Hyperstructures

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

We investigate the relation of directed graphs and hyperstructures
by virtue of the graph hyperoperation. A new class of graphs arises
in this way representing isomorphism classes of C-hypergroupoids
and we present the 17 such graphs that correspond to the 73 C-
hypergroupoids associated with binary relations on three element sets. As it is shown they constitute an upper semilattice with respect to graph inclusion.

The path hyperoperation, a generalization of Corsini’s hyperoperation deriving from graph theory, was recently introduced and applied for assembly line designing. In this paper we study the commutativity property for the corresponding class of hypergroupoids
and investigate their connection with Graph Theory. Moreover, we prove that such a (partial) hypergroupoid is commutative if and only if it can be obtained as a disjoint union of non-partial hypergroupoids.

The problem of multiperson and multiobjective decision making is considered. Models based on fuzzy measures are introduced. Moreover the problem of checking coherence of an assessment of scores to pairs (alternative, objective) is faced. The procedures of aggregating scores w.r.t. the objectives and w.r.t. the decision makers are studied. Geometrical interpretations of the concepts introduced and the results obtained are shown, based on hyperstructures and, in particular, join spaces.

The hyperstructures have applications in mathematics and other sciences such as biology, physics, linguistics, sociology, to mention but a few. For this, mainly, the largest class of the hyperstructures, the Hv-structures, is used, which satisfy the weak axioms where the non-empty intersection replaces the equality and they are straightly related to fuzzy set theory. The fundamental relations connect the Hv-structures with the classical ones, moreover, they reveal new concepts as the Hv-fields. Hv-numbers are called the elements of an Hv-field and they are used in representation theory. We introduce the raised finite Hv-fields, and present some results and examples on 2 × 2 representations on them.

The generalized Hyers-Ulam-Rassias stability proposition in respect of the quadratic functional equation namely f (x + y + z) + f (x − y) + f (x − z) = f (x − y − z) + f (x + y) + f (x + z) is what is taken into account to be dealt with in this paper.

In this paper, estimation of snow particles velocity and snow-drift density by mathematical modeling is studied. The snow particles ow while modeling from fluid dynamic concepts and micro- continuum approach (couple stresses fluid [1]). The present approach is compared to conventional classical approach of logarithmic law of snow-drift density [2]. It is shown that, the present approach yield better results than that of conventional approach. The snow-drift density has been estimated by using momentum equation and then it compared to snow-drift density [3, 4].

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

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