Evaluation of quantified propositions in generalized models of fuzzy quantification

摘要

The quantifiers found in natural language (NL) are not restricted to the absolute and proportional types usually considered in fuzzy set theory. In order to handle the wealth of NL quantifiers including quantifiers of exception ("all except about ten"), cardinal comparatives ("many more than") and others, it is necessary to consider generalized models of fuzzy quantification. Starting from an analysis in terms of semi-fuzzy quantifiers (specifications) and fuzzification mechanisms (prototypical models), the sequel develops a precise notion of generalized models which rests on a formalization of linguistic adequacy criteria. It also presents concrete examples of such models which generalize the FG-count and OWA approaches to fuzzy quantification. In order to let applications profit from the improved coverage and coherence of interpretations, the sequel is especially concerned with the issue of practical implementation. It presents efficient methods for implementing the main types of quantifying propositions which demonstrate the computational feasibility of the proposed models.