Multiplication, distributivity and fuzzy-integral. II

Wolfgang Sander; Jens Siedekum

Kybernetika (2005)

  • Volume: 41, Issue: 4, page [469]-496
  • ISSN: 0023-5954

Abstract

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Based on results of generalized additions and generalized multiplications, proven in Part I, we first show a structure theorem on two generalized additions which do not coincide. Then we prove structure and representation theorems for generalized multiplications which are connected by a strong and weak distributivity law, respectively. Finally – as a last preparation for the introduction of a framework for a fuzzy integral – we introduce generalized differences with respect to t-conorms (which are not necessarily Archimedean) and prove their essential properties.

How to cite

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Sander, Wolfgang, and Siedekum, Jens. "Multiplication, distributivity and fuzzy-integral. II." Kybernetika 41.4 (2005): [469]-496. <http://eudml.org/doc/33767>.

@article{Sander2005,
abstract = {Based on results of generalized additions and generalized multiplications, proven in Part I, we first show a structure theorem on two generalized additions which do not coincide. Then we prove structure and representation theorems for generalized multiplications which are connected by a strong and weak distributivity law, respectively. Finally – as a last preparation for the introduction of a framework for a fuzzy integral – we introduce generalized differences with respect to t-conorms (which are not necessarily Archimedean) and prove their essential properties.},
author = {Sander, Wolfgang, Siedekum, Jens},
journal = {Kybernetika},
keywords = {fuzzy measures; distributivity law; restricted domain; pseudo- addition; pseudo-multiplication; Choquet integral; Sugeno integral; fuzzy measure; distributivity law; restricted domain; pseudo-addition; pseudomultiplication; Choquet integral; Sugeno integral},
language = {eng},
number = {4},
pages = {[469]-496},
publisher = {Institute of Information Theory and Automation AS CR},
title = {Multiplication, distributivity and fuzzy-integral. II},
url = {http://eudml.org/doc/33767},
volume = {41},
year = {2005},
}

TY - JOUR
AU - Sander, Wolfgang
AU - Siedekum, Jens
TI - Multiplication, distributivity and fuzzy-integral. II
JO - Kybernetika
PY - 2005
PB - Institute of Information Theory and Automation AS CR
VL - 41
IS - 4
SP - [469]
EP - 496
AB - Based on results of generalized additions and generalized multiplications, proven in Part I, we first show a structure theorem on two generalized additions which do not coincide. Then we prove structure and representation theorems for generalized multiplications which are connected by a strong and weak distributivity law, respectively. Finally – as a last preparation for the introduction of a framework for a fuzzy integral – we introduce generalized differences with respect to t-conorms (which are not necessarily Archimedean) and prove their essential properties.
LA - eng
KW - fuzzy measures; distributivity law; restricted domain; pseudo- addition; pseudo-multiplication; Choquet integral; Sugeno integral; fuzzy measure; distributivity law; restricted domain; pseudo-addition; pseudomultiplication; Choquet integral; Sugeno integral
UR - http://eudml.org/doc/33767
ER -

References

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