Interpreting and extracting fuzzy decision rules from fuzzy information systems and their inference

Information systems, which contain only crisp data, precise and unique attribute values for all objects, have been widely investigated. Due to the fact that in realworld applications imprecise data are abundant, uncertainty is inherent in real information systems. In this paper, information systems are called fuzzy information systems, and formalized by (objects; attributes; f), in which f is a fuzzy set and expresses some uncertainty between an object and its attribute values. To interpret and extract fuzzy decision rules from fuzzy information systems, the meta-theory based on modal logic proposed by Resconi et al. is modified. The modified meta-theory not only expresses uncertainty between objects and their attributes, but also uncertainty in the process of recognizing fuzzy information systems. In addition, according to perception computing (proposed by Zadeh), granules of fuzzy information systems can be represented by fuzzy decision 0020-0255/$ see front matter 2005 Elsevier Inc. All rights reserved. doi:10.1016/j.ins.2005.04.003 * Corresponding author. Tel.: +860 288 7600760; fax: +860 288 7600764. E-mail address: [email protected] (Z. Pei). 1870 Z. Pei et al. / Information Sciences 176 (2006) 1869–1897 rules, so that, fuzzy inference methods can be used to obtain the decision attribute of a new object. Finally, a novel way of combining evidences based on the modified metatheory is introduced, which extends the concept of combining evidences based on Dempster–Shafer theory. 2005 Elsevier Inc. All rights reserved.