Hypersemigroups and Fuzzy Hypersemigroups

Authors

  • Niovi Kehayopulu Professor Docent Dr. University of Athens

Keywords:

Hypersemigroup, right (left) ideal, bi-ideal, fuzzy right (left) ideal, fuzzy bi-ideal, regular, intra-regular, left (right) quasi-regular, semisimple

Abstract

The aim is to show that the theory of hypersemigroups and the theory of fuzzy hypersemigroups are parallel to each other, in the following sense: An hypersemigroupH is intra-regular, for example, if and only if ABBA for every right ideal A and every left ideal B of H. And an hypersemigroupH is intra-regular if and only if fggf for every fuzzy right ideal f and every fuzzy left ideal g of H. An hypersemigroupH is left quasi-regular if and only if ABAB for every ideal A and every nonempty subset B of H. And an hypersemigroupH is left quasi-regular if and only if fgfg for every fuzzy ideal f and every fuzzy subset g of H.

Author Biography

  • Niovi Kehayopulu, Professor Docent Dr. University of Athens
    Professor Docent Dr. University of Athens, Department of Mathmatics, 15784 Panepistimiopolis, Greece

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Published

2017-11-02

Issue

Section

Algebra

How to Cite

Hypersemigroups and Fuzzy Hypersemigroups. (2017). European Journal of Pure and Applied Mathematics, 10(5), 929-945. https://www.ejpam.com/index.php/ejpam/article/view/3049