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Abstrakty
The geometric Bonferroni mean (GBM) is an important aggregation technique which reflects the correlations of aggregated arguments. Based on the GBM, in this paper, we develop the optimized weighted geometric Bonferroni mean (OWGBM) and the generalized optimized weighted geometric Bonferroni mean (GOWGBM), whose characteristics are to reflect the preference and interrelationship of the aggregated arguments. Furthermore, we develop the intuitionistic fuzzy optimized weighted geometric Bonferroni mean (IFOWGBM) and the generalized intuitionistic fuzzy optimized weighted geometric Bonferroni mean (GIFOWGBM), and study their desirable properties such as idempotency, commutativity, monotonicity and boundedness. Finally, based on the IFOWGBM and GIFOWGBM, we present an approach to multi-criteria decision making and illustrate it with a practical example.
Wydawca
Czasopismo
Rocznik
Tom
Strony
363--381
Opis fizyczny
Bibliogr. 29 poz., tab.
Twórcy
autor
- Department of Applied Mathematics, Pukyong National University, Busan 608-737, South Korea
autor
- Department of Applied Mathematics, Pukyong National University, Busan 608-737, South Korea
autor
- Department of Mathematics, Dong-A University, Busan 604-714, South Korea
Bibliografia
- [1] Yager RR. On ordered weighted averaging aggregation operators in multicriteria decision making,. IEEE Transactions on Systems, Man, and Cybernetics. 1988;18(1):183–190. doi:10.1109/21.87068.
- [2] Chiclana F, Herrera F, Herrera-Viedma E. The ordered weighted geometric operator: properties and application. In: in Proc. 8th Conf. Inform. Processing and Management of Uncertainty in Knowledgebased Systems (IPMU), Madrid, Spain; 2000. p. 985–991.
- [3] Xu ZS, Da QL. The ordered weighted geometric averaging operators. International Journal of Intelligent Systems. 2002;17(7):709–716. doi:10.1002/int.10045.
- [4] Yager RR. OWA aggregation over a continuous interval argument with applications to decision making. IEEE Transactions on Systems,Man, and Cybernetics. 2004;34(5):1952–1963. doi:10.1109/TSMCB.2004.831154.
- [5] Yager RR, Xu ZS. The continuous ordered weighted geometric operator and its application to decision making. Fuzzy Sets and Systems. 2006;157(10):1393–1402. doi:10.1016/j.fss.2005.12.001.
- [6] Xu ZS. On generalized induced linguistic aggregation operators. International Journal of General Systems. 2007;35(1):17–28. doi:10.1080/03081070500422836.
- [7] Xu ZS. EOWA and EOWG operators for aggregating linguistic labels based on linguistic reference relations. International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems. 2004;12:791–810. doi:10.1142/S0218488504003211.
- [8] Xu ZS. A method based on linguistic aggregation operators for group decision making. Information Sciences. 2004;166(1-4):19–30. doi:10.1016/j.ins.2003.10.006.
- [9] Yager RR. The power average operator. IEEE Transactions on Systems, Man and Cybernetics. 2001;31(6): 724–731. doi:10.1109/3468.983429.
- [10] Xu ZS, Yager R. Power-geometric operators and their use in group decision making,. IEEE Transactions on Fuzzy Systems. 2010;18(1):94–105. doi:1109/TFUZZ.2009.2036907.
- [11] Xu ZS. Approaches to multiple attribute group decision making based on intuitionistic fuzzy power aggregation operators. Knowledge-Based Systems. 2011;24(6):749–760. doi:10.1016/j.knosys.2011.01.011.
- [12] Choquet G. Theory of capacities. Annales de L’Institut Fourier (Crenoble). 1953;5:131–295. ISSN: 0373-0956.
- [13] Yager RR. Choquet aggregation using order inducing variables. International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems. 2004;12(1):69–88. doi:10.1142/S0218488504002667.
- [14] Z.S. Xu. Choquet integrals of weighted intuitionistic fuzzy information. 2010;180(5):726–736. doi:10.1016/j.ins.2009.11.011.
- [15] Tan CQ, Chen XH. Intuitionistic fuzzy Choquet integral operator for multi-criteria decision making. Expert Systems with Applications. 2010;37(1):149–157. doi:10.1016/j.eswa.2009.05.005.
- [16] Bonferroni C. Sulle medie multiple di potenze. Bollettino dell’UnioneMatematica Italiana. 1950;5(3-4):267–270. Available from: http://eudml.org/doc/196058.
- [17] Yager RR. On generalized Bonferroni mean operators for multi-criteria aggregation. International Journal of Approximate Reasoning. 2009;50(8):1279–1286. doi:10.1016/j.ijar.2009.06.004.
- [18] Beliakova G, James S, Mordelová J, Rückschlossová T, Yager RR. Generalized Bonferroni mean operators in multi-criteria aggregation. Fuzzy Sets and Systems. 2010;161(2227–2242):17. doi:10.1016/j.fss.2010.04.004.
- [19] Xu ZS, Yager R. Intuitionistic fuzzy Bonferroni means,. IEEE Transactions on Systems, Man and Cybernetics. 2011;41(2):568–578. doi:10.1109/TSMCB.2010.2072918.
- [20] Xia MM, Xu ZS, Zhu B. Generalized intuitionistic fuzzy Bonferroni means. International Journal of Intelligent Systems. 2012;27(1):23–47. doi:10.1002/int.20515.
- [21] Zhou W, He JM. Intuitionistic fuzzy geometric Bonferroni means and their application in multi-criteria decisin making. International Journal of Intelligent Systems. 2012;27(12):995–1019. doi:10.1002/int.21558.
- [22] ZhouW, He JM. Intuitionistic fuzzy normalizedweighted Bonferronimean and its application in multicriteria decision making. Journal of Applied Mathematics. 2012;2012:22. Article ID 136254. Available from: http://dx.doi.org/10.1155/2012/136254. doi:10.1155/2012/136254.
- [23] Xia MM, Xu ZS, Zhu B. Geometric Bonferroni means with their application in multi-criteria decision making. Knowledge-Based Systems. 2013;40:88–100. doi:10.1016/j.knosys.2012.11.013.
- [24] Wei GW, Zhao X, Lin R, Wang HJ. Uncertain linguistic Bonferroni mean operators and their application to multiple attribute decision making. Applied Mathematical Modelling. 2013;37(7):5277–5285. doi:10.1016/j.apm.2012.10.048.
- [25] Atanassov K. Intuitionistic fuzzy sets. Fuzzy Sets and Systems. 1986;20(1):87–96. doi:10.1016/S0165-0114(86)80034-3.
- [26] Atanassov K, Gargov G. Interval-valued intuitionistic fuzzy sets. Fuzzy Sets and Systems. 1989;31(3):343–349. doi:10.1016/0165-0114(89)90205-4.
- [27] Xu ZS. Intuitionistic fuzzy aggregation operators. IEEE Transactions on Fuzzy Systems. 2007;15(6):1179–1187. doi:10.1109/TFUZZ.2006.890678.
- [28] Xu ZS, Yager R. Some geometric aggregation operators based on intuitionistic fuzzy sets. International Journal of General Systems. 2006;35(4):417–433. doi:10.1080/03081070600574353.
- [29] Xu ZS, Hu H. Projection models for intuitionistic fuzzy multiple attribute decision making. International Journal of Information Technology and Decision Making. 2010;9(2):267–280. doi:10.1142/S0219622010003816.
Typ dokumentu
Bibliografia
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