Evaluation of methods in fuzzy data analysis

Abstract

In the preceding two chapters, several procedures in fuzzy data analysis have been discussed, but more from the point of view of descriptive data analysis and of the inner structure of the procedures. The aim of the present chapter is to evaluate, under specific assumptions, results of fuzzy data analysis and, if possible, the procedures behind these results. Hence we look, in a certain sense, to the procedures from outside and try to compare one with each other. This is a step towards a normative theory for fuzzy data analysis and requires a modelling of the environment of the fuzzy data. Unfortunately, such a normative theory is at its beginning. Therefore we are not able to evaluate all the useful and well-tested procedures presented in the Chapters 5 and 6. We are forced to restrict ourselves to some relatively simple but transparent cases. Taking into account this fact, we have decided to introduce the different ideas for an evaluation in a separate section (see Section 7.1), allowing for a quick overview and for an easy comparison of the principles. Concrete results for more or less specific cases the reader can find in the Sections 7.2 to 7.5 dealing with truth-based evaluation methods for parametric setups and with evaluation methods if the data are assumed to be generated by possibilistic (Section 7.3), probabilistic (Section 7.4) or general F-measure mechanism (Section 7.5).