Journal
IEEE TRANSACTIONS ON KNOWLEDGE AND DATA ENGINEERING
Volume 23, Issue 10, Pages 1455-1468Publisher
IEEE COMPUTER SOC
DOI: 10.1109/TKDE.2010.191
Keywords
OWA operators; aggregation; fuzzy sets; type-1 OWA operators; Alpha-cuts; Alpha level; uncertain information; soft decision making; breast cancer treatments
Categories
Funding
- EPSRC [EP/C542215/1]
- EPSRC [EP/H000968/1, EP/C542215/1] Funding Source: UKRI
- ESRC [ES/G007543/1] Funding Source: UKRI
- Economic and Social Research Council [ES/G007543/1] Funding Source: researchfish
- Engineering and Physical Sciences Research Council [EP/C542215/1, EP/H000968/1] Funding Source: researchfish
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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.
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