p -symmetric bi-capacities

Pedro Miranda; Michel Grabisch

Kybernetika (2004)

  • Volume: 40, Issue: 4, page [421]-440
  • ISSN: 0023-5954

Abstract

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Bi-capacities have been recently introduced as a natural generalization of capacities (or fuzzy measures) when the underlying scale is bipolar. They allow to build more flexible models in decision making, although their complexity is of order 3 n , instead of 2 n for fuzzy measures. In order to reduce the complexity, the paper proposes the notion of p -symmetric bi- capacities, in the same spirit as for p -symmetric fuzzy measures. The main idea is to partition the set of criteria (or states of nature, individuals,...) into subsets whose elements are all indifferent for the decision maker.

How to cite

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Miranda, Pedro, and Grabisch, Michel. "$p$-symmetric bi-capacities." Kybernetika 40.4 (2004): [421]-440. <http://eudml.org/doc/33709>.

@article{Miranda2004,
abstract = {Bi-capacities have been recently introduced as a natural generalization of capacities (or fuzzy measures) when the underlying scale is bipolar. They allow to build more flexible models in decision making, although their complexity is of order $3^n$, instead of $2^n$ for fuzzy measures. In order to reduce the complexity, the paper proposes the notion of $p$-symmetric bi- capacities, in the same spirit as for $p$-symmetric fuzzy measures. The main idea is to partition the set of criteria (or states of nature, individuals,...) into subsets whose elements are all indifferent for the decision maker.},
author = {Miranda, Pedro, Grabisch, Michel},
journal = {Kybernetika},
keywords = {bi-capacity; bipolar scales; $p$-symmetry; bi-capacity; bipolar scales; -symmetry},
language = {eng},
number = {4},
pages = {[421]-440},
publisher = {Institute of Information Theory and Automation AS CR},
title = {$p$-symmetric bi-capacities},
url = {http://eudml.org/doc/33709},
volume = {40},
year = {2004},
}

TY - JOUR
AU - Miranda, Pedro
AU - Grabisch, Michel
TI - $p$-symmetric bi-capacities
JO - Kybernetika
PY - 2004
PB - Institute of Information Theory and Automation AS CR
VL - 40
IS - 4
SP - [421]
EP - 440
AB - Bi-capacities have been recently introduced as a natural generalization of capacities (or fuzzy measures) when the underlying scale is bipolar. They allow to build more flexible models in decision making, although their complexity is of order $3^n$, instead of $2^n$ for fuzzy measures. In order to reduce the complexity, the paper proposes the notion of $p$-symmetric bi- capacities, in the same spirit as for $p$-symmetric fuzzy measures. The main idea is to partition the set of criteria (or states of nature, individuals,...) into subsets whose elements are all indifferent for the decision maker.
LA - eng
KW - bi-capacity; bipolar scales; $p$-symmetry; bi-capacity; bipolar scales; -symmetry
UR - http://eudml.org/doc/33709
ER -

References

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