OWA operators for discrete gradual intervals: implications to fuzzy intervals and multi-expert decision making

Zdenko Takáč

Kybernetika (2016)

  • Volume: 52, Issue: 3, page 379-402
  • ISSN: 0023-5954

Abstract

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A new concept in fuzzy sets theory, namely that of gradual element, was introduced recently. It is known that the set of gradual real numbers is not ordered linearly. We restrict our attention to a discrete case and propose a class of linear orders for discrete gradual real numbers. Then, using idea of the so-called admissible order of intervals, we present a class of linear orders for discrete gradual intervals. Once we have the linear orders it is possible to define OWA operator for discrete gradual real numbers and OWA operator for discrete gradual intervals. Recall that gradual intervals also encompass fuzzy intervals, hence our results are applicable to the setting of fuzzy intervals. Our approach is illustrated on a multi-expert decision making problem.

How to cite

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Takáč, Zdenko. "OWA operators for discrete gradual intervals: implications to fuzzy intervals and multi-expert decision making." Kybernetika 52.3 (2016): 379-402. <http://eudml.org/doc/281540>.

@article{Takáč2016,
abstract = {A new concept in fuzzy sets theory, namely that of gradual element, was introduced recently. It is known that the set of gradual real numbers is not ordered linearly. We restrict our attention to a discrete case and propose a class of linear orders for discrete gradual real numbers. Then, using idea of the so-called admissible order of intervals, we present a class of linear orders for discrete gradual intervals. Once we have the linear orders it is possible to define OWA operator for discrete gradual real numbers and OWA operator for discrete gradual intervals. Recall that gradual intervals also encompass fuzzy intervals, hence our results are applicable to the setting of fuzzy intervals. Our approach is illustrated on a multi-expert decision making problem.},
author = {Takáč, Zdenko},
journal = {Kybernetika},
keywords = {OWA operator; ordered weighted averaging operator; gradual number; gradual interval; fuzzy interval; linear order; total order; multi-expert decision making; type-2 fuzzy set},
language = {eng},
number = {3},
pages = {379-402},
publisher = {Institute of Information Theory and Automation AS CR},
title = {OWA operators for discrete gradual intervals: implications to fuzzy intervals and multi-expert decision making},
url = {http://eudml.org/doc/281540},
volume = {52},
year = {2016},
}

TY - JOUR
AU - Takáč, Zdenko
TI - OWA operators for discrete gradual intervals: implications to fuzzy intervals and multi-expert decision making
JO - Kybernetika
PY - 2016
PB - Institute of Information Theory and Automation AS CR
VL - 52
IS - 3
SP - 379
EP - 402
AB - A new concept in fuzzy sets theory, namely that of gradual element, was introduced recently. It is known that the set of gradual real numbers is not ordered linearly. We restrict our attention to a discrete case and propose a class of linear orders for discrete gradual real numbers. Then, using idea of the so-called admissible order of intervals, we present a class of linear orders for discrete gradual intervals. Once we have the linear orders it is possible to define OWA operator for discrete gradual real numbers and OWA operator for discrete gradual intervals. Recall that gradual intervals also encompass fuzzy intervals, hence our results are applicable to the setting of fuzzy intervals. Our approach is illustrated on a multi-expert decision making problem.
LA - eng
KW - OWA operator; ordered weighted averaging operator; gradual number; gradual interval; fuzzy interval; linear order; total order; multi-expert decision making; type-2 fuzzy set
UR - http://eudml.org/doc/281540
ER -

References

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