536
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• 2016

In this paper, we introduce the notions about int-soft mighty filters, int-soft n-fold mighty filters, and int-soft n-fold positive implicative filters of BE-algebras. We investigate their properties and provide conditions which have connecting relationship among int-soft filters, int-soft mighty filters, and int-soft positive implicative filters. Also, characterizations of int-soft n-fold mighty filters and int-soft n-fold positive implicative filters are provided in BE-algebras.

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

• Honam Mathematical Journal
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• v.40 no.3
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• pp.401-431
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• 2018

In this paper, some kinds of (skew) filters are defined and are studied in residuated skew lattices. Some relations are got between these filters and quotient algebras constructed via these filters. The Green filter is defined which establishes a connection between residuated lattices and residuated skew lattices. It is investigated that relationships between Green filter and other types of filters in residuated skew lattices and the relationship between residuated skew lattice and other skew structures are studied. It is proved that for a residuated skew lattice, skew Hilbert algebra and skew G-algebra are equivalent too.