Abstract
The notion of BCK-algebras was initiated by Imai and Iseki in 1966 as a generalization of both classical and non-classical positional calculus. In 1999, Huang and Chen introduced the notion of n-fold positive implicative ideals in BCK-algebras. In 2011, Satyanarayana and Durga Prasad introduced foldness of intuitionistic fuzzy positive implicative ideals in BCK-algebras. In this paper, we introduce the notion of n-fold positive implicative ideals, n-fold positive implicative Artinian (shortly, n PI -Artinian) and n-fold positive implicative Noe-therian (shortly, n PI -Noetherian) BCK-algebras and study some of its properties.
Highlights
It is known that mathematical logic is a discipline used in sciences and humanities with different point of view
In 1999, Huang and Chen [5] introduced the notion of n-fold positive implicative ideals in BCK-algebras
In [9], Jun and Kim consider the fuzzification of n-fold positive implicative ideals in BCK-algebras and Satyanarayana and Durga Prasad [12] studied foldness of intuitionistic fuzzy positive impli-cative ideals in BCK-algebras
Summary
It is known that mathematical logic is a discipline used in sciences and humanities with different point of view. The non-classical logic has become a formal and useful tool for computer science to deal with fuzzy information and uncertain information. The notion of logical algebra: BCK-algebras [7] were initiated by Imai and Iseki in 1966 as a generalization of both classical and non-classical positional calculus. Iseki introduced BCI-algebras [8] as a super class of the class of BCK-algebras. In 1999, Huang and Chen [5] introduced the notion of n-fold positive implicative ideals in BCK-algebras. In [9], Jun and Kim consider the fuzzification of n-fold positive implicative ideals in BCK-algebras and Satyanarayana and Durga Prasad [12] studied foldness of intuitionistic fuzzy positive impli-cative ideals in BCK-algebras. We introduce the notion of n-fold positive implycative Artinian (shortly, PI n -Artinian) and n-fold positive implicative Noetherian
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