The fuzzy-rough set (FRS) methodology, as a useful tool to handle discernibility and fuzziness, has been widely studied. Some researchers studied on the rough approximation of fuzzy sets, while some others focused on studying one application of FRS: attribute reduction (i.e., feature selection). However, constructing classifier by using FRS, as another application of FRS, has been less studied. In this paper, we build a rule-based classifier by using one generalized FRS model after proposing a new concept named as ¿consistence degree¿ which is used as the critical value to keep the discernibility information invariant in the processing of rule induction. First, we generalized the existing FRS to a robust model with respect to misclassification and perturbation by incorporating one controlled threshold into knowledge representation of FRS. Second, we propose a concept named as ¿consistence degree¿ and by the strict mathematical reasoning, we show that this concept is reasonable as a critical value to reduce redundant attribute values in database. By employing this concept, we then design a discernibility vector to develop the algorithms of rule induction. The induced rule set can function as a classifier. Finally, the experimental results show that the proposed rule-based classifier is feasible and effective on noisy data.

In this article a variation of fuzzy Petri net (FPN) model is proposed to accommodate for the possibility of mapping fuzzy production rule (FPR) having different threshold values in their propositions into FPN. the purpose of assigning a different threshold value for each proposition in the FPR and of using the rule checking and evaluation method proposed here is to prevent misfiring of the rule, which can result with other methods; the purpose of having variation of FPN model is to capture and represent more information of FPR in the FPN model. the rule checking and evaluation method is an enhancement of the approach proposed by Yeung (D. S. Yeung et al., Proceedings of the 6th International Conference on System Research Informatics and Cybernetics, Germany, 1992). As mentioned by the authors, the degree of subsethood between two vectors is the basis of the method. the subsethood method will first be used to make certain that each input value for the proposition in the antecedent is greater than or equal to its corresponding threshold value. When such condition holds, the subsethood method is used to infer the degree of truth of the consequent of the rule. an enhanced fuzzy reasoning algorithm is included. Comparison of this method with other methods is presented. Future research work in determining acceptable threshold values and certainty factors is addressed. © 1994 John Wiley & Sons, Inc.