Evaluation of Quantified Statements Using Gradual Numbers

Abstract

Linguistic quantifiers are quantifiers defined by linguistic expressions like “around 5” or “most of,” and many types of linguistic quantifiers can be found in the literature (Diaz-Hermida, Bugarin, & Barro, 2003; Glockner, 1997, 2004a, 2004b; Losada, Díaz-Hermida, & Bugarín, 2006) (as semifuzzy quantifiers which allow modeling expressions like “there are twice as many men as women”). We limit this presentation to the original linguistic quantifiers defined by Zadeh (1983) and the two types of quantified statements he proposes. Such linguistic quantifiers allow an intermediate attitude between the conjunction (expressed by the universal quantifier ∀) and the disjunction (expressed by the existential quantifier ∃). Two types of quantified statements can be distinguished. A statement of the first type is denoted “Q X are A” where Q is a linguistic quantifier, X is a crisp set and A is a fuzzy predicate. Such a statement means that “Q elements belonging to X satisfy A.” An example is provided by “most of employees are well-paid” where Q is most of and X is a set AbstrAct