Algorithmic aspects of fuzzy control
type: Item
instance of: scholarly article
title: Algorithmic aspects of fuzzy control
zbMATH Open document ID: 0874.93060
DOI: 10.1016/0888-613X(95)00016-A
author: László T. Kóczy
published in: International Journal of Approximate Reasoning
publication date: 1997-11-10T00:00:00Z
review text: The study concerns two design issues arising in the realm of fuzzy rule-based computing: its computational complexity and a reasoning carried out in the presence of sparse rulebases. The discussed fuzzy controller assumes either a relational or functional form where the rules read as: \[ \text{if \(X\) is \(A\) then \(y\) is \(B\)}\quad\text{or}\quad\text{if \(X\) is \(A\) then \(y= f(x)\)}, \] where \(A\) and \(B\) are fuzzy sets defined in the corresponding input and output (control) space. The computational complexity of such fuzzy controllers is analyzed in detail. Raised is the problem of reasoning in the case of a sparse rulebase, namely the rules with the union of their antecedents exhibiting some ``gaps'' in the input space (viz. the regions with zero membership values). The proposed interpolation scheme relies on the expression \[ {d(A^*,A_{i1})\over d(A^*,A_{i2})}= {d(B^*,B_{i1})\over d(B^*,B_{i2})}, \] where \(A^*\) is a given input, \(A_{i1}\) and \(A_{i2}\) are the two antecedents that are the closest to \(A^*\), \(d(.,.)\) stands for the distance function between two fuzzy sets and \(B^*\) is looked for.
reviewed by: Witold Pedrycz
Mathematics Subject Classification ID: 93C42
Mathematics Subject Classification ID: 93B40
zbMATH DE Number: 1004300
zbMATH Keywords: design
zbMATH Keywords: fuzzy rule-based computing
zbMATH Keywords: computational complexity
zbMATH Keywords: sparse rulebases
zbMATH Keywords: fuzzy controllers
zbMATH Keywords: interpolation scheme
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 1004300