Systems based on interpolative fuzzy reasoning work with sparse rule bases. In case of some input values the system should approximate the output value. Carrying out this task depends on the right selection of the suitable fuzzy similarity measure. The goal of this paper is presenting two of such measures, which are also applied in some interpolation based fuzzy reasoning methods.

One of the possible semantics of fuzzy sets is in terms of similarity, namely a grade of membership of an item in a fuzzy set can be viewed as the degree of resemblance between this item and prototypes of the fuzzy set. In such a framework, an interesting question is how to devise a logic of similarity, where inference rules can account for the proximity between interpretations. The aim is to c...

The “fuzzy dot” (or fuzzy relation) representation of fuzzy rules in fuzzy rule based systems, in case of classical fuzzy reasoning methods (e.g. the Zadeh-MamdaniLarsen Compositional Rule of Inference (CRI) (Zadeh, 1973) (Mamdani, 1975) (Larsen, 1980) or the Takagi Sugeno fuzzy inference (Sugeno, 1985) (Takagi & Sugeno, 1985)), are assuming the completeness of the fuzzy rule base. If there are...

This paper is continuation work of a research started in 2005. In the previous research, variety of fuzzy digital elevation models was constructed and the best fit model was selected in order to present an alternative in modelling height information. The previous study revealed that fuzzy digital elevation model gave satisfied result compared with the result from TIN (Triangulated Irregular Net...

This paper examines the fuzzy system for function approximation in a macroscopic level. The rules of a fuzzy function approximation system are expressed in the form of polynomials such that each rule forms a local approximator. We show that this kind of fuzzy function approximation is equivalent to piecewise polynomial interpolation between turning points when normalized fuzzy function membersh...

A core tool for granular modeling is the use of linguistic rules, e.g. in fuzzy control approaches. We provide the reader with basic mathematical tools to discuss the behavior of system of such linguistic rules. These mathematical tools range from fuzzy logic and fuzzy set theory, through the consideration of fuzzy relation equations, up to discussions of interpolation strategies and to the use...

In this paper we propose a natural approach to handle imprecise numbers as they arise for example from measurements. Fuzzy sets turn out to be a canonical representation for such imprecise numbers that are induced by taking diierent tolerance or error bounds into account. Fuzzy sets are induced by scaling factors that describe the magnitude of the imprecision. On the other, the scaling factors ...

This paper presents a new way to design a Fuzzy Terminal Iterative Learning Control (TILC) to control the heater temperature setpoints of a thermoforming machine. This fuzzy TILC is based on the inverse of a fuzzy model of this machine, and is built from experimental (or simulation) data with kriging interpolation. The Fuzzy Inference System usually used for a fuzzy model is the zero order Taka...

Due to its high performance and comprehensibility, fuzzy modelling is becoming more and more popular in dealing with nonlinear, uncertain and complex systems for tasks such as signal processing, medical diagnosis and financial investment. However, there are no principal routine methods to obtain the optimum fuzzy rule base which is not only compact but also retains high prediction (or classific...

In this paper, the (m+1)-step Adams-Bashforth, Adams-Moulton, and Predictor-Correctormethods are used to solve rst-order linear fuzzy ordinary dierential equations. The conceptsof fuzzy interpolation and generalised strongly dierentiability are used, to obtaingeneral algorithms. Each of these algorithms has advantages over current methods. Moreover,for each algorithm a convergence formula can b...