A rough logic formalism for fuzzy controllers: A hard and soft computing view

21 6 Conclusions Rough logic government in essence a mathematical model using rough logic to formulate the classical fuzzy control design theory. It give the informal practices a mathematical formalism. The "new" ingredients are the rule mining using rough set theory in Group 0 (See Section 3), evolutionary tuning using evolutionary computing in Group 5 and diierential geometric view of the whole process. We will report on more "serious" applications in the near future. The selection of a \correct" set of linguistic rules plays a very essential role in classical FLC design. One way to improve that is to invite more advice from domain experts. If each expert gives us a diierent set of linguistic rules, then how can we integrate these diierent sets of opinions productively? In other words, are there methodology to select the \best" portion out of each expert's advice, and to combine them coherently? We observed that if the experts are \perfect," then such a collection of sets of linguistic rules has to satisfy certain compatibility conditions. In fact, they should form an inverse limit systems 7,8]. Based on such observations, we believe that we can use evolutionary computing to select the \best components" from each expert's rules, and integrate them coherently. A more detail study will be reported in near future. 5.2 Integration of FLCs-Large Scale Applications The mechanic is similar to last subsection. Instead of the sets of linguistic rules of the same FLC, we may consider the sets of linguistic rules from diierent FLCs. In 5.1, we have a hierarchy of linguistic rules of the same FLC. Now we have a hierarchy of diierent FLCs. So the same procedure can be applied. This is the most important ingredient in large scale applications. We will report on the study of such integration in near future. 5.3 Stability Problems Rough logic government provide us an adequate mathematical structure to manage tubular neighborhoods of control functions. A solution with given initial condition forms an integral submanifold. According to Lyapunov 19], the stability problem is to investigate the behavior of the solutions lying within a neighborhood of a given integral manifold; such a neighborhood is called a tubular neighborhood 20]. We will reports the ndings in next paper.