Abstract
Dynamic multiattribute decision-making (DMADM) problems are very common in real life and meaningful as research topic. In this paper, the focus is the DMADM problems with correlated periods, in which the attribute assessment values take the form of 2-tuple linguistic values. The concept of the discrete time 2-tuple linguistic variable where is introduced to describe a collection of 2-tuple linguistic values collected from different periods. To aggregate 2-tuple information gathered in multiple periods whose importance are interdependent or interactive, the 2-tuple linguistic dynamic correlated averaging \(2\mathrm{TDCA}_{\vartheta }\) and the 2-tuple linguistic dynamic correlated geometric \(2\mathrm{TDCG}_{\vartheta }\) aggregation operators are developed based on the Choquet integral. A 2-tuple linguistic DMADM approach based on \(2\mathrm{TDCA}_{\vartheta }\) and \(2\mathrm{TDCG}_{\vartheta }\) aggregation operators is also presented. Finally, an illustrative example is given to verify the developed approach and to demonstrate its practicability and effectiveness.
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References
Beg I, Rashid T (2014) Aggregation operators of interval-valued 2-tuple linguistic information. Int J Intell Syst 29(7):634–667. https://doi.org/10.1002/int.21650
Beliakov G (2005) Learning weights in the generalized owa operators. Fuzzy Optim Decis Making 4(2):119–130. https://doi.org/10.1007/s10700-004-5868-3
Bonetti A, Bortot S, Fedrizzi M, Pereira RM, Molinari A (2012) Modelling group processes and effort estimation in project management using the choquet integral: an mcdm approach. Expert Syst Appl 39(18):13,366–13,375. https://doi.org/10.1016/j.eswa.2012.05.066
Büyüközkan G, Ruan D (2010) Choquet integral based aggregation approach to software development risk assessment. Inf Sci 180(3):441–451. https://doi.org/10.1016/j.ins.2009.09.009
Choquet G (1954) Theory of capacities. Ann de l’institut Fourier 5:131–295
Dempster A (2008) Upper and lower probabilities induced by a multivalued mapping. Springer, Berlin, Heidelberg, pp 57–72. https://doi.org/10.1007/978-3-540-44792-4-3
Dubois D, Prade H (1988) Possibility theory. Plenum Press, New York
Dutta B, Guha D (2015) Partitioned bonferroni mean based on linguistic 2-tuple for dealing with multi-attribute group decision making. Appl Soft Comput 37:166–179. https://doi.org/10.1016/j.asoc.2015.08.017
Grabisch M (1995) Fuzzy integral in multicriteria decision making. Fuzzy Sets Syst 69(3):279–298. https://doi.org/10.1016/0165-0114(94)00174-6
Grabisch M (1996) The application of fuzzy integrals in multicriteria decision making. Eur J Oper Res 89(3):445–456. https://doi.org/10.1016/0377-2217(95)00176-X
Grabisch M (1997) k-order additive discrete fuzzy measures and their representation. Fuzzy Sets Syst 92(2):167–189. https://doi.org/10.1016/S0165-0114(97)00168-1 (fuzzy Measures and Integrals)
Grabisch M, Murofushi T, Sugeno M (2000) Fuzzy measure and integrals. Physica-Verlag, New York
Greco S, Matarazzo B, Giove S (2011) The choquet integral with respect to a level dependent capacity. Fuzzy Sets Syst 175(1):1–35. https://doi.org/10.1016/j.fss.2011.03.012 (theme: Aggregation Functions, Generalised Measure Theory)
Gumus S, Bali O (2017) Dynamic aggregation operators based on intuitionistic fuzzy tools and einstein operations. Fuzzy Inf Eng 9(1):45–65. https://doi.org/10.1016/j.fiae.2017.03.003
Herrera F, Herrera-Viedma E (2000) Linguistic decision analysis: steps for solving decision problems under linguistic information. Fuzzy Sets Syst 115:67–82
Herrera F, Martínez L (2000) A 2-tuple fuzzy linguistic representation model for computing with words. IEEE Trans Fuzzy Syst 8(6):746–752
Herrera F, Alonso S, Chiclana F, Herrera-Viedma E (2009) Computing with words in decision making: foundations, trends and prospects. Fuzzy Optim Decis Making 8(4):337–364. https://doi.org/10.1007/s10700-009-9065-2
Jimenez G, Zulueta Y (2016) A dynamic decision making method with discrimination of alternatives using associative aggregation operators. IEEE Latin Am Trans 14(10):4310–4317. https://doi.org/10.1109/TLA.2016.7786310
Jimenez G, Zulueta Y (2017) A 2-tuple linguistic multi-period decision making approach for dynamic green supplier selection. Rev DYNA 84(202):199–206. https://doi.org/10.15446/dyna.v84n202.58032
Krishnan AR, Kasim MM, Bakar EMNEA (2015) A short survey on the usage of choquet integral and its associated fuzzy measure in multiple attribute analysis. Proc Comput Sci 59(Supplement C):427–434. https://doi.org/10.1016/j.procs.2015.07.560 [international Conference on Computer Science and Computational Intelligence (ICCSCI 2015)]
