Abstract
Despite the increasing complexity of real-world multi-attribute decision-making (MADM) situations, the decision-makers have no problems in providing some incomplete (also called imprecise or partial) information about attribute (importance) weights. Often, incomplete weight information takes the form of weights bounded between upper and lower limits, ranked weights, etc. In this work, we deal with the important class of multi-attribute choice problems (MACPs) in which incomplete weight information consists of a ranking of weights. Prominent solution methods for such MACPs can be classified into dominance measuring methods (DMMs), or ordinal surrogate-weighting schemes. The object of the present article is to circumvent the shortcomings of the most efficacious solution methods that can be used to solve the MACPs under-ranked weights. To that end, we devise here an original safe sequential screening technique named the "TCA-algo'' method. The newly devised method follows three steps: (1) the decision matrix is normalized (if needed) and Pareto dominated alternatives are screened out, (2) a tentative choice alternative (TCA) is nominated from among Pareto optimal alternatives, and (3) the nominated TCA is tested using an appropriate dominance rule established herein. The second and third steps of the suggested method are repeated until a final choice alternative (FCA) is reached. Numerical examples and experimental results show convincingly that the TCA-algo method outperforms prominent solution methods.
Similar content being viewed by others
References
Aguayo EA, Mateos A, Jimenez A (2014) A new dominance intensity method to deal with ordinal information about a DM’s preference within MAVT. Knowl Based Syst 69:159–169
Ahn BS, Park KS (2008) Comparing methods for multi-attribute decision-making with ordinal weights. Comput Oper Res 35:1660–1670
Barron FH (1992) Selecting a best multiattribute alternative with partial information about attribute weights. Acta Physiol (oxf) 80:91–103
Belton V, Stewart JT (2002) Multiple criteria decision analysis: an integrated approach. Kluwer Academic Publishers, London
Chen TH (2010) An outcome-oriented approach to multi-criteria decision analysis with intuitionistic fuzzy optimistic/pessimistic operators. Expert Syst Appl 37:7762–7774
Chen Y, Marc Kilgour DM, Hipel KW (2008) Screening in multiple criteria decision analysis. Decis Support Syst 45:278–290
Cook WD, Kress M (1991) A multiple criteria decision model with ordinal preference data. Eur J Oper Res 54:191–198
Eum Y, Park KS, Kim SH (2001) Establishing dominance and potential optimality in multi-criteria analysis with imprecise weight and value. Comput Oper Res 28:397–409
Hobbs BF, Meier P (2000) Energy decisions and the environment: a guide to the use of multicriteria methods. Kluwer, Massachusetts
Hwang CL, Yoon K (1981) Multiple attribute decision-making: methods and applications. Springer, New York
Keeney R, Raiffa H (1976) Decision with multiples objectives: preferences and value tradeoffs. Wiley, New York
Keshavarz-Ghorabaee M et al (2015) Multi-criteria inventory classification using a new method of evaluation based on distance from average solution (EDAS). Informatica 26:435–451
Kim JH, Ahn BS (2019) Extended VIKOR method using incomplete criteria weights. Expert Syst Appl 126:124–132
Kim SH, Choi SH, Kim JK (1999) An interactive procedure for multiple attribute group decision-making with incomplete information: range based approach. Eur J Oper Res 118:139–152
Kunsch PL, Ishizaka A (2019) A note on using centroid weights in additive multi-criteria decision analysis. Eur J Oper Res 277:391–393
Lee K, Park KS, Eum YS, Park K (2001) Extended methods for identifying dominance and potential optimality in multi-criteria analysis with imprecise information. Eur J Oper Res 134:557–563
Li J, Chen Y, Yue C, Song H (2007) Dominance measuring based approach for multiattribute decision-making with imprecise weights. J Inf Comput Sci 9:3305–3313
Liu D et al (2020) An integrated approach towards modeling ranked weights. Comput Ind Eng. https://doi.org/10.1016/j.cie.2020.106629 (Article 106629)
Liu P et al (2021a) A weighting model based on best-worst method and its application for environmental performance evaluation. Appl Soft Comput. https://doi.org/10.1016/j.asoc.2021.107168 (Article 107168)
Liu P et al (2021b) Identify and rank the challenges of implementing sustainable supply chain blockchain technology using the Bayesian Best Worst Method. Technol Econ Dev Econ 27:656–680
Liu Y et al (2021c) Ranking range models under incomplete attribute weight information in the selected six MADM methods. Expert Syst Appl. https://doi.org/10.1111/exsy.12696
