From Rough through Fuzzy to Crisp Concepts: Case Study on Image Color Temperature Description

Abstract

This chapter proposes a framework for designing interval-based classifiers for fuzzy categories based on rough information systems. The information systems is given by joining objective measurements of a quantized scalar feature t for a class of objects with subjective decision (votes) regarding the category c, to witch objects belong. Using the roughness degree, we estimate at sparse points unknown fuzzy membership functions for n categories. Having such sparse membership functions and original information system, we find a family of optimal partitions of features range for two important cost functions. In practice, only interval partitions are useful for fast decision. The algorithm generating optimal intervals is given and applied to extracting of image color temperature descriptions.