The usefulness of fuzzy input fuzzy output functions and their interpolation/approximation by different operators in fuzzy control motivate their deeper theoretical study. We obtain some properties of fuzzy B-spline series such as variation and uncertainty diminishing property. We also propose spline approximation of fuzzy input fuzzy output functions. Key–Words: Fuzzy numbers, Fuzzy splines, A...

Fuzzy interpolation property is among the most important properties of fuzzy inference systems. It has been showed that the normality plus Ruspini condition applying to the antecedent fuzzy sets is a sufficient condition with a high practical impact. Another important property is the monotone behavior of the resulting control function (after a defuzzification) derived from a monotone fuzzy rule...

A comparison is made of two approaches to approximate reasoning: Mamdani's interpolation method and the implication method. Both approaches are variants of Zadeh's compositional rule of inference. It is shown that the approaches are not equivalent. A correspondence between the approaches is established via the inverse of the implied fuzzy relation. The interpolation method has the lowest time-c...

The aim of this paper is to propose a criterion to estimate the design, from experimental data, of a fuzzy inference system, when data are sparse. This lack of data is important and may improve the generalisation ability of fuzzy systems (0). Several methods have been proposed to obtain automatic fuzzy rules from sparse training data. In (0), the authors first construct fuzzy rules from collect...

interpolation, the generalization of point data to scatter data, and combining maps are three cases of important applications of gis. in this study, it has been tried to make the estimation of rain erosion capacity (fournier method) more real through using gis capability in interpolation and the generalization of point data to scatter data. in fournier method, the rain erosion capacity is calcu...

Case-based reasoning is a recognized paradigm and has been explored in both applied and methodological directions. In the several phases of CBR, the adaptation phase is certainly the most problematic whereas the most characteristic and interesting phase. We propose to view this task through a fuzzy analogical scheme. The adaptation is realized by focusing on the relation existing between the pr...

The core point of fuzzy control approaches are finite lists of linguistic control rules. For computerbased automatic control these lists have to be transformed into control algorithms which can be realized on a computer. The main general idea of this fuzzy control approach is that such an algorithm should yield a fuzzy subset of the output space of the control problem if confronted with a fuzzy...

Some difficulties emerging during the construction of fuzzy rule bases are inherited from the type of the applied fuzzy reasoning. The fuzzy rule base requested for many classical reasoning methods needed to be complete. In case of fetching fuzzy rules directly from expert knowledge, the way of building a complete rule base is not always straightforward. One simple solution for overcoming the n...

The “Double Fuzzy Point” rule representation opens a new dimension for expressing changes of fuzziness in fuzzy rule-based systems. In the case of standard “Fuzzy Point” rule representations, it is difficult to describe fuzzy functions in which crisp observations are required to have fuzzy conclusions, or in which an increase in the fuzziness of observations leads to reduced fuzziness in conclu...