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Record type:
kapitola v odborné knize (C)
Home Department:
Ústav pro výzkum a aplikace fuzzy modelování (94410)
Title:
Generic View On Continuous T-Norms and T-Conorms
Citace
Perfilieva, I. Generic View On Continuous T-Norms and T-Conorms.
In:
Computational Intelligence, Theory and Applications.
Heidelberg,: Springer, 2005. s. 379-385. ISBN 3-540-22807-1.
Subtitle
Publication year:
2005
Obor:
Obecná matematika
Form of publication:
ISBN code:
3-540-22807-1
Book title in original language:
Computational Intelligence, Theory and Applications
Title of the edition and volume number:
Place of publishing:
Heidelberg,
Publisher name:
Springer
Issue reference (issue number):
:
Published:
Author of the source document:
Number of pages:
7
Book page count:
810
Page from:
379
Page to:
385
Book print run:
300
EID:
Key words in English:
t-norm; t-conorm; BL-algebra; additive generator
Annotation in original language:
We have suggested the representation of continuous t-norms and t-conorms with help of generalized additive generators. This representation shows similar origin of triangular operations (t-norms and t-conorms) as truncated sums of negative and positive reals, respectively. Moreover, we showed that a generalized additive generator establishes an isomorphic mapping between a standard BL-algebra on $[0,1]$ and the algebra on the set of couples of reals with truncated operations.
Annotation in english language:
We have suggested the representation of continuous t-norms and t-conorms with help of generalized additive generators. This representation shows similar origin of triangular operations (t-norms and t-conorms) as truncated sums of negative and positive reals, respectively. Moreover, we showed that a generalized additive generator establishes an isomorphic mapping between a standard BL-algebra on $[0,1]$ and the algebra on the set of couples of reals with truncated operations.
References
Reference
R01:
RIV/61988987:17610/05:A1000HK3
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