Affiliations: [a] School of Mathematics and Statistics, Anyang Normal University, Anyang, China
| [b] School of Information and Mathematics, Yangtze University, Jingzhou, China
| [c] School of Mathematics, Northwest University, Xi’an, China
Correspondence:
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Corresponding author. Kuanyun Zhu, School of Information and Mathematics, Yangtze University, Jingzhou 434023, China, E-mail: [email protected].
Abstract: The concepts of fuzzy weak hyper deductive systems and fuzzy sup-weak hyper deductive systems of hyper equality algebras as generalizations of fuzzy deductive systems are initiated in the paper. Moreover, several related properties and characterizations of fuzzy weak hyper deductive systems and fuzzy sup-weak hyper deductive systems are investigated, and the relationships between fuzzy sup-weak hyper deductive systems of homomorphic hyper equality algebras are also presented based on the introduced homomorphism in hyper equality algebras. It is known that a fuzzy weak hyper deductive system is a fuzzy set, while the converse is not true in general. In order to measure the degree of a fuzzy set becoming a fuzzy weak hyper deductive system, we introduce the notion of fuzzy weak hyper deductive system degrees, and put forward some equivalent characterizations of the fuzzy weak hyper deductive system.
