In this paper, we introduce the concept of fuzzy congruences on n-ary semigroups and describe quotient n-ary semigroups by fuzzy congruences. Some isomorphism theorems about n-ary semigroups are established. Moreover, we discuss a special kind of n-ary semigroups. We also establish relationships between normal fuzzy ideals and fuzzy congruences. In particular, we prove that there exists a prese...

n-ary transit functions are introduced as a generalization of binary (2-ary) transit functions. We show that they can be associated with convexities in natural way and discuss the Steiner convexity as a natural n-ary generalization of geodesicaly convexity. Furthermore, we generalize the betweenness axioms to n-ary transit functions and discuss the connectivity conditions for underlying hypergr...

Fuzzy n-ary hypergroups were introduced as suitable generalizations of fuzzy polygroups and a special case of fuzzy n-ary hyper groups. The aim of this paper is to introduce the notion of fuzzy n-ary factor polygroups of a polygroup. Based on the fuzzy n-ary factor group, we also study the product structures of the generating fuzzy factor n-ary groups. At the end of the paper, we prove the fund...

We characterize the set of all n-ary quasigroups of order 4: every n-ary quasigroup of order 4 is permutably reducible or semilinear. Permutable reducibility means that an n-ary quasigroup can be represented as a composition of k-ary and (n− k +1)-ary quasigroups for some k from 2 to n−1, where the order of arguments in the representation can differ from the original order. The set of semilinea...

The n-ary first and second recursion theorems formalize two distinct, yet similar, notions of self-reference. Roughly, the n-ary first recursion theorem says that, for any n algorithmic tasks (of an appropriate type), there exist n partial computable functions that use their own graphs in the manner prescribed by those tasks; the n-ary second recursion theorem says that, for any n algorithmic t...

The notion of an n-ary group is a natural generalization of the notion of a group and has many applications in different branches. In this paper, the notion of (normal) fuzzy n-ary subgroup of an n-ary group is introduced and some related properties are investigated. Characterizations of fuzzy n-ary subgroups are given.

This paper addresses the problem of automatic detection and prediction of abnormal human behaviours in public spaces. For this propose a novel classifier, called N-ary trees, is presented. The classifier processes time series of attributes like the object position, velocity, perimeter and area, to infer the type of action performed. This innovative classifier can detect three types of events: n...

We introduce the basic concepts on intuitionistic fuzzy subalgebras on n-ary groupoids, i.e., on algebras containing one fundamental n-ary operation. We describe some similarities and differences between the n-ary and binary case. In the case of n-ary quasigroups and groups we suggest the common method of investigations based on some methods used in the universal algebra.

The well-known connection between hyperidentities of an algebra and identities satisfied by the clone of this algebra is studied here in a restricted setting, that of n-ary strongly full hyperidentities and identities of the n-ary clone of term operations of an algebra induced by strongly full terms, both of a type consisting only of n-ary operation symbols. We call such a type an n-ary type. U...