Any complete hypergroup H may be represented as the union g g G H A ∈ =  , where G is a group and the subsets Ag of H satisfy certain properties. With any hypergroupoid 〈H, o〉 we may associate a particular fuzzy set μ . In this paper we determine sufficient and necessary conditions for a finite complete hypergroup 〈H, o〉, where p G (Z , ) ≅ + or 2p G (Z , ) ≅ + , p a prime number, such that t...

Abstract Isotopies and autotopies of n -ary groups are described. As a consequence, we obtain various characterizations the group automorphisms groups. We also determine number given group.

The paper is devoted to a concept of aggregation of binary fuzzy relations. Consider two n-ary vectors, when we know the degrees to which corresponding components are in relation we can measure the degree to which vectors are in relation. Tasks with such background justify the necessity of aggregation of binary fuzzy relations and we contribute to the topic in this paper. First we recall the ap...

A general mechanism for "breaking" commutativity in algebras is proposed: if the underlying set taken to be not a crisp set, but rather an obscure/fuzzy membership function, reflecting degree of truth that element belongs can incorporated into commutation relations. The special "deformations" and $\varepsilon $-commutativity are introduced such way equal degrees result "nondeformed" case. We al...

Complex query answering (CQA) is an essential task for multi-hop and logical reasoning on knowledge graphs (KGs). Currently, most approaches are limited to queries among binary relational facts pay less attention n-ary (n≥2) containing more than two entities, which prevalent in the real world. Moreover, previous CQA methods can only make predictions a few given types of cannot be flexibly exten...

Fuzzy logics are designed to support logical inferences on vague or uncertain premises, and they are useful in several theoretical and applicative areas of computer science. A central paradigm in mathematical fuzzy logic, popularized by Hájek [Háj98], is based on the idea of weakening Boolean logic starting from a suitable generalization of Boolean conjunction, namely, a class of [0, 1]-valued ...

We devise a condition strictly between the existence of an $n$-ary and $n{+}1$-ary near-unanimity term. evaluate exactly distributivity modularity levels implied by such condition.

Hyperstructure theory was born in 1934 when Marty [19] defined hypergroups as a generalization of groups. Let H be a non-empty set and let ℘∗(H) be the set of all non-empty subsets of H. A hyperoperation on H is a map ◦ : H ×H −→ ℘∗(H) and the couple (H, ◦) is called a hypergroupoid. If A and B are non-empty subsets of H, then we denote A◦B = ∪ a∈A, b∈B a◦b, x◦A = {x}◦A and A◦x = A◦{x}. Under c...