A Novel Method for Fuzzy Measure Identification

Fuzzy measure and Choquet integral are effective tools for handling complex multiple criteria decision making (MCDM) problems in which criteria are inter- dependent. The identification of a fuzzy measure requires the determination of 2n −2 values when the number of criteria is n. The complexity...

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Main Authors:	Larbani, Moussa, Huang, Chi-Yo, Tzeng, Gwo-Hshiung
Format:	Article
Language:	English
Published:	Taiwan Fuzzy Systems Association 2011
Subjects:	H Social Sciences (General) QA75 Electronic computers. Computer science
Online Access:	http://irep.iium.edu.my/4407/ http://irep.iium.edu.my/4407/1/ijfs11-1-r-4-A_Novel_Method_for_Fuzzy_Measure_Identifi.pdf

id	iium-4407
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spelling	iium-44072015-03-19T08:42:14Z http://irep.iium.edu.my/4407/ A Novel Method for Fuzzy Measure Identification Larbani, Moussa Huang, Chi-Yo Tzeng, Gwo-Hshiung H Social Sciences (General) QA75 Electronic computers. Computer science Fuzzy measure and Choquet integral are effective tools for handling complex multiple criteria decision making (MCDM) problems in which criteria are inter- dependent. The identification of a fuzzy measure requires the determination of 2n −2 values when the number of criteria is n. The complexity of this problem increases exponentially, which makes it practically very difficult to solve. Many methods have been proposed to reduce the number of values to be determined including the introduction of new special fuzzy measures like the λ -fuzzy measures. However, manipulations of the proposed methods are difficult from the aspects of high data complexity as well as low computation efficiency. Thus, this paper proposed a novel fuzzy measure identification method by reducing the data complexity to n(n−1)/2 and enhancing the computation efficiency by leveraging a relatively small number of variables and constraints for linear programming. The proposed method was developed based on the evaluation of pair-wise additivity degrees or interdependence coefficients between the criteria. Depending on the information being provided by decision-makers on the individual density of each criterion, the fuzzy measure can be constructed by solving a simple system of linear inequalities or a linear programming problem. This novel method is validated through a supplier selection problem which occurs frequently in real-world decision-making problems. Validation results demonstrate that the newly-proposed method can model real-world MCDM problems successfully. Taiwan Fuzzy Systems Association 2011-03 Article PeerReviewed application/pdf en http://irep.iium.edu.my/4407/1/ijfs11-1-r-4-A_Novel_Method_for_Fuzzy_Measure_Identifi.pdf Larbani, Moussa and Huang, Chi-Yo and Tzeng, Gwo-Hshiung (2011) A Novel Method for Fuzzy Measure Identification. International Journal of Fuzzy Systems, 13 (1). pp. 24-34. ISSN 1562-2479
repository_type	Digital Repository
institution_category	Local University
institution	International Islamic University Malaysia
building	IIUM Repository
collection	Online Access
language	English
topic	H Social Sciences (General) QA75 Electronic computers. Computer science
spellingShingle	H Social Sciences (General) QA75 Electronic computers. Computer science Larbani, Moussa Huang, Chi-Yo Tzeng, Gwo-Hshiung A Novel Method for Fuzzy Measure Identification
description	Fuzzy measure and Choquet integral are effective tools for handling complex multiple criteria decision making (MCDM) problems in which criteria are inter- dependent. The identification of a fuzzy measure requires the determination of 2n −2 values when the number of criteria is n. The complexity of this problem increases exponentially, which makes it practically very difficult to solve. Many methods have been proposed to reduce the number of values to be determined including the introduction of new special fuzzy measures like the λ -fuzzy measures. However, manipulations of the proposed methods are difficult from the aspects of high data complexity as well as low computation efficiency. Thus, this paper proposed a novel fuzzy measure identification method by reducing the data complexity to n(n−1)/2 and enhancing the computation efficiency by leveraging a relatively small number of variables and constraints for linear programming. The proposed method was developed based on the evaluation of pair-wise additivity degrees or interdependence coefficients between the criteria. Depending on the information being provided by decision-makers on the individual density of each criterion, the fuzzy measure can be constructed by solving a simple system of linear inequalities or a linear programming problem. This novel method is validated through a supplier selection problem which occurs frequently in real-world decision-making problems. Validation results demonstrate that the newly-proposed method can model real-world MCDM problems successfully.
format	Article
author	Larbani, Moussa Huang, Chi-Yo Tzeng, Gwo-Hshiung
author_facet	Larbani, Moussa Huang, Chi-Yo Tzeng, Gwo-Hshiung
author_sort	Larbani, Moussa
title	A Novel Method for Fuzzy Measure Identification
title_short	A Novel Method for Fuzzy Measure Identification
title_full	A Novel Method for Fuzzy Measure Identification
title_fullStr	A Novel Method for Fuzzy Measure Identification
title_full_unstemmed	A Novel Method for Fuzzy Measure Identification
title_sort	novel method for fuzzy measure identification
publisher	Taiwan Fuzzy Systems Association
publishDate	2011
url	http://irep.iium.edu.my/4407/ http://irep.iium.edu.my/4407/1/ijfs11-1-r-4-A_Novel_Method_for_Fuzzy_Measure_Identifi.pdf
first_indexed	2023-09-18T20:12:36Z
last_indexed	2023-09-18T20:12:36Z
_version_	1777407577481543680

A Novel Method for Fuzzy Measure Identification

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