Divergence measure between fuzzy sets using cardinality

Vladimír Kobza

Kybernetika (2017)

  • Volume: 53, Issue: 3, page 418-436
  • ISSN: 0023-5954

Abstract

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In this paper we extend the concept of measuring difference between two fuzzy subsets defined on a finite universe. The first main section is devoted to the local divergence measures. We propose a divergence measure based on the scalar cardinalities of fuzzy sets with respect to the basic axioms. In the next step we introduce the divergence based on the generating function and the appropriate distances. The other approach to the divergence measure is motivated by class of the rational similarity measures between fuzzy subsets expressed using some set operations (namely intersection, complement, difference and symmetric difference) and their scalar cardinalities. Finally, this concept is extended into the fuzzy cardinality in the last part. Some open problems omitted in this paper are discussed in the concluding remarks section.

How to cite

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Kobza, Vladimír. "Divergence measure between fuzzy sets using cardinality." Kybernetika 53.3 (2017): 418-436. <http://eudml.org/doc/294480>.

@article{Kobza2017,
abstract = {In this paper we extend the concept of measuring difference between two fuzzy subsets defined on a finite universe. The first main section is devoted to the local divergence measures. We propose a divergence measure based on the scalar cardinalities of fuzzy sets with respect to the basic axioms. In the next step we introduce the divergence based on the generating function and the appropriate distances. The other approach to the divergence measure is motivated by class of the rational similarity measures between fuzzy subsets expressed using some set operations (namely intersection, complement, difference and symmetric difference) and their scalar cardinalities. Finally, this concept is extended into the fuzzy cardinality in the last part. Some open problems omitted in this paper are discussed in the concluding remarks section.},
author = {Kobza, Vladimír},
journal = {Kybernetika},
keywords = {fuzzy set; divergence measure; scalar cardinality; fuzzy cardinality},
language = {eng},
number = {3},
pages = {418-436},
publisher = {Institute of Information Theory and Automation AS CR},
title = {Divergence measure between fuzzy sets using cardinality},
url = {http://eudml.org/doc/294480},
volume = {53},
year = {2017},
}

TY - JOUR
AU - Kobza, Vladimír
TI - Divergence measure between fuzzy sets using cardinality
JO - Kybernetika
PY - 2017
PB - Institute of Information Theory and Automation AS CR
VL - 53
IS - 3
SP - 418
EP - 436
AB - In this paper we extend the concept of measuring difference between two fuzzy subsets defined on a finite universe. The first main section is devoted to the local divergence measures. We propose a divergence measure based on the scalar cardinalities of fuzzy sets with respect to the basic axioms. In the next step we introduce the divergence based on the generating function and the appropriate distances. The other approach to the divergence measure is motivated by class of the rational similarity measures between fuzzy subsets expressed using some set operations (namely intersection, complement, difference and symmetric difference) and their scalar cardinalities. Finally, this concept is extended into the fuzzy cardinality in the last part. Some open problems omitted in this paper are discussed in the concluding remarks section.
LA - eng
KW - fuzzy set; divergence measure; scalar cardinality; fuzzy cardinality
UR - http://eudml.org/doc/294480
ER -

References

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