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L-fuzzy cosets in universal algebras

  • Gezahagne Mulat Addis EMAIL logo
Published/Copyright: June 8, 2021
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Abstract

In this paper, we introduce the notion of fuzzy costs in a more general context, in universal algebra by the use of coset terms. We study the structure of fuzzy cosets by applying the general theory of algebraic fuzzy systems. Fuzzy cosets generated by a fuzzy set are characterized in different ways. It is also proved that the class of fuzzy cosets determined by an element forms an algebraic closure fuzzy set system. Finally, we give a set of necessary and sufficient conditions for a given variety of algebras to be congruence permutable by applying the theory of fuzzy cosets.

MSC 2010: 08A30; 08A72; 08B99

Acknowledgement

The author would like to thank the anonymous referee whose comments improved the original version of this manuscript.

  1. (Communicated by Anatolij Dvurečenskij)

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Received: 2020-04-09
Accepted: 2020-07-03
Published Online: 2021-06-08
Published in Print: 2021-06-25

© 2021 Mathematical Institute Slovak Academy of Sciences

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