Madić M, Radovanović M, Manić M (2016) Application of the ROV method for the selection of cutting fluids. Decis Sci Lett 5:245–254
Mateos A, Jimenez A, Aguayo EA, Sabio P (2014) Dominance intensity measuring methods in MCDM with ordinal relations regarding weights. Eur J Oper Res 70:26–32
McCrimmon KR (1968) Decision making among multiple-attribute alternatives: a survey and consolidated approach. RAND Memorandum. RM-4823-ARPA. The RAND Corporation, Santa Monica
Muscat J (2014) Functional analysis: an introduction to metric spaces, Hilbert spaces, and Banach algebras. Springer, Berlin
Opricovic S (1998) Multicriteria optimization of civil engineering systems. Faculty of Civil Engineering, Belgrade
Ozerol G, Karasakal E (2008) Interactive outranking approaches for multicriteria decision-making problem with imprecise information. J Oper Res Soc 59:1253–1268
Park KS (2004) Mathematical programming models for characterizing dominance and potential optimality when multicriteria alternative values and weights are simultaneously incomplete. IEEE Trans Syst Man Cybern 34:601–614
Park KS, Jeong I (2011) How to treat strict preference information in multicriteria decision analysis. J Oper Res Soc 62:1771–1783
Park KS, Kim SH (1997) Tools for interactive multi-attribute decision-making with incompletely identified information. Eur J Oper Res 98:111–123
Rezaei J (2016) Best-worst multi-criteria decision-making method: Some properties and a linear model. Omega 64:26–130
Rebaï A, Martel JM (2000) Rangements BBTOPSIS fondés sur des intervalles de proximités relatives avec qualification des préférences. RAIRO Oper Res 34:449–465
Salo A, Punkka A (2005) A rank inclusion in criteria hierarchies. Eur J Oper Res 163:338–356
Sarin RK (1977) Screening of multiattribute alternatives. Omega 5:481–489
Song W, Zhu J (2019) Three-reference-point decision-making method with incomplete weight information considering independent and interactive characteristics. Inf Sci 503:148–168
Voorneveld M (2003) Characterization of Pareto dominance. Oper Res Lett 31:7–11
Walker WE (1986) The use of screening in policy analysis. Manag Sci 32:389–402
Wang J (2006) Multi-criteria decision-making approach with incomplete certain information based on ternary AHP. J Syst Eng Electron 17:109–114
Wang X, Wang J, Chen X (2016) Fuzzy multicriteria decision-making method based on fuzzy structured element with incomplete weight information. Iran J Fuzzy Syst 13:1–17
Weir JD, Hendrix J, Gutman AJ (2014) The triage method: screening alternatives over time with multi-objective decision analysis. Int J Multicrit Decis Mak 4:311–331
Xu Z (2007) A method for multiple attribute decision-making with incomplete weight information in linguistic setting. Knowl Based Syst 20:719–725
Yakowitz DS, Lane L, Szidaravoshy F (1993) Multiattribute decision-making dominance with respect to an importance order of the attributes. Appl Math Comput 54:167–181
Yang JB (2000) Minimax reference point approach and its application for multiobjective optimization. Eur J Oper Res 126:541–556
Yazdani M, Zaraté P, Zavadskas EK, Turskis Z (2019) A combined compromise solution (CoCoSo) method for multi-criteria decision-making problems. Manag Decis 57:2501–2519
Zadeh LA (1975) Calculs of fuzzy restrictions. In: Zadeh LA, Fu KS, Tanaka K, Shimura M (eds) Fuzzy sets and their applications to cognitive and decision processes. Academic Press, New York, pp 1–39
Zavadskas EK, Turskis Z (2010) A new additive ratio assessment (ARAS) method in multicriteria decision-making. Technol Econ Dev Econ 16:159–172
Zavadskas EK, Turskis Z, Antucheviciene J, Zakarevicius A (2012) Optimization of weighted aggregated sum product assessment. Elektronika Ir Elektrotechnika 122:3–6
Zhang XL, Xu ZS, Wang H (2015) Heterogeneous multiple criteria group decision making with incomplete weight information: a deviation modeling approach. Inf Fus 25:49–62
Acknowledgements
The authors are highly thankful to the four anonymous reviewers for their valuable comments and suggestions.
Funding
This research did not receive any specific funding.
Author information
Authors and Affiliations
Corresponding author
Ethics declarations
Conflict of interest
The authors have no conflicts of interest to declare.
Additional information
Communicated by Anibal Tavares de Azevedo.
Publisher's Note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
Appendix
Appendix
See Table 17.
Rights and permissions
About this article
Cite this article
Souissi, M., Hnich, B. A safe sequential screening technique for solving multi-attribute choice problems under ranked weights. Comp. Appl. Math. 41, 163 (2022). https://doi.org/10.1007/s40314-022-01843-0
Received:
Revised:
Accepted:
Published:
DOI: https://doi.org/10.1007/s40314-022-01843-0