Interpolation and extrapolation of fuzzy quantities -- the multiple-dimensional case
The objective of this study is to deliver a comprehensive methodology for interpolation and extrapolation in multivariable rule-based systems. Proceeding with the standard format of multiple input rule-based systems of the form ``if condition\(_1\) is \(A_i\) and condition\(_2\) is \(B_i\dots\) then conclusion is \(Z_i\)'' involving fuzzy sets defined in the corresponding spaces \((A_i,B_i, \dots,Z_i)\) and a collection of formal interpolation requirements (such as compatibility with the rule base, monotonicity, continuity, linearity, etc.), techniques are discussed for constructing fuzzy sets that interpolate and extrapolate in fuzzy rule bases. This process is discussed at the level of computing realized for antecedents and conclusions of the rules. Furthermore the properties of the resulting interpolation/extrapolation mapping are studied.
scientific article; zbMATH DE number 1883908