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...

This paper proves convergence rates for local scattered data interpolation by polyharmonic splines. To this end, it is shown that the Lagrange basis functions of polyharmonic spline interpolation are invariant under uniform scalings. Consequences of this important result for the numerical stability of the local interpolation scheme are discussed. A stable algorithm for the evaluation of polyhar...

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We provide an overview of spline and wavelet techniques with an emphasis on applications in pattern recognition. The presentation is divided in three parts. In the first one, we argue that the spline representation is ideally suited for all processing tasks that require a continuous model of the underlying signals or images. We show that most forms of spline fitting (interpolation, least-square...

This paper focuses on the acquisition of abstract information, i.e. information which are not analytically related to conventional physical quantities as for example the comfort. In these complex cases, we propose to use fuzzy sensors which compute and report linguistic assessment of numerical acquired values. Two methods are proposed to realize the aggregation from basic measurements. The firs...

This paper introduces a new approach for fuzzy interpolation and extrapolation of sparse rule base comprising of membership functions with finite number of characteristic points. The approach calls for representing membership functions as points in high-dimensional Cartesian spaces using the locations of their characteristic points as coordinates. Hence, a fuzzy rule base can be viewed as a set...