The Kóczy-Hirota Fuzzy Interpolation (“KH” method, Kóczy and Hirota, 1991) is the first method adapting the declarative way of fuzzy function definition and the related “fuzzy dot” rule representation by introducing the concept of Fuzzy Rule Interpolation (FRI). The original KH method had many followers. Most of the FRI methods have difficulties in freely defining the relation of the observatio...

Some difficulties emerging during the construction of fuzzy behaviour-based control structures 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 e.g. for the behaviour coordination module, the way of building a complete rule base is n...

In this special issue on "Fuzzy Expert Systems," six papers cover a wide range of concerns--from theory to applications including: (1) a rule base reorganization, (2) a linear interpolation, (3) a neuro-fuzzy approach to pairwise comparison, (4) properties of reduction, in transitive matrices, (5) a consistency checking procedure, and (6) a context dependency model. We present a brief review of...

We propose a general framework for the interpolation problem. Our framework stems from the classical elaboration of the problem. We introduce the notion of an interpolating fuzzy function and show how this function can be characterized. We examine and analyze previously published fuzzy interpolation algorithms to choose those algorithms that can be represented analytically. We also propose an a...

A novel interpolation algorithm, fuzzy interpolation, is presented and compared with other popular interpolation methods widely implemented in industrial and manufacturing applications. Different interpolation algorithms have been developed, reported and implemented in many industrial applications in recent years. Most of them are based on looking for the optimal interpolation trajectories base...

The aim of this paper is to introduce a novel two-step Fuzzy Rule Interpolation Technique (FRIT) “VEIN”, based on the concept of Vague Environment. The strength of FRIT against classical fuzzy reasoning methods is the ability of gaining conclusion even in case where the knowledge is represented by sparse fuzzy rule bases. The FRIT “VEIN” introduced in this paper is following the structure the G...

Approximate fuzzy reasoning methods serves the task of inference in case of fuzzy systems built on sparse rule bases. This paper is a part of a longer survey that aims to provide a qualitative view through the various ideas and characteristics of interpolation based fuzzy reasoning methods. It also aims to define a general condition set for fuzzy rule interpolation methods brought together from...

Systems applying fuzzy logic are rule based ones. The collection of the rules the so called rule base can be characterized as dense or sparse depending on whether there exist rules for all the possible observations. In the sparse case for some observations there are no rules whose antecedent part would overlap the observation at least partially. Therefore the classical compositional reasoning m...

In this paper, we proposed another new form of type-2 fuzzy data points(T2FDPs) that is perfectly normal type-2 data points(PNT2FDPs). These kinds of brand-new data were defined by using the existing type-2 fuzzy set theory(T2FST) and type-2 fuzzy number(T2FN) concept since we dealt with the problem of defining complex uncertainty data. Along with this restructuring, we included the fuzzificati...