<abstract xmlns="http://www.w3.org/1999/xhtml"><p>In this paper, we study the reducibility property of special hyper-groups, called Corsini hypergroups, named after the mathematician who introduced them. The concept of reducibility was introduced by Jantosciak, who noticed that it can happen that hyperproduct does not distinguish between a pair of elements. He defined a certain equivalences in order to identify elements which play the same role with respect to the hyperoperation. First we will determine specific conditions under which the Corsini hypergroups are reduced. Next, we will present some properties of these hypergroups necessary for studying the fuzzy reducibility property. The fuzzy reducibility will be considered with respect to the grade fuzzy set μ̃, used for defining the fuzzy grade of a hypergroup. Finally, we will study the reducibility and the fuzzy reducibility of the direct product of Corsini hypergroups.</p></abstract>

In this paper, we study the reducibility property of special hyper-groups, called Corsini hypergroups, named after the mathematician who introduced them. The concept of reducibility was introduced by Jantosciak, who noticed that it can happen that hyperproduct does not distinguish between a pair of elements. He defined a certain equivalences in order to identify elements which play the same role with respect to the hyperoperation. First we will determine specific conditions under which the Corsini hypergroups are reduced. Next, we will present some properties of these hypergroups necessary for studying the fuzzy reducibility property. The fuzzy reducibility will be considered with respect to the grade fuzzy set μ̃, used for defining the fuzzy grade of a hypergroup. Finally, we will study the reducibility and the fuzzy reducibility of the direct product of Corsini hypergroups.

Reducibility in Corsini hypergroups

Analele ştiinţifice ale Universităţii "Ovidius" Constanţa. Seria Matematică

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

{"article-title":"Reducibility in Corsini hypergroups"}

In this paper, we study the reducibility property of special hyper-groups, called Corsini hypergroups, named after the mathematician who introduced them. The...

Reducibility in Corsini hypergroups

Published Online: Apr 13, 2021

Page range: 93 - 109

Received: May 15, 2020

Accepted: Jul 07, 2020

DOI: https://doi.org/10.2478/auom-2021-0007

Keywords
Hypergroup, equivalence relations, reducibility, Corsini hypergroups

© 2021 Milica Kankaras, published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

Reducibility in Corsini hypergroups

Published Online: Apr 13, 2021

Page range: 93 - 109

Received: May 15, 2020

Accepted: Jul 07, 2020

DOI: https://doi.org/10.2478/auom-2021-0007

KeywordsHypergroup, equivalence relations, reducibility, Corsini hypergroups

© 2021 Milica Kankaras, published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

Keywords
Hypergroup, equivalence relations, reducibility, Corsini hypergroups