P-FUZZY IDEALS AND H-FUZZY IDEALS IN BCI ALGEBRAS

Abstract

In this paper we investigate P‑fuzzy ideals and H‑fuzzy ideals in BCI‑algebras. After recalling the notions of ideals, P‑ideals and H‑ideals, we consider fuzzy subsets satisfying suitable P‑type and H‑type conditions and regard them as P‑fuzzy and H‑fuzzy ideals, respectively. For a P‑fuzzy (resp. H‑fuzzy) ideal f of a BCI‑algebra X, we study the level subset  and prove that  is a crisp P‑ideal (resp. H‑ideal) of X. This establishes a direct connection between fuzzy ideals and their corresponding classical counterparts. Furthermore, by using a simple lemma on infima of families of real numbers, we show that arbitrary pointwise infima of P‑fuzzy ideals (resp. H‑fuzzy ideals) are again P‑fuzzy ideals (resp. H‑fuzzy ideals). Several examples on a finite BCI‑algebra are provided to illustrate the main results. These structural properties supply basic tools for the later study of the lattice‑theoretic behavior of P‑fuzzy and H‑fuzzy ideals in BCI‑algebras.