Definition and classification of semi-fuzzy quantifiers for the evaluation of fuzzy quantified sentences

This paper describes a classification of semi-fuzzy quantifiers that considerably improves the division between what Zadeh calls quantifiers of the first kind and those of the second kind. A number of cases are contemplated that are not habitually described in the literature on fuzzy quantification (e.g., comparative and exception quantifiers). Models are also defined for all the types of semi-fuzzy quantifiers framed in the classification. Thus in order to construct fuzzy quantifiers it is sufficient to apply a suitable quantifier fuzzification method. This paper also deals with the application of semi-fuzzy quantifiers and fuzzy quantifiers to fuzzy relations. The solution of this problem is of interest in various fields; amongst which, perhaps the most noteworthy is that of fuzzy databases.

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