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

Abstract

Based on hard and soft computing, an integrated design process, called rough logic government, is proposed. In this process, fuzzy logic is viewed as a methodology of a grand scale interpolation based on qualitative information. The design process is a sequence of transformations of mathematical models. It starts with a symbolic model that describes the control system in terms of predicates in rough logic. Predicates may include not only the usual linguistic rules, but also some hard computing information. These predicates are derived from either (1) experts' experience or (2) some training data using rough set methodology (rules mining). The next step is a transformation of the symbolic model into a fuzzy model, called a possible fuzzy world. It is accomplished by replacing every symbol that represents certain real world phenomena with a membership function that represents the same phenomena according to a fuzzy view. In formal logic, the symbolic model is called a theory and the transformation an interpretation of the theory. Of course, interpretations are usually not unique. The collection of all such possible fuzzy worlds is called a rough fuzzy model. It is a highly structured set, and can be treated as a differential geometric object. Using some inference methods, each possible fuzzy world is transformed into a “virtual” trajectory or integral submanifold which is a candidate for the solution of the unconstructed system equations. So a rough fuzzy model will produce a family of candidates. To verify and validate these candidates, the method of evolutionary computing is adopted. Some of these “virtual” objects may actually become “real world” trajectories or integral submanifolds, which are the design goal. Several new applications are identified.