Abstract
As an extension of the prioritized aggregation operators by Yager (Int J Approx Reason 48:263–274, 2008), this paper uses the priority labels to express the prioritized relationship between criteria and presents some scaled prioritized aggregation operators, including the scaled prioritized score operator and the scaled prioritized averaging operator. Moreover, we consider the priority under uncertain environment and develop the uncertain prioritized aggregation operators, including the uncertain prioritized scoring operator and the uncertain prioritized averaging operator. We investigate the properties of these operators and build the models to derive the weights by maximizing square deviations from a possible range to distinguish the candidate alternatives mostly. Furthermore, approaches to multi-attribute decision making based on the proposed operators are given, which have benefits over the TOPSIS method (Behzadian, Expert Syst Appl 39:13051–13069, 2012) and the methods based on the OWA operator (Zhou and Chen, Fuzzy Sets Syst 168:18–34, 2011) when prioritized relationship between criteria is considered. Finally, examples are illustrated to show the feasibility and validity of the new approaches to the application of decision making.
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Atanassov K (1986) Intuitionistic fuzzy sets. Fuzzy Sets Syst 80:87–96
Butnariu D (1983) Additive fuzzy measures and integrals. J Math Anal Appl 93:423–452
Behzadian M, Otaghsara SK, Yazdani M, Ignatius J (2012) A state-of the-art survey of TOPSIS applications. Expert Syst Appl 39:13051–13069
Das B, Maity K, Maiti M (2007) A two warehouse supply-chain model under possibility/necessity/credibility measures. Math Comput Modell 46:398–409
Dubois D, Prade H (1980) Fuzzy sets and systems: theory and applications. Academic Press, New York
Dubois D, Prade H (1998) Possibility theory: qualitative and quantitative aspects. In: Quantified representation of uncertainty and imprecision, Handbook of Defeasible Reasoning and Uncertainty Management Systems, vol 1. Kluwer Academic Publishers, The Netherlands, pp 169–226
Dubois D, Prade H (2009) Possibility theory and formal concept analysis in information systems. In: Proceedings of IFSA’09, International Fuzzy Systems Association World Congress, Lisbon, pp 1021–1026
Dubois D (2006) Possibility theory and statistical reasoning. Comput Statistics Data Anal 51:47–69
Djouadi Y, Dubois D, Prade H (2010) Possibility theory and formal concept analysis: context decomposition and uncertainty handling. In: Hüllermeier E, Kruse R, Hoffmann F (eds) Proceedings of the International Conference on Information Processing and Management of Uncertainty in Knowledge-based Systems (IPMU), Lecture Notes in Artificial Intelligence, vol 6178. Springer, Dortmund, pp 260–269
Gong ZW, Forrest J, Yang YJ (2013) The optimal group consensus models for 2-tuple linguistic preference relations. Knowl Based Syst 37:427–437
Greene R, Devillers R, Luther JE (2011) GIS-based multi-criteria analysis. Geogr Compass 5(6):412–432
Harsanyi JC (1955) Cardinal welfare, individualistic ethics, and interpersonal comparisons of utility. J Polit Econ 63:309–321
He YD, Chen HY, Zhou LG, Liu JP, Tao ZF (2014) Intuitionistic fuzzy geometric interaction averaging operators and their application to multi-criteria decision making. Inf Sci 259:142–159
He YD, Chen HY, Zhou LG, Han B, Zhao QY, Liu JP (2014) Generalized intuitionistic fuzzy geometric interaction operators and their application to decision making. Expert Syst Appl 41:2484–2495
Huang IB, Keisler J, Linkov I (2011) Multi-criteria decision analysis in environmental science: ten years of applications and trends. Sci Total Environ 409:3578–3594
Hwang CL, Yoon K (1981) Multiple attribute decision making: methods and applications. Springer, New York
Hwang CL, Lai YJ, Liu TY (1993) A new approach for multiple objective decision making. Comput Oper Res 20:889–889
Loquin K, Dubois D (2012) A fuzzy interval analysis approach to kriging with ill-known variogram and data. Soft Comput 16:769–784
