Specification and optimization of fuzzy systems using convolution techniques

Abstract

Fuzzy logic is now widely accepted as a formal tool for describing control or decision-making processes that are based on incomplete, vague or uncertain information. This paper presents a new approach for the description and efficient computation of fuzzy rules based on fuzzy logic and also on convolution techniques. The fuzzy rules { R r } of the MISO considered are an extension of the zero-order Takagi–Sugeno fuzzy model and are given in the form of R r : If X 1 is A r1 and … and X N is A rN then z is c r , where X j are fuzzified input variables, A rj are fuzzy numbers which belong to the corresponding partition of unity { A rj } and c r is a nonfuzzy singleton term of output variable z. The global consideration of the fuzziness (imprecision) of each input X j and the fuzziness (vagueness) of the corresponding fuzzy partition { A rj } greatly simplifies the corresponding specification process and the involved matching computation. Two general fuzzy partitions are introduced: F-splines and φ-splines, both capture the fuzziness of input variables and fuzzy terms considered, and the smoothness constraints of outputs. As an application example, the control of an inverted pendulum is analyzed.