[1] Xu Yejun, Da Qingli,. Approach to obtaining weights of uncertain ordered weightedgeometric averaging operator [J]. Journal of Southeast University (English Edition), 2008, 24 (1): 110-113. [doi:10.3969/j.issn.1003-7985.2008.01.024]

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Approach to obtaining weights of uncertain ordered weightedgeometric averaging operator()

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Journal of Southeast University (English Edition)[ISSN:1003-7985/CN:32-1325/N]

Volumn:

24

Issue:

2008 1

Page:

110-113

Research Field:

Economy and Management

Publishing date:

2008-03-30

Info

Title:

Approach to obtaining weights of uncertain ordered weightedgeometric averaging operator

Author(s):

Xu Yejun¹;  2;  Da Qingli¹

¹School of Economics and Management, Southeast University, Nanjing 210096, China
² College of Economics and Management, Nanjing Forestry University, Nanjing 210037, China

Keywords:

interval numbers;  uncertain ordered weighted geometric averaging operator;  possibility degree

PACS:

C934

DOI:

10.3969/j.issn.1003-7985.2008.01.024

Abstract:

The ordered weighted geometric averaging(OWGA)operator is extended to accommodate uncertain conditions where all input arguments take the forms of interval numbers.First, a possibility degree formula for the comparison between interval numbers is introduced.It is proved that the introduced formula is equivalent to the existing formulae, and also some desired properties of the possibility degree is presented.Secondly, the uncertain OWGA operator is investigated in which the associated weighting parameters cannot be specified, but value ranges can be obtained and the associated aggregated values of an uncertain OWGA operator are known.A linear objective-programming model is established; by solving this model, the associated weights vector of an uncertain OWGA operator can be determined, and also the estimated aggregated values of the alternatives can be obtained. Then the alternatives can be ranked by the comparison of the estimated aggregated values using the possibility degree formula.Finally, a numerical example is given to show the feasibility and effectiveness of the developed method.

References:

[1] Yager R R.On ordered weighted averaging aggregation operators in multicriteria decision making [J].IEEE Transactions on Systems, Man, and Cybernetics, 1988, 18(1):183-190.
[2] Yager R R, Kacpizyk J.The ordered weighted averaging operator:theory and applications [M].Boston, MA:Kluwer Academic Publishers, 1997:10-50.
[3] Yager R R.Families of OWA operators [J].Fuzzy Sets and Systems, 1993, 59(2):125-148.
[4] Torra V.The weighted OWA operator[J].International Journal of Intelligent Systems, 1997, 12(2):153-166.
[5] Filev D, Yager R R.On the issue of obtaining OWA operator weights [J].Fuzzy Sets and Systems, 1998, 94(2):157-169.
[6] Yager R R, Filev D P.Induced ordered weighted averaging operators[J].IEEE Transactions on Systems, Man, and Cybernetics, Part B:Cybernetics, 1999, 29(2):141-150.
[7] Yager R R.Induced aggregation operators [J].Fuzzy Sets and Systems, 2003, 137(1):59-69.
[8] Schaefer P A, Mitchell H B.A generalized OWA operator[J].International Journal of Intelligent Systems, 1999, 14(2):123-143.
[9] Ovchinnikov S.An analytic characterization of some aggregation operator [J].International Journal of Intelligent Systems, 1998, 13(1):59-68.
[10] Xu Z S, Da Q L.The uncertain OWA operator [J].International Journal of Intelligent Systems, 2002, 17(6):569-575.
[11] Bordogna G, Fedrizzi M, Pasi G.A linguistic modeling of consensus in group decision making based on OWA operator [J].IEEE Transactions on Systems, Man, and Cybernetics, 1997, 27(1):126-132.
[12] Herrera F, Herrera-Viedma E.Linguistic decision analysis:steps for solving decision problems under linguistic information[J].Fuzzy Sets and Systems, 2000, 115(1):67-82.
[13] Xu Z S, Da Q L.The ordered weighted geometric averaging operators [J].International Journal of Intelligent Systems, 2002, 17(7):709-716.
[14] Herrera F, Herrera-Viedma E, Chiclana F.Multiperson decision-making based on multiplicative preference relations[J].European Journal of Operational Research, 2001, 129(2):372-385.
[15] Xu Z S, Da Q L.Approaches to obtaining the weights of the ordered weighted aggregation operators[J].Journal of Southeast University:Natural Science Edition, 2003, 33(1):94-96.
[16] Xu Y J, Da Q L.Uncertain ordered weighted geometric averaging operator and its application to decision making [J].Systems and Engineering and Electronics, 2005, 27(6):1038-1040.
[17] Facchinetti G, Ricci R G, Muzzioli S.Note on ranking fuzzy triangular numbers[J].International Journal of Intelligent Systems, 1998, 13(6):613-622.

Memo

Memo:

Biographies: Xu Yejun(1979—), male, graduate;Da Qingli(corresponding author), male, professor, dqlseunj@126.com.
Foundation item: The Technological Innovation Foundation of Nanjing Forestry University(No.163060033).
Citation: .Xu Yejun, Da Qingli.Approach to obtaining weights of uncertain ordered weighted geometric averaging operator[J].Journal of Southeast University(English Edition), 2008, 24(1):110-113.

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