FUZZY CONTROL AND ROUGH SETS

Zdzislaw Pawlak introduced the notion of rough sets [1]. It was a result of fundamental research on logical properties of information systems that are instances (snapshots) of relational databases. The theory of rough sets is concerned with the classificatory analysis of imprecise, uncertain or incomplete information or knowledge expressed in terms of data acquired from experience. Over the past one and half decade the theory has evolve into a new technology. It has proven to be a viable technique in data mining, especially extracting rules from databases. In this paper, we explore, however, another direction, intelligent control. As in [2], [3], [4], rough set theory, fuzzy logic control, and modern differential geometric view of non-linear dynamic systems are integrated into one mathematical formalism, called rough logic government. Under this formalism, fuzzy logic can be viewed as a methodology of constructing solutions of system equations, without explicitly constructed system models. Equivalently, fuzzy logic chooses to model the control subsystem directly. Among others, it allows us to investigate simple kind of Lyapunov stability problem [5] that is a relatively unexplored area of fuzzy logic control. A shipmounted satellite tracking antenna is used to illustrate the notion.