Li J, Yao X, Sun X, Wu D (2018) Determining the fuzzy measures in multiple criteria decision aiding from the tolerance perspective. Eur J Oper Res 264(2):428–439. https://doi.org/10.1016/j.ejor.2017.05.029
Liao H, Xu Z, Xu J (2014) An approach to hesitant fuzzy multi-stage multi-criterion decision making. Kybernetes 43(9):1447–1468
Liu H, Cai J, Martínez L (2013) The importance weighted continuous generalized ordered weighted averaging operator and its application to group decision making. Knowl Based Syst 48(1):24–36. https://doi.org/10.1016/j.knosys.2013.04.002
Liu Y (2014) A method for 2-tuple linguistic dynamic multiple attribute decision making with entropy weight. J Intell Fuzzy Syst 27(4):1803–1810. https://doi.org/10.3233/IFS-141147
Martínez L, Herrera F (2012) An overview on the 2-tuple linguistic model for computing with words in decision making: extensions, applications and challenges. Inf Sci 207(1):1–18. https://doi.org/10.1016/j.ins.2012.04.025
Martínez L, Rodríguez RM, Herrera F (2015) The 2-tuple Linguistic Model. Computing with Words in Decision Making, 1st edn. Springer International Publishing, New York. https://doi.org/10.1007/978-3-319-24714-4
Meng F, Chen X (2015) An approach to uncertain linguistic multi-attribute group decision making based on interactive index. Int J Uncertain Fuzziness Knowl Based Syst 23(03):319–344. https://doi.org/10.1142/s0218488515500130
Meng F, Tan C (2017) A method for multi-attribute group decision making based on generalized interval-valued intuitionistic fuzzy choquet integral operators. Int J Uncertain Fuzziness Knowl Based Syst 25(05):821–849. https://doi.org/10.1142/S0218488517500350
Meng F, Tang J (2013) Extended 2-tuple linguistic hybrid aggregation operators and their application to multi-attribute group decision making. Int J Comput Intell Syst 4(2):1–14
Merigó J, Gil-Lafuente A (2013) Induced 2-tuple linguistic generalized aggregation operators and their application in decision-making. Inf Sci 236:1–16
Merigó J, Casanovas M, Martínez L (2010) Linguistic aggregation operators for linguistic decision making based on the Dempster-Shafer theory of evidence. Int J Uncertain Fuzziness Knowl Based Syst 18(3):287–304. https://doi.org/10.1142/S0218488510006544
Miranda P, Grabish M, Gil P (2002) p-symmetric fuzzy measures. Int J Uncertain Fuzziness Knowl Based Syst 10(supp01):105–123. https://doi.org/10.1142/S0218488502001867
Pedrycz W, Chen S (2011) Granular computing and intelligent systems: design with information granules of higher order and higher type. Springer, Heidelberg
Pedrycz W, Chen S (2015a) Granular computing and decision-making: interactive and iterative approaches. Springer, Heidelberg
Pedrycz W, Chen S (2015b) Information granularity, big data, and computational intelligence. Springer, Heidelberg
Peláez J, Dońa J (2003) LAMA: A linguistic aggregation of majority additive operator. Int J Intell Syst 18(7):809–820. https://doi.org/10.1002/int.10117
Peng D, Wang H (2014) Dynamic hesitant fuzzy aggregation operators in multi-period decision making. Kybernetes 43(5):715–736
Shafer G (1976) A mathematical theory of evidence. Princeton University Press, Princeton, NJ
Sirbiladze G, Badagadze O (2017) Intuitionistic fuzzy probabilistic aggregation operators based on the choquet integral: Application in multicriteria decision-making. Int J Inf Technol Decis Mak 16(01):245–279. https://doi.org/10.1142/S0219622016500449
Sugeno M (1974) Theory of fuzzy integral and its application, doctorial dissertation. Ph.D. thesis, Tokyo Institute of Technology
Sun B, fei Xu X (2016) A dynamic stochastic decision-making method based on discrete time sequences. Knowl Based Syst 105(Supplement C):23–28. https://doi.org/10.1016/j.knosys.2016.04.001
Tan C, Chen X (2010) Intuitionistic fuzzy choquet integral operator for multi-criteria decision making. Expert Syst Appl 37(1):149–157. https://doi.org/10.1016/j.eswa.2009.05.005
Teng D (2011) Topsis method for dynamic evaluation of hi-tech enterprise’s strategic performance with intuitionistic fuzzy information. Adv Inf Sci Serv Sci 3(11):443–449
Wan S (2013) Some hybrid geometric aggregation operators with 2-tuple linguistic information and their applications to multi-attribute group decision making. Int J Comput Intell Syst 6(4):750–763. https://doi.org/10.1080/18756891.2013.804144
Wang J, Wang D, Zhang H, Chen X (2013) Multi-criteria group decision making method based on interval 2-tuple linguistic information and choquet integral aggregation operators. Soft Comput 19(2):389–405
