A New Representation for the Fuzzy Systems

Representing Fuzzy Systems Universal Approximators

“…Using the sinusoidal inferences, the approximating function is comprised of sine/ cosine, and cross product terms. With appropriate designs [7,8,15], sinusoidal inferences can be further manipulated into an orthonormal set.…”

“…In the example of exponential subsystem inferences, the inference of the fuzzy system constitutes [7,8,15] a piecewise linear approximation to an exponential term.…”

“…. e 0 e The inferred output of subsystem   2 A will be [7,8,15]: The inferred output of subsystem   2 B is [7]: (14) where:…”

“…The equations are a pair of first-order, non-linear, differential equations. They are needed to describe [8] the dynamics of biological systems in which two species interact with each other.…”

“…The paper is organized as follows: the first section provides a brief review on product sum fuzzy inference and introduces the concepts of additive and multiplicative decomposable systems; the second section presents a subsystem inference representation; the next sections discuss the cases of polynomial, sinusoidal, orthonormal and other designs of subsystem inferences; the last section presents some conclusions on the matter. [7,8,15]. The inferred output is [7,8,15]:…”