Affiliations: [a] Department of Mathematics Education, Gyeongsang National University, Jinju, Korea
| [b] School of Science, Xi’an Polytechnic University, Xi’an, China
| [c] School of Mathematics, Northwest University, Xi’an, China
Abstract: 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.
