### A Note on Fuzzy Groups

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In this paper, we give some theorems which characterize the intraregular semigroups in terms of intuitionistic fuzzy left, right, and biideals.

The purpose of this paper is to introduce the notions of ∈, ∈ ∨qk-fuzzy ideals of a fuzzy ordered semigroup with the ordering being a fuzzy relation. Several characterizations of ∈, ∈ ∨qk-fuzzy left (resp. right) ideals and ∈, ∈ ∨qk-fuzzy interior ideals are derived. The lattice structures of all ∈, ∈ ∨qk-fuzzy (interior) ideals on such fuzzy ordered semigroup are studied and some methods are given to construct an ∈, ∈ ∨qk-fuzzy (interior) ideals from an arbitrary fuzzy subset. Finally, the characterizations...

Given a complete and atomic Boolean algebra B, there exists a family taugamma of triangular norms on B such that, under the partial ordering of triangular norms, taugamma is a Boolean algebra isomorphic to B, where gamma is the set of all atoms in B. In other words, as we have shown in this note, every complete and atomic Boolean algebra can be represented by its own triangular norms. What we have not shown in this paper is our belief that taugamma is not unique for B and that, for such a representation,...

In this paper, we introduce the concept of bipolar-valued fuzzification of ordered 𝓐𝓖-groupoids and discuss some structural properties of bipolar-valued fuzzy two-sided ideals of an intra-regular ordered 𝓐𝓖-groupoid.