The Path Hyperoperation

The Path Hyperoperation

A new class of hypergroupoids, deriving from binary relations, is presented, via the introduced path hyperoperation. Its properties are investigated and its connections with Graph Theory are also delineated. Moreover, we present an application of this hyperoperation to assembly line designing and management.

n-ARY Hv-MODULES WITH EXTERNAL n-ARY P -HYPEROPERATION

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...

Being on the right path

Being on the right pathThe 1st issue of the Iranian Journal of Radiation Research (IJRR) was published two years ago (June 2003). This journal was initiated to bring together the various disciplines of radiation oncology, radiation biology, medical physics, nuclear medicine and other related subjects to intensify the dialogue between basic and clinical researchers especially those working in Ir...

Some remarks on congruences obtained from the L-fuzzy Nakano hyperoperation

In this paper we study relations which are congruences with respect to ∧ and ⊔p, where ⊔pis the p-cut of the L-fuzzy hyperoperation ⊔. The main idea is to start from an equivalence relation R1 which is a congruence with respect to ∧ and ⊔1and, for each p ∈ X , construct an equivalence relation Rp which is a congruence with respect to ∧ and ⊔p. Furthermore, for each x ∈ Rp we construct a quotien...

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