Implicative neutrosophic LI-ideals of lattice implication algebras

Lattice implication algebra is a new logical algebraic system which is established by combining lattice and implication algebra. As a generalization of intuitionistic fuzzy set, neutrosophic set is introduced which deals with indeterminate membership in addition to degree of membership and degree of...

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Bibliographic Details
Published in:Journal of intelligent & fuzzy systems 2020-01, Vol.38 (2), p.2141-2149
Main Authors: Jun, Young Bae, Xin, Xiao Long
Format: Article
Language:English
Subjects:
Algebra
Fuzzy logic
Fuzzy set theory
Fuzzy sets
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Summary:Lattice implication algebra is a new logical algebraic system which is established by combining lattice and implication algebra. As a generalization of intuitionistic fuzzy set, neutrosophic set is introduced which deals with indeterminate membership in addition to degree of membership and degree of non-membership. In this article, the notion of neutrosophic set theory is applied to lattice implication algebras. The concept of implicative neutrosophic LI-ideals of a lattice implication algebra is introduced, and several properties are investigated. Relationship between a neutrosophic LI-ideal and an implicative neutrosophic LI-ideal is discussed, and conditions for a neutrosophic LI-ideal to be an implicative neutrosophic LI-ideal are provided. Characterizations of an implicative neutrosophic LI-ideal are considered, and the extension property of an implicative neutrosophic LI-ideal is studied.
ISSN:1064-1246
1875-8967
DOI:10.3233/JIFS-190866