Mathematical justification for the fuzzy set modeling of uncertain systems

Current difficulties in combining different forms of knowledge about a system stem from the fact that existing system modeling and control design tools can process only one form of knowledge. A horizontal combination of different forms of knowledge can be possible only if a unified representation of knowledge is developed offering an integrated framework for knowledge representation and processing. The objective of this paper is twofold: 1) the paper provides a justification for the fuzzy set modeling of systems with parametric uncertainty by showing that uncertainty induces ambiguity in system analysis that can be resolved using fuzzy set modeling; 2) it presents a preliminary development of a different approach to fuzzy representation of uncertain mathematical models, where the fuzzy model is described by Mamdani-type fuzzy IF-THEN rules