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Issue No. 10 - October (2011 vol. 23)
ISSN: 1041-4347
pp: 1455-1468
Jonathan M. Garibaldi , University of Nottingham, Nottingham
Shang-Ming Zhou , Swansea University, Swansea
Francisco Chiclana , De Montfort University, Leicester
Robert I. John , De Montfort University, Leicester
ABSTRACT
Type-1 Ordered Weighted Averaging (OWA) operator provides us with a new technique for directly aggregating uncertain information with uncertain weights via OWA mechanism in soft decision making and data mining, in which uncertain objects are modeled by fuzzy sets. The Direct Approach to performing type-1 OWA operation involves high computational overhead. In this paper, we define a type-1 OWA operator based on the \alpha-cuts of fuzzy sets. Then, we prove a Representation Theorem of type-1 OWA operators, by which type-1 OWA operators can be decomposed into a series of \alpha-level type-1 OWA operators. Furthermore, we suggest a fast approach, called Alpha-Level Approach, to implementing the type-1 OWA operator. A practical application of type-1 OWA operators to breast cancer treatments is addressed. Experimental results and theoretical analyses show that: 1) the Alpha-Level Approach with linear order complexity can achieve much higher computing efficiency in performing type-1 OWA operation than the existing Direct Approach, 2) the type-1 OWA operators exhibit different aggregation behaviors from the existing fuzzy weighted averaging (FWA) operators, and 3) the type-1 OWA operators demonstrate the ability to efficiently aggregate uncertain information with uncertain weights in solving real-world soft decision-making problems.
INDEX TERMS
OWA operators, aggregation, fuzzy sets, type-1 OWA operators, Alpha-cuts, Alpha level, uncertain information, soft decision making, breast cancer treatments.
CITATION
Jonathan M. Garibaldi, Shang-Ming Zhou, Francisco Chiclana, Robert I. John, "Alpha-Level Aggregation: A Practical Approach to Type-1 OWA Operation for Aggregating Uncertain Information with Applications to Breast Cancer Treatments", IEEE Transactions on Knowledge & Data Engineering, vol. 23, no. , pp. 1455-1468, October 2011, doi:10.1109/TKDE.2010.191
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