Ordered fuzzy numbers that make possible to deal with fuzzy inputs quantitatively, exactly in the same way as with real numbers, are defined together with four algebraic operations. For defuzzyfication operators that play the main role when dealing with fuzzy controllers and fuzzy inference systems an approximation formula is given. In order to determine it when a training set is given a dedica...

We suggest the use of piecewise monotonic interpolations to approximate and represent a fuzzy number (or interval) and to derive a procedure to control the absolute error associated to the arithmetic operations (+,−, ·, :) between fuzzy numbers, in order to reduce the distance between the true result of the operation and its approximation. The monotonic functions are then used to define a param...

NeuroFAST is an on-line fuzzy modeling learning algorithm, featuring high function approximation accuracy and fast convergence. It is based on a first-order Takagi-Sugeno-Kang (TSK) model, where the consequence part of each fuzzy rule is a linear equation. Structure identification is performed by a fuzzy adaptive resonance theory (ART)-like mechanism, assisted by fuzzy rule splitting and adding...

most of the researches in the domain of fuzzy number comparisons serve the fuzzy number ordering purpose. for making a comparison between two fuzzy numbers, beyond the determination of their order, it is needed to derive the magnitude of their order. in line with this idea, the concept of inequality is no longer crisp however it becomes fuzzy in the sense of representing partial belonging or de...

The problem to find the nearest trapezoidal approximation of a fuzzy number with respect to a well-knownmetric, which preserves the expected interval of the fuzzy number, is completely solved. The previously proposed approximation operators are improved so as to always obtain a trapezoidal fuzzy number. Properties of this new trapezoidal approximation operator are studied. © 2007 Elsevier B.V. ...

It is given a new algorithm to compute a lower T-transitive approximation of a fuzzy relation that preserves symmetry. Given a reflexive and symmetric fuzzy relation, the new algorithm computes a T-indistinguishability that is contained in the fuzzy relation. It has been developed a C++ program that generates random symmetric fuzzy relations or random symmetric and reflexive fuzzy relations and...

We present an efficient method for extracting fuzzy rules directly from numerical input-output data for function approximation problems. First, we convert a given function approximation problem into a pattern classification problem. This is done by dividing the universe of discourse of the output variable into multiple intervals, each regarded as a class, and then by assigning a class to each o...

Most fuzzy systems including fuzzy decision support and fuzzy control systems provide out­ puts in the form of fuzzy sets that represent the inferred conclusions. Linguistic interpretation of such outputs often involves the use of linguistic approximation that assigns a linguistic label to a fuzzy set based on the predefined primary terms, linguistic modifiers and linguistic connectives. More g...

Neural Networks (NN), Type-1 Fuzzy Logic Systems (T1FLS) and Interval Type-2 Fuzzy Logic Systems (IT2FLS) are universal approximators, they can approximate any non-linear function. Recent research shows that embedding T1FLS on an NN or embedding IT2FLS on an NN can be very effective for a wide number of non-linear complex systems, especially when handling imperfect information. In this paper we...

In order to improve the approximation property of the past fuzzy clustering algorithms when identifying systems, a fuzzy clustering neural network (FCNN) is proposed and is applied to conjunction speech recognition system. Based on the fuzzy system model, FCNN presents every state as a fuzzy system and uses continuous frames as the system input. With improving fuzzy clustering identification al...