We consider the interpolation problem for functions whose range and whose domain both consist of convex or fuzzy subsets of a real Euclidean space. This problem arises in fuzzy controlling, namely when the functional dependence between two fuzzy vectors is known only for finitely many cases. To have a criterion for an appropriate choice of an interpolation function, we generalise the well-known...

In this paper, we purposed a new method in modeling the uncertainty data based on the theory of fuzzy sets and the interpolation B-spline model curve. The uncertainty data firstly defined by using fuzzy number concept and fuzzy relation by defined them in real data form. The existed coefficient control of interpolation B-spline basis function is substituted with the fuzzy data points(FDPs) whic...

In most control and engineering applications, the use of fuzzy system as a way to improve the humtzn-computer interaction has becoming popular. This paper reports on the use of fuzzy system in mineral processing specifically in determining the parameter d50c of hydrocyclone. However, wit,h the inputoutput data provided to build the fuzzy rule base, it normally results in a sparse fuzzy rule bas...

Fuzzy rule-based systems have been very popular in many engineering applications. In mineral engineering, fuzzy rules are normally constructed using some fuzzy rule extraction techniques to establish the determination model in predicting the d50c of hydrocyclones. However, when generating fuzzy rules from the available information, it may result in a sparse fuzzy rule base. The use of more than...

In this paper, rst a design is proposed for representing fuzzy polynomials withinput fuzzy and output fuzzy. Then, we sketch a constructive proof for existenceof such polynomial which can be fuzzy interpolation polynomial in a set given ofdiscrete points rather than a fuzzy function. Finally, to illustrate some numericalexamples are solved.

Fuzzy rule based systems have been very popular in many engineering applications. In petroleum engineering, fuzzy rules are normally constructed using some fuzzy rule extraction techniques to establish the petrophysical properties prediction model. However, when generating fizzy rules from the available information, it may result in a sparse fuzzy rule base. The use of more than one input varia...

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...