Fuzzy quantifiers: a linguistic technique for data fusion

Fuzzy quantifiers like “few”, “almost”, “about” and many others abound in natural language. They are used by humans for describing uncertain facts, quantitative relations and processes. An adequate contradiction-free computer-operational implementation of these quantifiers would provide a class of powerful yet human-understandable operators both for aggregation and fusion of data but also for steering the fusion process on a higher level through a safe transfer of expert-knowledge expressed in natural language. In this chapter we show by a number of examples of image data that the traditional theories of fuzzy quantification (Sigma-count, FE-count, FG-count and OWA-approach) are linguistically inconsistent and produce implausible results in many common and relevant situations. To overcome the deficiencies of these approaches, we developed a new theory of fuzzy quantification, DFS, that rests on the foundation of the theory of generalised quantifiers TGQ. It provides a linguistically sound basis for the most important case of multi-place quantification with proportional quantifiers. Its axiomatic basis guarantees compliance with linguistic adequacy considerations. The underlying models generalize the basic FG-count approach/Sugeno integral and the basic OWA approach/Choquet integral. We have also developed an efficient implementation based on histogram computations. At the end of the chapter the power of the theory and its implementation are illustrated by image data examples.