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...

This paper build a structure of fuzzy neural network, which is well sufficient to gain a fuzzy interpolation polynomial of the form [Formula: see text] where [Formula: see text] is crisp number (for [Formula: see text], which interpolates the fuzzy data [Formula: see text]. Thus, a gradient descent algorithm is constructed to train the neural network in such a way that the unknown coefficients ...

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...

It is well known that a fuzzy rule base is a characterization of a partially given mapping (fuzzy function) between fuzzy universes. For practical applications, it is desirable to interpolate that function in order to compute its values at points (fuzzy or crisp) other than fuzzy sets (nodes) in antecedents of the rule base. Moreover, interpolation requires that in the case of coincidence betwe...

Systems of fuzzy relation equations are considered as models of fuzzy inference systems. A proper use of an inference mechanism connected to a fuzzy relation modelling a fuzzy rule base is certified by keeping the fundamental interpolation condition. The paper aims at new solutions of systems of fuzzy relation equations and introduces new solvability criteria.