The Type-1 OWA Operator and the Centroid of Type-2 Fuzzy Sets
- Francisco Chiclana, Shang-Ming Zhou
- Corresponding Author
- Francisco Chiclana
Available Online August 2011.
- https://doi.org/10.2991/eusflat.2011.138How to use a DOI?
- Type-1 fuzzy sets, type-2 fuzzy sets, type-1 OWA operators, -level, centroid, representation theorem.
- 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.
- Open Access
- This is an open access article distributed under the CC BY-NC license.
Cite this article
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 PB - Atlantis Press SP - 15 EP - 20 SN - 1951-6851 UR - https://doi.org/10.2991/eusflat.2011.138 DO - https://doi.org/10.2991/eusflat.2011.138 ID - Chiclana2011/08 ER -