Ever since the first hybrid fuzzy rough set model was proposed in the early 1990?s, many researchers have focused on the definition of the lower and upper approximation of a fuzzy set by means of a fuzzy relation. In this paper, we review those proposals which generalize the logical connectives and quantifiers present in the rough set approximations by means of corresponding fuzzy logic operati...

Although Dubois and Prade’s fuzzy elements and gradual sets cannot be represented as objects or fuzzy predicates in first-order versions of known systems of propositional fuzzy logic, they can be represented in higher-order fuzzy logic. However, this logical representation does not simplify handling these notions, compared to informal semantic methods of traditional fuzzy mathematics. Finding a...

In this paper, we construct two fuzzy sets using the notions of level subsets and strong level subsets of a given fuzzy set in a ring R. These fuzzy sets turn out to be identical and provide a universal construction of a fuzzy ideal generated by a given fuzzy set in a ring. Using this construction and employing the technique of strong level subsets, we provide the shortest and direct fuzzy set ...

this paper continues the study of the connection between hyper- groups and fuzzy sets, investigating the length of the sequence of join spaces associated with a hypergroup. the classes of complete hypergroups and of 1-hypergroups are considered and analyzed in this context. finally, we give a method to construct a nite hypergroup with the strong fuzzy grade equal to a given natural number