scholarly journals Vague Congruences and Quotient Lattice Implication Algebras

2014 ◽  
Vol 2014 ◽  
pp. 1-7 ◽  
Author(s):  
Xiaoyan Qin ◽  
Yi Liu ◽  
Yang Xu
Keyword(s):  
Lattice Implication Algebra ◽  
Implication Algebras ◽  
Homomorphism Theorem ◽  
Similarity Relations ◽  
Implication Algebra ◽  
Congruence Theory ◽  
Congruence Relations

The aim of this paper is to further develop the congruence theory on lattice implication algebras. Firstly, we introduce the notions of vague similarity relations based on vague relations and vague congruence relations. Secondly, the equivalent characterizations of vague congruence relations are investigated. Thirdly, the relation between the set of vague filters and the set of vague congruences is studied. Finally, we construct a new lattice implication algebra induced by a vague congruence, and the homomorphism theorem is given.

scholarly journals Fantastic filters of lattice implication algebras

2000 ◽  
Vol 24 (4) ◽  
pp. 277-281 ◽  
Author(s):  
Young Bae Jun
Keyword(s):  
Extension Property ◽  
Equivalent Condition ◽  
Lattice Implication Algebra ◽  
Implication Algebras ◽  
Implication Algebra ◽  
Fantastic Filter ◽  
Positive Implicative Filter

The notion of a fantastic filter in a lattice implication algebra is introduced, and the relations among filter, positive implicative filter, and fantastic filter are given. We investigate an equivalent condition for a filter to be fantastic, and state an extension property for fantastic filter.

scholarly journals Weak LI-ideals in implicative almost distributive lattices

2021 ◽  
Vol 14 (3) ◽  
pp. 207-217
Author(s):  
Tilahun Mekonnen Munie
Keyword(s):  
Distributive Lattice ◽  
Research Area ◽  
Distributive Lattices ◽  
Lattice Implication Algebra ◽  
Implication Algebra ◽  
New Development

In the field of many valued logic, lattice valued logic (especially ideals) plays an important role. Nowadays, lattice valued logic is becoming a research area. Researchers introduced weak LI-ideals of lattice implication algebra. Furthermore, other scholars researched LI-ideals of implicative almost distributive lattice. Therefore, the target of this paper was to investigate new development on the extension of LI-ideal theories and properties in implicative almost distributive lattice. So, in this paper, the notion of weak LI-ideals and maximal weak LI- ideals of implicative almost distributive lattice are defined. The properties of weak LI- ideals in implicative almost distributive lattice are studied and several characterizations of weak LI-ideals are given. Relationship between weak LI-ideals and weak filters are explored. Hence, the extension properties of weak LI-ideal of lattice implication algebra to that of weak LI-ideal of implicative almost distributive lattice were shown.

scholarly journals Attribute Extended Algorithm of Lattice-Valued Concept Lattice Based on Congener Formal Context

2014 ◽  
Vol 2014 ◽  
pp. 1-9 ◽  
Author(s):  
Li Yang ◽  
Yang Xu
Keyword(s):  
Parallel Processing ◽  
Distributed Storage ◽  
Concept Lattice ◽  
Research Work ◽  
Sufficient Conditions ◽  
Formal Context ◽  
Concept Lattices ◽  
Lattice Implication Algebra ◽  
Implication Algebra ◽  
Necessary And Sufficient

This paper is the continuation of our research work about lattice-valued concept lattice based on lattice implication algebra. For a better application of lattice-valued concept lattice into data distributed storage and parallel processing, it is necessary to research attribute extended algorithm based on congener formal context. The definitions of attribute extended formal context and congener formal context are proposed. On condition that the extent set stays invariable when the new attribute is increased, the necessary and sufficient conditions of forming attribute values are researched. Based on these conditions, the algorithms of generating lattice-valued congener formal context and establishing concept lattice are given, by which we can provide a useful basis for union algorithm and constructing algorithm of lattice-valued concept lattices in distributed and parallel system.

Filters and structure of lattice implication algebra

1997 ◽  
Vol 42 (18) ◽  
pp. 1517-1520 ◽  
Author(s):  
Liu Jun ◽  
Xu Yang
Keyword(s):  
Lattice Implication Algebra ◽  
Implication Algebra
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