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Record type:	kapitola v odborné knize (C)
Home Department:	Ústav pro výzkum a aplikace fuzzy modelování (94410)
Title:	Normal Forms for Fuzzy Relations and their Contribution to Universal Approximation
Citace	Perfilieva, I. Normal Forms for Fuzzy Relations and their Contribution to Universal Approximation. In: Intelligent Systems for Information Processing: From Representation to Applications. 1. vyd. Amsterdam: Elsevier, 2003. s. 381-392. ISBN 0-444-51379-5.

Subtitle
Publication year:	2003
Obor:	Obecná matematika
Form of publication:
ISBN code:	0-444-51379-5
Book title in original language:	Intelligent Systems for Information Processing: From Representation to Applications
Title of the edition and volume number:
Place of publishing:	Amsterdam
Publisher name:	Elsevier
Issue reference (issue number):	1:
Published:
Author of the source document:
Number of pages:	12
Book page count:
Page from:	381
Page to:	392
Book print run:
EID:

Key words in English:	fuzzy relation; disjunctive normal form; conjunctive normal form; extensional function
Annotation in original language:	This paper continues the investigation of approximating properties of generalized normal forms in fuzzy logic. The problem is formalized and solved algebraically. Normal forms are considered in two variants: infinite and finite. It is proved that infinite normal forms are universal representation formulas whereas finite normal forms are universal approximation formulas for extensional functions. The estimation of the quality of approximation is suggested. Moreover, functions which can be precisely represented by the discrete normal forms are considered.
Annotation in english language:	This paper continues the investigation of approximating properties of generalized normal forms in fuzzy logic. The problem is formalized and solved algebraically. Normal forms are considered in two variants: infinite and finite. It is proved that infinite normal forms are universal representation formulas whereas finite normal forms are universal approximation formulas for extensional functions. The estimation of the quality of approximation is suggested. Moreover, functions which can be precisely represented by the discrete normal forms are considered.

References

Reference

R01:	RIV/61988987:17310/03:00000045

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