A Framework for Evaluating Approaches to Fuzzy Quantification

Fuzzy linguistic quantifiers – operators intended to model vague quantifying expressions in natural language like “almost all” or “few” – have gained importance as operators for information combination and data summarisation. They are particularly appealing because of their ease-of-use: people are familiar with these operators, which can be applied for technical aggregation purposes in the same way as in everyday language. Because of the irregular and rather intangible phenomena it tries to model – viz, those of imprecision and uncertainty – fuzzy logic should be particularly specific about its foundations. However, work on mathematical foundations and linguistic justification of fuzzy linguistic quantifiers is scarce. In the paper, we propose a framework for evaluating approaches to fuzzy quantification which relates these to the logico-linguistic theory of generalized quantifiers (TGQ). By reformulating these approaches as fuzzification mechanisms, we can investigate preservation and homomorphism properties of the fuzzification mappings which express important aspects of the meaning of natural language quantifiers.1 1Parts of this report will be published in [11] (discussion of -count approach) and [10] (discussion of OWA approach).