Primary-fuzzy-sets-based normal fuzzy reasoning methodology and its applications

Abstract

Based on more useful and more heuristic primary fuzzy sets contained by conventionally used fuzzy sets, a novel normal fuzzy reasoning methodology is proposed in order to overcome the weakness of many conventional fuzzy systems. Analysis indicated that the compositional rule of inference Zadeh [IEEE Transactions on Systems, Man, and Cybernetics, 3, 28-44 (1973)] and related defuzzification schemes are not effective since they may generate unreasonable results such as the constant-speed problem and the unstable cart-pole problem. The new normal fuzzy system is a generalized framework of many conventional fuzzy systems such as Takagi-Sugeno's fuzzy system Sugeno and Yasukawa [IEEE Transactions on Fuzzy Systems, 1, 7-30 (1993)] and Takagi and Sugeno [IEEE Transactions on Systems, Man, and Cybemetics, SMC-15, 116-132 (1985)], Wang's fuzzy system Wang [Adaptive Fuzzy Systems and Control Design and Stability Analysis, Prentice-Hall, Englewood Cliffs, 1994], Lin's fuzzy system Lin [Neural Fuzzy Control Systems with Structure and Parameter Leaming, World Scientific, Singapore, 1994] and the fuzzy system using Yager's level set method Figueirdo et al. [IEEE Transactions on Fuzzy Systems, 1, 156-159 (1993)]. According to the normal fuzzy reasoning methodology, Takagi-Sugeno's fuzzy system can be constructed directly from high-level fuzzy rules without using the complex parameter estimation algorithm Lin [Neural Fuzzy Control Systems with Structure and Parameter Leaming, World Scientific, Singapore, 1994] and Sugeno and Yasukawa [IEEE Transactions on Fuzzy Systems, 1, 7-30 (1993)]. Simulations of the constant-speed problems, the fuzzy multiplications and the cart-pole system strongly indicated that the new normal fuzzy system is more effective and more robust than many conventional fuzzy systems. Therefore, the normal fuzzy reasoning methodology can be used to efficiently construct robust fuzzy systems.