Nonsingleton fuzzy logic systems: theory and application
- 1 February 1997
- journal article
- Published by Institute of Electrical and Electronics Engineers (IEEE) in IEEE Transactions on Fuzzy Systems
- Vol. 5 (1) , 56-71
- https://doi.org/10.1109/91.554447
Abstract
In this paper, we present a formal derivation of general nonsingleton fuzzy logic systems (NSFLSs) and show how they can be efficiently computed. We give examples for special cases of membership functions and inference and we show how an NSFLS can be expressed as a "nonsingleton fuzzy basis function" expansion and present an analytical comparison of the nonsingleton and singleton fuzzy logic systems formulations. We prove that an NSFLS can uniformly approximate any given continuous function on a compact set and show that our NSFLS does a much better job of predicting a noisy chaotic time series than does a singleton fuzzy logic system (FLS).Keywords
This publication has 25 references indexed in Scilit:
- Back-propagation fuzzy system as nonlinear dynamic system identifiersPublished by Institute of Electrical and Electronics Engineers (IEEE) ,2003
- Fuzzy systems as universal approximatorsPublished by Institute of Electrical and Electronics Engineers (IEEE) ,2003
- Fuzzy neural network with fuzzy signals and weightsInternational Journal of Intelligent Systems, 1993
- Fuzzy basis functions, universal approximation, and orthogonal least-squares learningIEEE Transactions on Neural Networks, 1992
- Kolmogorov's theorem and multilayer neural networksNeural Networks, 1992
- Generating fuzzy rules by learning from examplesIEEE Transactions on Systems, Man, and Cybernetics, 1992
- Kolmogorov's Theorem Is RelevantNeural Computation, 1991
- Arbitrary nonlinearity is sufficient to represent all functions by neural networks: A theoremNeural Networks, 1991
- Determining Lyapunov exponents from a time seriesPhysica D: Nonlinear Phenomena, 1985
- On the structure of continuous functions of several variablesTransactions of the American Mathematical Society, 1965