An n-ary operation Q : Σ → Σ is called an n-ary quasigroup of order |Σ| if in the equation x0 = Q(x1, . . . , xn) knowledge of any n elements of x0, . . . , xn uniquely specifies the remaining one. Q is permutably reducible ifQ(x1, . . . , xn) = P ` R(xσ(1), . . . , xσ(k)), xσ(k+1), . . . , xσ(n) ́ where P and R are (n − k + 1)-ary and k-ary quasigroups, σ is a permutation, and 1 < k < n. An m-a...

This work studies the L-fuzzy context sequences when L is a complete lattice extending the results obtained in previous works with L = [0, 1]. To do this, we will use n-ary OWA operators on complete lattices. With the aid of these operators, we will study the different contexts values of the sequence using some new relations. As a particular case, we have the study when L = J ([0, 1]). Finally,...

An n-ary operation q : Σn → Σ is called an n-ary quasigroup of order |Σ| if in x0 = q(x1, . . . , xn) knowledge of any n elements of x0, . . . , xn uniquely specifies the remaining one. An n-ary quasigroup q is permutably reducible if q(x1, . . . , xn) = p(r(xσ(1), . . . , xσ(k)), xσ(k+1), . . . , xσ(n)) where p and r are (n− k + 1)-ary and k-ary quasigroups, σ is a permutation, and 1 < k < n. ...

In this paper n-ary regular division associative algebras are discussed. It is shown that every operation in algebra will be endo-linearly represented over the same binary group. Schauffler like theorem proved for those algebras.

The main tools in the theory of n-ary hyperstructures are the fundamental relations. The fundamental relation on an n-ary hypersemigroup is defined as the smallest equivalence relation so that the quotient would be the n-ary semigroup. In this paper we study neutral elements in n-ary hypersemigroups and introduce a new strongly compatible equivalence relation on an n-ary hypersemigroup so that ...