Fuzzy 2-absorbing Filters in an Almost Distributive Lattice

Fuzzy 2-absorbing Filters

Abstract

In this study, we present the notion of fuzzy 2-absorbing filters and 2-absorbing fuzzy filters in an Almost Distributive Lattice (ADL). Furthermore, we prove that both the image and the pre-image of fuzzy 2-absorbing filters remain as fuzzy 2-absorbing filters. Mainly, we discuss the connections among the fuzzy prime filter and the fuzzy 2-absorbing filter, the prime fuzzy filter and the 2-absorbing fuzzy filter, as well as the relationship between the 2-absorbing fuzzy filter and the fuzzy 2-absorbing filters. In conclusion, we further introduce the 2-absorbing fuzzy filters in terms of the 2-absorbing filter of an ADL and the 2-absorbing element in a frame.