On choosing the fuzziness parameter for identifying TS models with multidimensional membership functions
Andreas Kroll · 2011
Fuzzy clustering is a well-established method for identifying the structure/fuzzy partition-ing of Takagi-Sugeno (TS) fuzzy models. The clustering algorithms require choosing the fuzziness parameter m. Prior work in the area of pattern recognition shows, that a suit-able choice of m is application- dependent. Yet, the default of m=2 is commonly chosen. This paper examines the suitable choice of m for identifying TS models. The focus is on models that use the classifiers resulting from fuzzy clustering as multi-dimensional mem-bership functions or their projection and approximation. At first, the differentiability and grouping properties of the fuzzy classifiers are analyzed to make a general recommenda-tion of choosing m∈(1;3). Besides, the effect of the cluster number c on the classification fuzziness is examined. Finally, requirements that are specific to TS modeling are intro-duced, which narrow down the suitable range for m. Building on algorithm analysis and four case studies (function approximation, a vehicle engine and an axial compressor ap-plication for nonlinear regression), it is demonstrated that choosing m∈(1;1.3) for local and m∈(1;1.5) for global estimation will typically provide for good results. 1