We study the problem of classification as this is presented in the context of data mining. Among the various approaches that are investigated, we focus on the use of Fuzzy Logic for pattern classification, due to its close relation to human thinking. More specifically, this paper presents a heuristic fuzzy method for the classification of numerical data, followed by the design and the implement...

We prove that three independent fuzzy systems can uniformly approximate Bayesian posterior probability density functions by approximating the prior and likelihood probability densities as well as the hyperprior probability densities that underly the priors. This triply fuzzy function approximation extends the recent theorem for uniformly approximating the posterior density by approximating just...

Wang and Mendel proved (1991) that fuzzy systems with product inference, cen-troid defuzziication, and everywhere positive membership functions (in particular, Gaus-sians, Wang, 1992) are capable of approximating any real continuous control function on a compact set to arbitrary accuracy. Kosko (1992) proved that fuzzy systems, in which membership functions have compact support, and combination...

One of the reasons why fuzzy methodology is successful is that fuzzy systems are universal approximators, i.e., that we can approximate an arbitrary continuous function within any given accuracy by a fuzzy system. In some practical applications (e.g., in control), it is desirable to approximate not only the original function, but also its derivatives (so that, e.g., a fuzzy control approximatin...

Recent studies have shown that both Mamdani-type and Takagi-Sugeno-type fuzzy systems are universal approximators in that they can uniformly approximate continuous functions defined on compact domains with arbitrarily high approximation accuracy. In this paper, we investigate necessary conditions for general multiple-input single-output (MISO) Mamdani fuzzy systems as universal approximators wi...

This study presents a novel controller of magnetic levitation system by using new neuro-fuzzy structures which called flexible neuro-fuzzy systems. In this type of controller we use sliding mode control with neuro-fuzzy to eliminate the Jacobian of plant. At first, we control magnetic levitation system with Mamdanitype neuro-fuzzy systems and logical-type neuro-fuzzy systems separately and then...

In this brief note we make three remarks concerning adaptive implementations of neural networks and fuzzy systems. First, we bring to the readers attention the fact that the potential power of these systems as function approximators is lost when, as done in recently published work, the adjustable parameters are only the linear combination weights of the basis functions. Second, we show that the...

OBJECTIVES To develop a neuro-fuzzy system to predict the presence of prostate cancer. Neuro-fuzzy systems harness the power of two paradigms: fuzzy logic and artificial neural networks. We compared the predictive accuracy of our neuro-fuzzy system with that obtained by total prostate-specific antigen (tPSA) and percent free PSA (%fPSA). METHODS The data from 1030 men (both outpatients and ho...