Fuzzy System with Positive and Negative Rules

A typical rule in the rule base of a traditional fuzzy system contains only positive rules (weight is positive). In this case, mining algorithms only search for positive associations like “IF A Then do B”, while negative associations such as “IF A Then do not do B” are ignored. The concept of fuzzy sets was introduced by Zadeh in 1965 as a mathematical tool able to model the partial memberships. Since then, fuzzy set theory (Zadeh, 1973) has found a promising field of application in the domain of image processing, as fuzziness is an intrinsic property of images and the natural outcome of many image processing techniques. The interest in using fuzzy rule-based models arises from the fact that they provide a good platform to deal with noisy, imprecise or incomplete information which is often handled exquisitely by the human-cognition system. In a fuzzy system, we can generate fuzzy rule-bases of one of the following three types: (a) Fuzzy rules with a class in the consequent (Abe & Thawonmas, 1997; Gonzalez & Perez, 1998). This kind of rule has the following structure: