Normal Bipolar Fuzzy Ideals in Non-involutive Residuated Lattices

摘要

In this paper, the problem of bipolar fuzzy ideal is further studied in non-involutive residuated lattices. The notion of normal bipolar fuzzy ideal is introduced, some important properties and equivalent characterizations of normal bipolar fuzzy ideals are obtained. In addition, two special types of normal bipolar fuzzy ideals are defined, which are called maxima and completely normal bipolar fuzzy ideals, respectively, and their relationships are discussed.This work further expands the way for revealing the structural characteristics of non-involutive residuated lattices.