Abstract
This study examines a general scheme of multicriteria decision-making under uncertainty based on quantitative and qualitative information. In its original form, the general scheme uses qualitative information at the final decision stage, only if the quantitative information is unable to generate unique solutions. Considering that many problems require objectives based on qualitative information at all decision stages, the results of Ramalho et al. (2019) can provide such solutions. However, the processing of qualitative information in Ramalho et al. (2019) is based on applying a very simple approach to aggregating individual preferences without analyzing any type of consensus information. Therefore, the present study sets out to show that representative combinations of initial data, states of nature or scenarios can be constructed by using qualitative information directly, based on aggregating individual preferences after achieving the necessary consensus. In particular, a new scheme for consensus construction is proposed. Using this scheme enables negative points inherent in traditional approaches to be avoided and uncertainty levels to be reduced when estimating coefficients of objective functions based on qualitative information. An illustrative example is presented to demonstrate the results that the new proposal can achieve.
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References
Alonso S, Herrera-Viedma E, Cabrerizo FJ, Chiclana F, Herrera F (2007) Visualizing consensus in group decision making situations. In: Proceedings of the 2007 IEEE International Conference on Fuzzy Systems, p. 1–6. London. https://doi.org/10.1109/FUZZY.2007.4295642
Bellman RE, Zadeh LA (1970) Decision-making in a fuzzy environment. Management Science 17(4), 17:B141–B164. https://doi.org/10.1287/mnsc.17.4.B141
Belyaev LS (1977) A practical approach to choosing alternate solutions to complex optimization problems under uncertainty. IIASA, Laxenburg
Cabrerizo FJ, Al-Hmouz R, Morfeq A, Balamash AS, Martínez M, Herrera-Viedma E (2017) Soft consensus measures in group decision making using unbalanced fuzzy linguistic information. Soft Comput 21(11):3037–3050. https://doi.org/10.1007/s00500-015-1989-6
Chen SM, Lee LW, Yang SW, Sheu TW (2012) Adaptive consensus support model for group decision making systems. Expert Syst Appl 39(16):12580–12588. https://doi.org/10.1016/j.eswa.2012.05.026
Chen SM, Tsai BH (2013) A new method for autocratic decision making using group recommendations. In: Proceedings of the 2013 International Conference on Machine Learning and Cybernetics, vol. 3, pp. 1250–1255. IEEE, Tianjin. https://doi.org/10.1109/ICMLC.2013.6890780
Coello CAC (2003) Evolutionary multi-objective optimization: A critical review. In: Evolutionary Optimization. International Series in Operations Research & Management ScienceSpringer, Boston
Dong Y, Li CC, Xu Y, Gu X (2015) Consensus-based group decision making under multi-granular unbalanced 2-tuple linguistic preference relations. Group Decis Negot 24(2):217–242. https://doi.org/10.1007/s10726-014-9387-5
Ehrgott M (2005) Multicriteria optimization lecture notes in economics and mathematical systems. Springer, Heidelberg
Ekel P, Kokshenev I, Parreiras R, Pedrycz W, Pereira J Jr (2016) Multiobjective and multiattribute decision making in a fuzzy environment and their power engineering applications. Inf Sci 361:100–119. https://doi.org/10.1016/j.ins.2016.04.030
Ekel P, Pedrycz W, Pereira J Jr (2019) Multicriteria decision-making under conditions of uncertainty: fuzzy set Perspective. Wiley, Hoboken
Ekel P, Pedrycz W, Schinzinger R (1998) A general approach to solving a wide class of fuzzy optimization problems. Fuzzy Sets Syst 97(1):49–66. https://doi.org/10.1016/S0165-0114(96)00334-X
Ekel PY (2002) Fuzzy sets and models of decision making. Comput Math Appl 44(7):863–875. https://doi.org/10.1016/S0898-1221(02)00199-2
Ekel PY, Martini J, Palhares RM (2008) Multicriteria analysis in decision making under information uncertainty. Appl Math Comput 200(2):501–516
Ekel PY, Neto FHS (2006) Algorithms of discrete optimization and their application to problems with fuzzy coefficients. Inf Sci 176(19):2846–2868. https://doi.org/10.1016/j.ins.2005.06.001
Herrera F, Herrera-Viedma E, Chiclana F (2001) Multiperson decision-making based on multiplicative preference relations. Europ J Op Res 129(2):372–385. https://doi.org/10.1016/S0377-2217(99)00197-6
Herrera-Viedma E, Cabrerizo FJ, Kacprzyk J, Pedrycz W (2014) A review of soft consensus models in a fuzzy environment. Inf Fusion 17:4–13. https://doi.org/10.1016/j.inffus.2013.04.002
Hwang CL, Masud AS (1979) Multiple attribute decision making: methods and applications: a state-of-the-art survey. Lecture notes in economics and mathematical systems. Springer, Heidelberg
Hwang CL, Yoon K (1981) Multiple attribute decision making: methods and applications: a state-of-the-art survey. Lecture notes in economics and mathematical systems. Springer, New York
Koksalmis E, Kabak Ö (2019) Deriving decision makers’ weights in group decision making: an overview of objective methods. Inf Fusion 49:146–160. https://doi.org/10.1016/j.inffus.2018.11.009
Koksalmis E, Koksalmis GH, Kabak O (2019) A combined method for deriving decision makers’ weights in group decision making environment: An application in medical decision making. In: Industrial Engineering in the Big Data Era, Springer, New York