Wang Z, Klir G (1992) Fuzzy measure theory
Wei G (2011) Grey relational analysis model for dynamic hybrid multiple attribute decision making. Knowl Based Syst 24(5):672–679. https://doi.org/10.1016/j.knosys.2011.02.007
Wei G, Zhao X (2012) Some dependent aggregation operators with 2-tuple linguistic information and their application to multiple attribute group decision making. Expert Syst Appl 39(5):5881–5886. https://doi.org/10.1016/j.eswa.2011.11.120
Wei G, Alsaadi FE, Hayat T, Alsaedi A (2016) Picture 2-tuple linguistic aggregation operators in multiple attribute decision making. Soft Comput. https://doi.org/10.1007/s00500-016-2403-8
Xu Z (2008) On multi-period multi-attribute decision making. Knowl Based Syst 21(2):164–171
Xu Z (2009a) A method based on the dynamic weighted geometric aggregation operator for dynamic hybrid multi-attribute group decision making. Int J Uncertain Fuzziness Knowl Based Syst 17(1):15–33. https://doi.org/10.1142/S0218488509005711
Xu Z (2009b) Multi-period multi-attribute group decision-making under linguistic assessments. Int J Gen Syst 38(8):823–850. https://doi.org/10.1080/03081070903257920
Xu Z (2010) Choquet integrals of weighted intuitionistic fuzzy information. Inf Sci 180(5):726–736. https://doi.org/10.1016/j.ins.2009.11.011
Xu Z (2011) Approaches to multi-stage multi-attribute group decision making. Int J Inf Technol Decis Mak 10(01):121–146. https://doi.org/10.1142/S0219622011004257
Xu Z, Chen J (2007) Binomial distribution based approach to deriving time series weights. Industrial Engineering and Engineering Management, IEEE International Conference on pp 23–28. https://doi.org/10.1109/IEEM.2007.4419170
Xu Z, Wang H (2016) Managing multi-granularity linguistic information in qualitative group decision making: an overview. Granul Comput 1(1):21–35. https://doi.org/10.1007/s41066-015-0006-x
Xu Z, Yager R (2008) Dynamic intuitionistic fuzzy multi-attribute decision making. Int J Approx Reason 48(1):246–262
Yager R, Alajlan N (2015) Fuzzy measures in multi-criteria decision making. Proc Comput Sci 62(Supplement C):107–115. https://doi.org/10.1016/j.procs.2015.08.421 [proceedings of the 2015 International Conference on Soft Computing and Software Engineering (SCSE’15)]
Yang W (2013) Induced Choquet integrals of 2-tuple linguistic information. Int J Uncertain Fuzziness Know Based Syst 21(02):175–200. https://doi.org/10.1142/S0218488513500104
Yang W, Chen Z (2012) New aggregation operators based on the choquet integral and 2-tuple linguistic information. Expert Syst Appl 39(3):2662–2668. https://doi.org/10.1016/j.eswa.2011.08.121
Yang Z, Huang L (2017) Dynamic stochastic multiattribute decision-making that considers stochastic variable variance characteristics under time-sequence contingency environments. Math Probl Eng. https://doi.org/10.1155/2017/7126856
Zadeh L (1975) The concept of a linguistic variable and its application to approximate reasoning-I, II and III. Inf Sci 8(3):199–249. https://doi.org/10.1016/0020-0255(75)90036-5
Zadeh L (1996) Fuzzy logic = computing with words. Trans Fuzzy Syst 4(2):103–111. https://doi.org/10.1109/91.493904
Zadeh LA (1997) Toward a theory of fuzzy information granulation and its centrality in human reasoning and fuzzy logic. Fuzzy Sets Syst 90(2):111–127. https://doi.org/10.1016/S0165-0114(97)00077-8
Zhang L, Zou H, Yang F (2011) A dynamic web service composition algorithm based on topsis. J Netw 6(9):1296–1304
Zhang S (2011) A model for evaluating computer network security systems with 2-tuple linguistic information. Comput Math Appl 62(4):1916–1922. https://doi.org/10.1016/j.camwa.2011.06.035
Zhu H, Zhao J, Xu Y (2016) 2-dimension linguistic computational model with 2-tuples for multi-attribute group decision making. Knowl Based Syst 103:132–142. https://doi.org/10.1016/j.knosys.2016.04.006
Zulueta Y, Martell V, Martínez L (2013a) A dynamic multi-expert multi-criteria decision making model for risk analysis. In: Lectures Notes in Computer Science, Lectures Notes in Artificial intelligence, vol 8265, pp 132–143
Zulueta Y, Martínez J, Bello R, Martínez L (2013b) A discrete time variable index for supporting dynamic multi-criteria decision making. Int J Uncertain Fuzziness Knowl Based Syst 22(1):1–22
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Zulueta-Veliz, Y., García-Cabrera, L. A Choquet integral-based approach to multiattribute decision-making with correlated periods. Granul. Comput. 3, 245–256 (2018). https://doi.org/10.1007/s41066-018-0095-4
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DOI: https://doi.org/10.1007/s41066-018-0095-4