An overview of fuzzy quantifiers. (I). Interpretations
Fuzzy Sets and SystemsPublished 1 April 1998
Yaxin Liu, Etienne Kerre
Citations119
SJR quartileQ1
SJR score0.75
SNIP1.25
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TL;DR
Different to classical logic, various semantics of propositions in fuzzy logic fall into different frameworks which are known as the possibility distribution-based reasoning system and the many-valued fuzzy logics.
Abstract
Quantification is an important topic in fuzzy theory and its applications. An overview is presented for quantification in fuzzy theory. After a brief review of quantifiers in first-order logic, two approaches of generalizing quantifiers are given, the algebraic method and the substitution method. By distinguishing the fuzziness of predicates and quantifiers, various approaches to quantification in fuzzy logic can be organized. Quantifiers in first-order logic can be generalized in crisp sense, and these generalized quantifiers can also be applied to fuzzy sets. Moreover, quantifiers themselves can be fuzzy, i.e., they can only be represented by a fuzzy set. These different kinds of quantifications are identified. Quantifiers relate close to the concept of the cardinality of a fuzzy set, which is summarized before investigating fuzzy quantifications. Different to classical logic, various semantics of propositions in fuzzy logic fall into different frameworks which are known as the possibility distribution-based reasoning system and the many-valued fuzzy logics. Accordingly, numerical and possibilistic interpretation explored in literature are reviewed conforming to these two frameworks.
Keywords
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