Liao H, Li Z, Zeng XJ, Liu W (2017) A comparison of distinct consensus measures for group decision making with intuitionistic fuzzy preference relations. Int J Comput Intell Syst 10(1):456–469. https://doi.org/10.2991/ijcis.2017.10.1.31
Liu Y, Qin Y, Xu L, Liu HB, Liu J (2019) Multiattribute group decision-making approach with linguistic pythagorean fuzzy information. IEEE Access 7:143412–143430. https://doi.org/10.1109/ACCESS.2019.2945005
Lootsma FA (2007) Multi-criteria decision analysis via ratio and difference judgement. Springer, Boston
Luce RD, Raiffa H (1958) Games and decisions: introduction and critical survey. New York. https://doi.org/10.1090/S0002-9904-1958-10180-9
de Morais Bezerra F, Melo P, Costa JP (2014) Visual and interactive comparative analysis of individual opinions: a group decision support tool. Group Decis Negot 23(1):101–125. https://doi.org/10.1007/s10726-012-9330-6F
Orlovsky S (1983) Problems of decision-making with fuzzy information. IIASA, Laxenburg
Parreiras R, Ekel P, Bernardes F Jr (2012) A dynamic consensus scheme based on a nonreciprocal fuzzy preference relation modeling. Inform Sci 211:1–17. https://doi.org/10.1016/j.ins.2012.05.001
Parreiras R, Ekel PY, Morais D (2012) Fuzzy set based consensus schemes for multicriteria group decision making applied to strategic planning. Group Decis Negot 21(2):153–183. https://doi.org/10.1007/s10726-011-9231-0
Parreiras RO, Ekel PY, Martini J, Palhares RM (2010) A flexible consensus scheme for multicriteria group decision making under linguistic assessments. Inf Sci 180(7):1075–1089. https://doi.org/10.1007/s10726-011-9231-0
Pedrycz W, Ekel P, Parreiras R (2011) Fuzzy multicriteria decision-making: models, methods and applications. Wiley, Chichester
Pedrycz W, Gomide F (1998) An introduction to fuzzy sets: analysis and design. Mit Press, Cambridge
Pereira J Jr, Ekel PY, Palhares RM, Parreiras RO (2015) On multicriteria decision making under conditions of uncertainty. Inf Sci 324:44–59
Raiffa H (1968) Decis Anal. Addison-Wesley, Reading
Ramalho F, Ekel P, Pedrycz W, Pereira J, Soares G (2019) Multicriteria decision making under conditions of uncertainty in application to multiobjective allocation of resources. Inf Fusion 49:249–261. https://doi.org/10.1016/j.inffus.2018.12.010
Ramalho FD (2017) Use of qualitative information in the decision-making process (in portuguese). Master’s thesis, Pontifícia Universidade Católica de Minas Gerais
Ramanathan R, Ganesh L (1994) Group preference aggregation methods employed in AHP: an evaluation and an intrinsic process for deriving members’ weightages. Europ J Op Res 79(2):249–265. https://doi.org/10.1016/0377-2217(94)90356-5
Roy B (2010) To better respond to the robustness concern in decision aiding: four proposals based on a twofold observation. In: Handbook of multicriteria analysis, pp. 3–24. Springer, Berlin/Heidelberg. https://doi.org/10.1007/978-3-540-92828-7_1
Saaty TL (1980) The analytic hierarchy process. McGraw-Hill, New York
Saaty TL, Peniwati K, Shang JS (2007) The analytic hierarchy process and human resource allocation: half the story. Math Comput Model 46(7–8):1041–1053. https://doi.org/10.1016/j.mcm.2007.03.01
Saaty TL, Vargas LG, Dellmann K (2003) The allocation of intangible resources: the analytic hierarchy process and linear programming. Socio-Econ Plan Sci 37(3):169–184. https://doi.org/10.1016/S0038-0121(02)00039-3
Sobol I, Statnikov R (2006) The choice of optimal parameters in problems with many criteria (in russian)
Sobol’ I (1979) On the systematic search in a hypercube. SIAM J Numeric Anal 16(5):790–793. https://doi.org/10.1137/0716058
Toloie-Eshlaghy A, Nazari Farokhi E (2011) Measuring the importance and the weight of decision makers in the criteria weighting activities of group decision making process. Am J Sci Res 24:6–12
Webster T (2003) Managerial economics: theory and practice. Academic Press, London
Yager RR (1988) On ordered weighted averaging aggregation operators in multicriteria decision making. IEEE Trans Syst, Man, Cybern 18(1):183–190. https://doi.org/10.1109/21.87068
Zhang Q, Chen JC, Chong PP (2004) Decision consolidation: criteria weight determination using multiple preference formats. Decis Support Syst 38(2):247–258. https://doi.org/10.1016/S0167-9236(03)00094-0
Zio E, Pedroni N (2013) Methods for representing uncertainty: A literature review. Numéro 2013-03 des Cahiers de la Sécurité Industrielle. Fondation pour une Culture de Sécurité Industrielle
Acknowledgements
This study was financed in part by the Coordenação de Aperfeiçoamento de Pessoal de Nível Superior – Brasil (CAPES) – Finance Code 001, Vale S.A. (within the Research, Development, and Innovation Partnership Agreement), and Conselho Nacional de Desenvolvimento Científico e Tecnológico — Brasil (CNPq) — Grant 311032/2016-8.
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Figueiredo, L.R., Frej, E.A., Soares, G.L. et al. Group Decision-Based Construction of Scenarios for Multicriteria Analysis in Conditions of Uncertainty on the Basis of Quantitative and Qualitative Information. Group Decis Negot 30, 665–696 (2021). https://doi.org/10.1007/s10726-021-09728-z
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DOI: https://doi.org/10.1007/s10726-021-09728-z