The Type-1 OWA Operator and the Centroid of Type-2 Fuzzy Sets

DOI

10.2991/eusflat.2011.138How to use a DOI?

Keywords

Type-1 fuzzy sets, type-2 fuzzy sets, type-1 OWA operators, -level, centroid, representation theorem.

Abstract

This paper aims to establish the relationship between two apparent disparate problems: (i) the aggregation of uncertain information modelled by type-1 fuzzy sets via OWA mechanism, and (ii) the computation of the centroid of type-2 fuzzy sets. In order to cut down the computational complexity of the direct approach to performing type-1 OWA operation, the -level approach to type-1 OWA operators was developed. This new approach is based on the decomposition of a type-1 OWA operator via its -levels and the corresponding Representation Theorem of type-1 OWA operators. A close inspection of the mathematical representation of the centroid of type-2 fuzzy sets reveals that this is a special case of type-1 OWA operator. This relationship will allow for the computation of the centroid of a general type-2 fuzzy sets to be carried out via the application of the representation theorem to its equivalent type-1 OWA representation.

Copyright

© 2011, the Authors. Published by Atlantis Press.

Open Access

This is an open access article distributed under the CC BY-NC license (http://creativecommons.org/licenses/by-nc/4.0/).

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TY  - CONF
AU  - Francisco Chiclana
AU  - Shang-Ming Zhou
PY  - 2011/08
DA  - 2011/08
TI  - The Type-1 OWA Operator and the Centroid of Type-2 Fuzzy Sets
BT  - Proceedings of the 7th conference of the European Society for Fuzzy Logic and Technology (EUSFLAT-11)
PB  - Atlantis Press
SP  - 15
EP  - 20
SN  - 1951-6851
UR  - https://doi.org/10.2991/eusflat.2011.138
DO  - 10.2991/eusflat.2011.138
ID  - Chiclana2011/08
ER  -