Inference in Fuzzy Signature Based Models

Abstract

The concept of fuzzy signatures was introdneed to help model the many complex and weil structured problems, where a hierarchical structure within the observed data is present This means that one or several components of the structure can be determined at a higher level by a subtree of other components. In this way, the data components can be represented in tree form. By examining the problem, an arbitrary structure belonging to the data set can be deternlined. Due to the tact that some components might be missing from a data element, the actual tree structures of the data may slightly differ. So that these data can be evaluated and compared, aggregation operators are given for each node in the arbitrary structure for the purpose of modifying the stmcture. To model problems with this type of dataset, fuzzy signature based rules can be constructed. lnferring a coneiusion from such a model is a key issue. In this paper fuzzy signature based rule bases will be introduced, then the generalization of the widely used Mamdani-type fuzzy inference system for fuzzy signature based rules will be presented step-by-step. Furthermore, a working software implementation of the generalized Mamdani-type inference systems will be presented. The software will be demonstrated through a possible application of the system on a realistic example. First, the problem's fuzzy signature model will be constructed, and then the process of inference for an observation wi th some missing data components will be shown.