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.

This work deals with spatial interpolation and problems related to the imprecision and the uncertainty of the data. Previous works led us to define a semantic-based aggregation process, which allows the combination of spatial data defined by fuzzy sets and possibility degrees. This article proposes to modify this aggregation process, in order to take into account a fuzzy variogram describing th...

In support of reasoning with sparse rule bases, fuzzy rule interpolation (FRI) offers a helpful inference mechanism for deriving an approximate conclusion when a given observation has no overlap with any rule in the existing rule base. One of the recent and popular FRI approaches is the scale and move transformation-based rule interpolation, known as T-FRI in the literature. It supports both in...

This paper presents an approach to a system based on fuzzy logic for the design of interpolative curves and surfaces in the context of Computer Aided Geometric Design (CAGD). Some problems arising from a previous model are studied by using a similarity approach. Keywords— Fuzzy interpolation, indistinguishability operator, fuzzy number, Computer Aided Geometric Design,approximate reasoning, t-n...

This papers aims at clarifying the meaning of diierent interpretations of the Max-Min or, more generally, the Max-t-norm rule in fuzzy systems. It turns out that basically two distinct approaches play an important role in fuzzy logic and its applications: fuzzy interpolation on the basis of an imprecisely known function and logical inference in the presence of fuzzy information .

Inference mechanisms and interpretations of fuzzy rule bases are studied together from the point of view of systems of fuzzy relation equations. A proper use of an inference mechanism connected to a fuzzy relation interpreting a fuzzy rule base is certified by keeping the fundamental interpolation condition. The paper aims at new solutions of systems of fuzzy relation equations which are motiva...