A HYPEROPERATION DEFINED ON A GROUPOID EQUIPPED WITH A MAP

The Hv-structures are hyperstructures where the equality is replaced by the non-empty intersection. The fact that this class of the hyperstructures is very large, one can use it in order to define several objects that they are not possible to be defined in the classical hypergroup theory. In the present paper we introduce a kind of hyperoperations which are defined on a set equipped with an operation or a hyperoperation and a map on itself

Bar and Theta Hyperoperations

In questionnaires the replacement of the scale of Likert by a bar was suggested in 2008 by Vougiouklis & Vougiouklis. The use of the bar was rapidly accepted in social sciences. The bar is closely related with fuzzy theory and has several advantages during both the filling-in questionnaires and mainly in the research processing. In this paper we relate hyperstructure theory with questionnaires and we study the obtained hyperstructures which are used as an organising device of the problem

Interval valued intuitionistic (S,T)(S,T)-fuzzy HvH_v-submodules

On the basis of the concept of the interval valued intuitionistic fuzzy sets introduced by K.Atanassov, the notion of interval valued intuitionistic fuzzy $H_v$-submodules of an $H_v$-module with respect to $t$-norm $T$ and $s$-norm $S$ is given and the characteristic properties are described. The homomorphic image and the inverse image are investigated.In particular, the connections between interval valued intuitionistic $(S,T)$-fuzzy $H_v$-submodules and interval valued intuitionistic $(S,T)$-fuzzy submodules are discussed

Helix-Hopes on Finite Hyperfields

Hyperstructure theory can overcome restrictions which ordinary algebraic structures have. A hyperproduct on non-square ordinary matrices can be defined by using the so called helix-hyperoperations. We study the helix-hyperstructures on the representations using ordinary fields. The related theory can be faced by defining the hyperproduct on the set of non square matrices. The main tools of the Hyperstructure Theory are the fundamental relations which connect the largest class of hyperstructures, the Hv-structures, with the corresponding classical ones. We focus on finite dimensional helix-hyperstructures and on small Hv-fields, as well.

The LV-hyperstructures

The largest class of hyperstructures is the one which satisfy the weak properties and they are called H v -structures introduced in 1990. The H v(c)-structures have a partial order (poset) on which gradations can be defined. We introduce the LV-construction based on the Levels Variable

On geometrical hyperstructures of finite order

It is known that a concrete representation of a finite k-dimensional Projective Geometry can be given by means of marks of a Galois Field GF [p^n], denoted by PG(k, p^n).In this geometry, we define hyperoperations, which create hyperstructures of finite order and we present results, propositions and examples on this topic. Additionally, we connect these hyperstructures to Join Spaces

On P-H_v-Structures in a Two-Dimensional Real Vector Space

In this paper we study P-Hv-structures in connection with Hv-structures, arising from a specific P-hope in a two-dimensional real vector space. The visualization of these P-Hv-structures is our priority, since visual thinking could be an alternative and powerful resource for people doing mathematics. Using position vectors into the plane, abstract algebraic properties of these P-Hv-structures are gradually transformed into geometrical shapes, which operate, not only as a translation of the algebraic concept, but also, as a teaching process. 

The Divisors’ Hyperoperations

In the set N of the Natural Numbers we define two hyperoperations based on the divisors of the addition and multiplication of two numbers. Then, the properties of these two hyperoperations are studied together with the resulting hyperstructures. Furthermore, from the coexistence of these two hyperoperations in N ∗ , an H v -ring is resulting which is dual