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Alpha-Level Aggregation: A Practical Approach to Type-1 OWA Operation for Aggregating Uncertain Information with Applications to Breast Cancer Treatments

Shang-ming Zhou Orcid Logo, Francisco Chiclana, Robert I. John, Jonathan M. Garibaldi

IEEE Transactions on Knowledge and Data Engineering, Volume: 23, Issue: 10, Pages: 1455 - 1468

Swansea University Author: Shang-ming Zhou Orcid Logo

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DOI (Published version): 10.1109/TKDE.2010.191

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 t...

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Published in: IEEE Transactions on Knowledge and Data Engineering
ISSN: 1041-4347
Published: IEEE Transactions on Knowledge and Data Engineering 2011
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URI: https://cronfa.swan.ac.uk/Record/cronfa10024
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spelling 2019-07-17T14:59:07.2918210 v2 10024 2012-03-21 Alpha-Level Aggregation: A Practical Approach to Type-1 OWA Operation for Aggregating Uncertain Information with Applications to Breast Cancer Treatments 118578a62021ba8ef61398da0a8750da 0000-0002-0719-9353 Shang-ming Zhou Shang-ming Zhou true false 2012-03-21 BMS 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. Journal Article IEEE Transactions on Knowledge and Data Engineering 23 10 1455 1468 IEEE Transactions on Knowledge and Data Engineering 1041-4347 14 10 2011 2011-10-14 10.1109/TKDE.2010.191 COLLEGE NANME Biomedical Sciences COLLEGE CODE BMS Swansea University 2019-07-17T14:59:07.2918210 2012-03-21T16:17:09.0000000 Swansea University Medical School Medicine Shang-ming Zhou 0000-0002-0719-9353 1 Francisco Chiclana 2 Robert I. John 3 Jonathan M. Garibaldi 4 0010024-26042019162927.pdf TKDE-2009-02-0062-2nd_proofreading.pdf 2019-04-26T16:29:27.1300000 Output 1526031 application/pdf Accepted Manuscript true 2019-04-26T00:00:00.0000000 true eng
title Alpha-Level Aggregation: A Practical Approach to Type-1 OWA Operation for Aggregating Uncertain Information with Applications to Breast Cancer Treatments
spellingShingle Alpha-Level Aggregation: A Practical Approach to Type-1 OWA Operation for Aggregating Uncertain Information with Applications to Breast Cancer Treatments
Shang-ming Zhou
title_short Alpha-Level Aggregation: A Practical Approach to Type-1 OWA Operation for Aggregating Uncertain Information with Applications to Breast Cancer Treatments
title_full Alpha-Level Aggregation: A Practical Approach to Type-1 OWA Operation for Aggregating Uncertain Information with Applications to Breast Cancer Treatments
title_fullStr Alpha-Level Aggregation: A Practical Approach to Type-1 OWA Operation for Aggregating Uncertain Information with Applications to Breast Cancer Treatments
title_full_unstemmed Alpha-Level Aggregation: A Practical Approach to Type-1 OWA Operation for Aggregating Uncertain Information with Applications to Breast Cancer Treatments
title_sort Alpha-Level Aggregation: A Practical Approach to Type-1 OWA Operation for Aggregating Uncertain Information with Applications to Breast Cancer Treatments
author_id_str_mv 118578a62021ba8ef61398da0a8750da
author_id_fullname_str_mv 118578a62021ba8ef61398da0a8750da_***_Shang-ming Zhou
author Shang-ming Zhou
author2 Shang-ming Zhou
Francisco Chiclana
Robert I. John
Jonathan M. Garibaldi
format Journal article
container_title IEEE Transactions on Knowledge and Data Engineering
container_volume 23
container_issue 10
container_start_page 1455
publishDate 2011
institution Swansea University
issn 1041-4347
doi_str_mv 10.1109/TKDE.2010.191
publisher IEEE Transactions on Knowledge and Data Engineering
college_str Swansea University Medical School
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hierarchy_top_id swanseauniversitymedicalschool
hierarchy_top_title Swansea University Medical School
hierarchy_parent_id swanseauniversitymedicalschool
hierarchy_parent_title Swansea University Medical School
department_str Medicine{{{_:::_}}}Swansea University Medical School{{{_:::_}}}Medicine
document_store_str 1
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description 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.
published_date 2011-10-14T03:19:02Z
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