A piecewise linear (PWL) function approximation scheme is described by a lattice algebra of modified operators that allows for the interpolation of PWL function vertexes. A new recursive method called Centred Recursive Interpolation (CRI) based on such modified operators is analysed for successive function smoothing and more accurate approximation. This approximation method, simple but accurate...

This paper connects two thoroughly investigated universal approximator techniques to each other. Recently, it has been shown that the input-output function of the general fuzzy KH interpolation method [1, 2] as well as its modification [3] are stable in the mathematical sense, or in other words, they can be considered as universal approximators with respect to the Lp (p ∈ [1,∞]) norm in the spa...

Fuzzy inference systems are studied from the point of view of systems of fuzzy relation equations. A fundamental interpolation condition is considered to be a crucial point of study in choosing proper inference method as well as a proper interpretation of a fuzzy rule base. The paper aims at additive interpretations and investigates their utilization from a theoretical point of view while their...

Several Fuzzy Rule Interpolation (FRI) techniques have limitations from the direct application point of view, for example their applicability is limited to the one dimensional case, or they can be defined only based on the two closest surrounding rules of the actual observation. This is the reason why relatively few FRI methods can be found among the practical fuzzy rule based applications. Wit...

Fuzzy control accounts for the biggest industrial success of fuzzy logic. We review an interpretation of Mamdani’s heuristic control approach. It can be seen as knowledge-based interpolation based on input-output points of a vaguely known function. We reexamine two real-world control problems that have been fortunately solved based on this interpretation.

Two extensions of classical Shepard operators to the fuzzy case are presented. We study Shepard-type interpolation/approximation operators for functions with domain and range in the fuzzy number’s space and max-product approximation operators. Error estimates are obtained in terms of the modulus of continuity.

This paper addresses complex, variable-order fractional derivatives, enlarging the definitions for the real case. Implementations combining discretised Crone approximations using fuzzy logic and interpolation are also addressed.

Fuzzy rule interpolation based reasoning methods are the most common choices for cases when the applied rule base is not dense. This paper presents a new technique called LESFRI, which is based on the method of least squares. Its central idea is the conservation of the shape type specific to a fuzzy partition. The method has low computational complexity.

Keywords--Fuzzy reasoning, Fuzzy transform, Fuzzy optimization, Multiple rules, Interpolation, Scheduling. *Author to whom all correspondence should be addressed. This work is supported by the National Key Basic Research and Development Program (No. 2002CB312200), the National Natural Science Foundation of China (No. 60004010, No. 60274045, No. 60443009). 0898-1221/06/$ see front matter (~) 200...

The paper focuses on the fuzzy extensions of two data analysis methods, namely the fuzzy cluster analysis and the fuzzy interpolation of spatial data (the so-called fuzzy kriging) and their suitability for ecological applications. Both extensions utilize exact (crisp) measurement data as well as imprecise data defined as fuzzy numbers or fuzzy vectors. Fuzzy clustering of fuzzy data (conical fu...