Fuzzy Filters in Pseudo-CI-Algebras

Abstract

In this paper, the notion of fuzzy pseudo-CI-filter in a pseudo-CI-algebra is introduced and its elementary properties are investigated. With the upper level set, the relationship between pseudo-CI-filter and fuzzy pseudo-CI-filter is shown and this relationship is illustrated with an example. Some type of fuzzy pseudo-CI-filters and the relationships between them and the fuzzy pseudo-CI-filter are checked. We study generated fuzzy pseudo-CI-filter by a fuzzy set. In addition, the properties of fuzzy pseudo-CI-filter are studied in Noetherian and Artinian pseudo-CI-algebra. We construct a fuzzy pseudo-CI-filter by a strictly ascending sequence of pseudo-CI-filter of pseudo-CI-algebra and any strictly decreasing sequence in [Formula: see text].