Štěpán Křehlík

EL-hyperstructures revisited

In the paper we study ordered sets in which multi-valued aspects are important. To be more precise, we focus on EL-hyperstructures, i.e. semihypergroups constructed from partially ordered semigroups. We show that when certain slight modifications of the concept (motivated by real-life situations) are introduced, the applicability of this model increases as we are able to reduce the number of its assumptions, bypass some existing problems and at the same time apply the idea in a greater number of contexts.

From lattices to H_v - matrices

Abstract In this paper we study the concept of sets of elements, related to results of an associative binary operation. We discuss this issue in the context of matrices and lattices. First of all, we define hyperoperations similar to those used when constructing hyperstructures from quasi-ordered semigroups. This then enables us to show that if entries of matrices are elements of lattices, these considerations provide a natural link between matrices, some basic concepts of the hyperstructure theory including Hv-rings and Hv-matrices and also one recent construction of hyperstructures.

A hyperstructure model of underwater wireless sensor network (UWSN) design

We discuss some challenges of underwater wireless sensor networks (UWSN) and show that in the architecture of commonly used types of UWSNs certain hyperstructure concepts, which make use of ordering, can be naturally identified.We discuss some challenges of underwater wireless sensor networks (UWSN) and show that in the architecture of commonly used types of UWSNs certain hyperstructure concepts, which make use of ordering, can be naturally identified.