Algorithms and computations for (m,n)-fold p-ideals in BCI-algebras

Abstract

In this paper we observe that, the notions of (m, n)-fold p-ideals and fuzzy (m, n)-fold p-ideals, for each positive integers m, n, are indeed the natural generalization of p-ideals and fuzzy p-ideals, respectively. A characterization of (m, n)-fold p-ideals and fuzzy (m, n)-fold p-ideals is given, and conditions for which an ideal (respectively fuzzy ideal) is an (m, n)-fold p-ideal (respectively fuzzy (m, n)-fold p-ideal) are studied. We also establish extension properties for (m, n)-fold p-ideals and fuzzy (m, n)-fold p-ideals. Furthermore, we construct some algorithms to determine whether certain finite sets provided with a well defined operation, are BCI-algebras, (m, n)-fold p-ideals, fuzzy subsets or fuzzy (m, n)-fold p-ideals.