Abstract
The new concept of the fuzzy filter degree was given by means of the implication operator, which enables to measure a degree to which a fuzzy subset of a BL-algebra is a fuzzy filter. In this paper, we put forward several equivalent characterizations of the fuzzy filter degree by studying its properties and the relationship with level cut sets. Furthermore, we study the fuzzy filter degrees of the intersection and fuzzy direct products of fuzzy subsets and investigate the fuzzy filter degrees of the image and the preimage of a fuzzy subset under a homomorphism.
Highlights
As we know, nonclassical logic algebras are one of the focuses in the basic study of artificial intelligence
In the application of fuzzy theory, a series of concepts of degree were introduced to depict the level of similarity among objects. When these thoughts are applied in the research of fuzzy logic algebras, the question is how to measure the degree to which a fuzzy subset is a fuzzy logic algebra
Shi proposed the concept of fuzzy subgroup degree in the paper to depict the degree to which a fuzzy subset is a fuzzy subgroup
Summary
Nonclassical logic algebras are one of the focuses in the basic study of artificial intelligence. In the application of fuzzy theory, a series of concepts of degree were introduced to depict the level of similarity among objects When these thoughts are applied in the research of fuzzy logic algebras, the question is how to measure the degree to which a fuzzy subset is a fuzzy logic algebra. Shi proposed the concept of fuzzy subgroup degree in the paper to depict the degree to which a fuzzy subset is a fuzzy subgroup Using this idea, Wang, Shi, Liao, and others have done a lot of work in recent years and got a lot of good results [4,5,6,7,8,9,10,11,12,13,14,15].
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