Liu B, Iwamura KB (1998) Chance constraint programming with fuzzy parameters. Fuzzy Sets Syst 94:227–237
Liu B, Iwamura KB (1998) A note on chance constrained programming with fuzzy coefficients. Fuzzy Sets Syst 100:229–233
Merigó JM, Gil-Lafuente AM, Zhou LG, Chen HY (2011) Generalization of the linguistic aggregation operator and its application in decision making. J Syst Eng Electron 22:593–603
Wu ZB, Chen YH (2007) The maximizing deviation method for group multiple attribute decision making under linguistic environment. Fuzzy Sets Syst 158:1608–1617
Wei GW (2012) Hesitant fuzzy prioritized operators and their application to multiple attribute decision making. Knowl Based Syst 31:176–182
Xu ZS (2001) Algorithm for priority of fuzzy complementary judgment matrix. J Syst Eng 16(4):311–314
Xu ZS (2007) Intuitionistic fuzzy aggregation operations. IEEE Trans Fuzzy Syst 15:1179–1187
Xu ZS, Da QL (2003) Possibility degree method for ranking interval numbers and its application. J Syst Eng 18(1):67–70
Xu ZS (2008) Group decision making based on multiple types of linguistic preference relations. Inf Sci 178:452–467
Xu ZS (2007) Intuitionistic preference relations and their application in group decision making. Inf Sci 177:2363–2379
Xu ZS (2004) Uncertain multiple attribute decision making: methods and applications. Tsinghua University Press, Beijing
Yager RR (1988) On ordered weighted averaging aggregation operators in multi-criteria decision making. IEEE Trans Syst Man Cybern 18:183–190
Yager RR (1996) Quantifier guided aggregation using OWA operators. Int J Intell Syst 11:49–73
Yager RR (2004) OWA aggregation over a continuous interval argument with applications to decision making. IEEE Trans Syst Man Cybern Part B 34:1952–1963
Yager RR (2008) Prioritized aggregation operators. Int J Approx Reason 48:263–274
Yoon K (1987) A reconciliation among discrete compromise situations. J Oper Res Soc 38:277–286
Yoon KP, Hwang C (1995) Multiple attribute decision making: an introduction. SAGE publications, California
Yu DJ, Wu YY, Lu T (2012) Interval-valued intuitionistic fuzzy prioritized operators and their application in group decision making. Knowl Based Syst 30:57–66
Yu XH, Xu ZS (2013) Prioritized intuitionistic fuzzy aggregation operators. Inf Fusion 14:108–116
Zadeh LA (1965) Fuzzy set. Inf Control 8:338–353
Zadeh LA (1978) Fuzzy sets as a basis for a theory of possibility. Fuzzy Sets Syst 1:3–28
Zavadskas EK, Zakarevicius A, Antucheviciene J (2006) Evaluation of ranking accuracy in multi-criteria decisions. Informatica 17:601–618
Zhou LG, Chen HY (2011) Continuous generalized OWA operator and its application to decision making. Fuzzy Sets Syst 168:18–34
Zhou LG, Chen HY, Merigó JM, Gil-Lafuente AM (2012) Uncertain generalized aggregation operators. Expert Syst Appl 39:1105–1117
Zhu B, Xu ZS, Xia MM (2012) Hesitant fuzzy geometric Bonferroni means. Inf Sci 205:72–85
Acknowledgments
The authors are thankful to the anonymous reviewers and the editor for their valuable comments and constructive suggestions that have led to an improved version of this paper. The work was supported by National Natural Science Foundation of China (Nos. 71071002, 71225006, 71371011, 71301001), Higher School Specialized Research Fund for the Doctoral Program (No. 20123401110001), The Scientific Research Foundation of the Returned Overseas Chinese Scholars, Anhui Provincial Natural Science Foundation (No. 1308085QG127), Provincial Natural Science Research Project of Anhui Colleges (No. KJ2012A026), Humanity and Social Science Youth Foundation of Ministry of Education (No. 13YJC630092), Humanities and social science Research Project of Department of Education of Anhui Province (No. SK2013B041).
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He, Y., Chen, H., He, Z. et al. Scaled prioritized aggregation operators and their applications to decision making. Soft Comput 20, 1021–1039 (2016). https://doi.org/10.1007/s00500-014-1562-8
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DOI: https://doi.org/10.1007/s00500-014-1562-8