title: |
The Type-1 OWA Operator and the Centroid of Type-2 Fuzzy Sets |
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publication: |
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part of series: |
Advances in Intelligent Systems Research | |
| pages: | 15 - 20 | |
DOI: |
To be assigned soon (how to use a DOI) | |
author(s): |
Francisco Chiclana, Shang-Ming Zhou |
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publication date: |
July 2011 |
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keywords: |
Type-1 fuzzy sets, type-2 fuzzy sets,
type-1 OWA operators, -level, centroid, representation theorem. |
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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. |
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copyright: |
©
Atlantis Press. This article is distributed under the
terms of the Creative Commons Attribution License, which permits
non-commercial use, distribution and reproduction in any medium,
provided the original work is properly cited. |
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full text: |