Intuitionistic Fuzzy Filters of Residuated Lattices

Abstract

In this paper, the concept of intuitionistic fuzzy sets is applied to residuated lattices. The notion of intuitionistic fuzzy¯lters of a residuated lattice is introduced and some related properties are investigated. The characterizations of intuitionistic fuzzy¯lters are obtained. We show that the set of all the intuitionistic fuzzy¯lters of a residuated lattice forms a complete lattice and we¯nd the distributive sublattices of it. Finally, the correspondence theorem for intuitionistic fuzzȳ lters is established.

Regularity of Intuitionistic Fuzzy Relations on Hypergroupoids

“…First we recall their definitions from [4,16,23]. i) For any α ∈ [0, 1] and a fuzzy relation µ on a nonempty set X, the set…”

“…Let α, β ∈ [0, 1]. Accordingly with Theorem 3.6 [16], the cuts U (µ R , α) and L(ν R , β) are equivalence relations on H.…”

“…Conversely, suppose that, for any α, β ∈ [0, 1], the cuts U (µ R , α) and L(ν R , β) are regular crisp relations on H. Again, accordingly with Theorem 3.6 [16], R = (µ R , ν R ) is an IFER on H. It remains to prove that R is intuitionistic fuzzy regular on H.…”

Interval Valued Intuitionistic Fuzzy β-Filters on β-Algebras

“…Jun et al [8] proposed the concept of fuzzy BCIsubalgebras with interval valued membership functions. In 2011, Ghorbani [4] proposed the notion of intuitioistic fuzzy filters of residuated lattices. They have illustrated that a residual lattice's collection of all intuitionistic fuzzy filters is a complete lattice and identified its distributive sublattices.…”

Neutrosophic Filters in Pseudo-Bci Algebras

“…Moreover, pseudo-BCI algebra is also as a generalization of pseudo-BCK algebra (which has a close connection with various noncommutative fuzzy logic formal systems; see [17][18][19][20][21][22][23][24]). For nonclassical logic algebra systems, the theory of filters (ideals) plays an important role (see [25][26][27][28][29][30][31][32][33]). In 2006, the notion of a pseudo-BCI filter (ideal) of pseudo-BCI algebras was introduced in [34].…”