Statistical Techniques for Rough Set Data Analysis
Günther Gediga, Ivo Düntsch · Studies in fuzziness and soft computing · 2000
Concept forming and classification in the absence of complete or certain information has been a major concern of artificial intelligence for some time. Traditional “hard” data analysis based on statistical models or are in many cases not equipped to deal with uncertainty, relativity, or non—monotonic processes. Even the recently popular “soft” computing approach with its principal components “... fuzzy logic, neural network theory, and probabilistic reasoning” [16] uses quite hard parameters outside the observed phenomena, e.g. representation and distribution assumptions, prior probabilities, beliefs, or membership degrees, the origin of which is not always clear; one should not forget that the results of these methods are only valid up to the — stated or unstated — model assumptions. The question arises, whether there is a step in the modelling process which is informative for the researcher and, at the same time, does not require additional assumptions about the data. To make this clearer, we follow [9] in assuming that a data model consists of1. A domain D of interest. 2. An empirical system E, which consists of a body of data and relations among the data, and a mapping e : D → E, called operationalisation. 3. A (structural or numerical) model M, and a mapping m : ε → M, called representation.