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Fuzzy deductive systems of RM algebras

Veröffentlicht/Copyright: 10. Dezember 2020
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Abstract

The theory of fuzzy deductive systems in RM algebras is developed. Various characterizations of fuzzy deductive systems are given. It is proved that the set of all fuzzy deductive systems of a RM algebra đť’ś is a complete lattice (it is distributive if đť’ś is a pre-BBBCC algebra). Some characterizations of Noetherian RM algebras by fuzzy deductive systems are obtained. In pre-BBBZ algebras, the fuzzy deductive system generated by a fuzzy set is constructed. Finally, closed fuzzy deductive systems are defined and studied. It is showed that in finite CI and pre-BBBZ algebras, every fuzzy deductive system is closed. Moreover, the homomorphic properties of (closed) fuzzy deductive systems are provided.

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Received: 2019-10-20
Accepted: 2020-03-30
Published Online: 2020-12-10
Published in Print: 2020-12-16

© 2020 Mathematical Institute Slovak Academy of Sciences

Heruntergeladen am 16.12.2025 von https://www.degruyterbrill.com/document/doi/10.1515/ms-2017-0431/html
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