<abstract xmlns="http://www.w3.org/1999/xhtml"><p> We prove that an hypersemigroup H is regular if and only, for any fuzzy subset f of H, we have f ≼ f ο 1 ο f and it is intra-regular if and only if, for any fuzzy subset f of H, we have f ≼1 ο f ο f ο 1. An hypersemigroup H is left (resp. right) quasi-regular if and only if, for any fuzzy subset f of H we have f ≼ 1 ο f ο 1 ο f (resp. f ≼ f ο 1 ο f ο 1) and it is semisimple if and only if, for any fuzzy subset f of H we have f ≼ 1 ο f ο 1 ο f ο 1. The characterization of regular and intra-regular hypersemigroups in terms of fuzzy subsets are very useful for applications. </p></abstract>

We prove that an hypersemigroup H is regular if and only, for any fuzzy subset f of H, we have f ≼ f ο 1 ο f and it is intra-regular if and only if, for any fuzzy subset f of H, we have f ≼1 ο f ο f ο 1. An hypersemigroup H is left (resp. right) quasi-regular if and only if, for any fuzzy subset f of H we have f ≼ 1 ο f ο 1 ο f (resp. f ≼ f ο 1 ο f ο 1) and it is semisimple if and only if, for any fuzzy subset f of H we have f ≼ 1 ο f ο 1 ο f ο 1. The characterization of regular and intra-regular hypersemigroups in terms of fuzzy subsets are very useful for applications.

A characterization of regular, intra-regular, left quasi-regular and semisimple hypersemigroups in terms of fuzzy sets

Pure Mathematics and Applications

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

We prove that an hypersemigroup H is regular if and only, for any fuzzy subset f of H, we have f ≼ f ο 1 ο f and it is intra-regular if and only if, for any...

A characterization of regular, intra-regular, left quasi-regular and semisimple hypersemigroups in terms of fuzzy sets

Published Online: Jul 14, 2017

Page range: 46 - 56

Received: Jun 20, 2016

DOI: https://doi.org/10.1515/puma-2015-0021

Keywords
hypersemigroup, fuzzy subset, regular, intra-regular, left quasi-regular, semisimple

© 2017

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

A characterization of regular, intra-regular, left quasi-regular and semisimple hypersemigroups in terms of fuzzy sets

Published Online: Jul 14, 2017

Page range: 46 - 56

Received: Jun 20, 2016

DOI: https://doi.org/10.1515/puma-2015-0021

Keywordshypersemigroup, fuzzy subset, regular, intra-regular, left quasi-regular, semisimple

© 2017

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

Keywords
hypersemigroup, fuzzy subset, regular, intra-regular, left quasi-regular, semisimple