Lukasiewicz fuzzy positive implicative ideals in BCK-algebras

Document Type : Original Article

Authors

1 Department of Mathematics, Jeju National University, Jeju 63243, Korea

2 Department of Mathematics Education, Gyeongsang National University, Jinju 52828, Korea

Abstract

In BCK-algebras, the notion of Lukasiewicz fuzzy positive implicative ideal is introduced, and several properties are investigated. The relationship between Lukasiewicz fuzzy ideal and Lukasiewicz fuzzy positive implicative ideal is discussed, and characterizations of a Lukasiewicz fuzzy positive implicative ideal are considered. Conditions for a Lukasiewicz fuzzy ideal to be a Lukasiewicz fuzzy positive implicative ideal are provided, and conditions for the ∈-set, q-set and O-set to be positive implicative ideals are explored.

Keywords