L-Fuzzy Filters of a Poset

Abstract

Many generalizations of ideals and filters of a lattice to an arbitrary poset have been studied by different scholars. The authors of this paper introduced several generalizations of L-fuzzy ideal of a lattice to an arbitrary poset in [1]. In this paper, we introduce several L-fuzzy filters of a poset which generalize the L-fuzzy filter of a lattice and give several characterizations of them.

The Fuzzy Prime Spectrum of Partially Ordered Sets

“…Te present paper is the continuation of Assaye Alaba et al's work [11][12][13], and so we will follow the same notations, defnitions, and results on fuzzy ideals, u-fuzzy ideals, fuzzy flters, l-fuzzy flters, prime fuzzy ideals, prime fuzzy flters, maximal fuzzy ideals, and maximal fuzzy flters in a poset.…”

“…Tis concept has proven to be a powerful tool in modeling uncertainty and vagueness, making it particularly well-suited for analyzing posets where precise membership may not always be applicable. In this context, the notion of fuzzy ideals and flters in posets has been studied by Assaye Alaba et al [11,12] as a natural extension of fuzzy ideals in lattices. Fuzzy ideals provide a fexible framework for studying the behavior of fuzzy subsets that possess certain desirable properties within a poset.…”

P-Fuzzy Ideals and P-Fuzzy Filters in P-Algebras

“…Rosenfeld's paper inspired the development of fuzzy abstract algebra. Since then, several authors have developed interesting results on fuzzy theory (see [3][4][5][6][7][8][9][10][11][12][13][14]). In this paper, we introduce the concept of p-fuzzy ideals and p-fuzzy filters in p-algebra.…”

L-Fuzzy Semiprime Ideals of a Poset

“…In [36,37], the authors of this paper introduced several types of L-fuzzy ideals and filters of a partially ordered set whose truth values are in a complete lattice satisfying the infinite meet distributive law. In addition, in [38], we have introduced and presented certain comprehensive results on the notion of L-fuzzy prime ideals and maximal L-fuzzy ideals of a poset by applying the general theory of algebraic fuzzy systems introduced in [39,40].…”