Abstract
Dominance-based Rough Set Approach (DRSA) has been proposed as a machine learning and knowledge discovery methodology to handle Multiple Criteria Decision Aiding (MCDA). Due to its capacity of asking the decision maker (DM) for simple preference information and supplying easily understandable and explainable recommendations, DRSA gained much interest during the years and it is now one of the most appreciated MCDA approaches. In fact, it has been applied also beyond MCDA domain, as a general knowledge discovery and data mining methodology for the analysis of monotonic (and also non-monotonic) data. In this contribution, we recall the basic principles and the main concepts of DRSA, with a general overview of its developments and software. We present also a historical reconstruction of the genesis of this methodology, with a specific focus on the contribution of Roman Słowiński.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Similar content being viewed by others
Notes
- 1.
- 2.
- 3.
- 4.
- 5.
References
Błaszczyński J, Greco S, Słowiński R, Szeląg M (2006) On variable consistency dominance-based rough set approaches. In: Greco S, Hata Y, Hirano S, Inuiguchi M, Miyamoto S, Nguyen HS, Słowiński R (eds) Rough sets and current trends in computing 2006. Lecture notes in artificial intelligence, vol 4259. Springer, Berlin, Heidelberg, pp 191–202
Błaszczyński J, Greco S, Słowiński R (2007) Multi-criteria classification – a new scheme for application of dominance-based decision rules. Eur J Oper Res 181(3):1030–1044
Błaszczyński J, Greco S, Słowiński R, Szeląg M (2007) Monotonic variable consistency rough set approaches. In: Yao J, Lingras P, Wu W, Szczuka M, Cercone NJ, Ślezak D (eds) Rough sets and knowledge technology 2007. Lecture notes in artificial intelligence, vol 4481. Springer, New York, pp 126–133
Błaszczyński J, Greco S, Słowiński R, Szeląg M (2009) Monotonic variable consistency rough set approaches. Int J Approx Reason 50(7):979–999.
Błaszczyński J, Słowiński R, Szeląg M (2011) Sequential covering rule induction algorithm for variable consistency rough set approaches. Inf Sci 181:987–1002.
Błaszczyński J, Greco S, Słowiński R (2012) Inductive discovery of laws using monotonic rules. Eng Appl Artif Intell 25:284–294.
Błaszczyński J, Słowiński R, Szeląg M (2012) Induction of ordinal classification rules from incomplete data. In: Yao J, et al (eds) Rough sets and current trends in computing 2012. LNAI, vol 7413. Springer, New York, pp 56–65
Błaszczyński J, Greco S, Matarazzo B, Słowiński R, Szeląg M (2013) jMAF – Dominance-based Rough Set Data Analysis Framework. In: Skowron A, Suraj Z (eds) Rough sets and intelligent systems – Professor Zdzisław Pawlak in memoriam: Volume 1, Intelligent systems reference library, vol 42. Springer, New York, pp 185–209
Bouyssou D (1992) Ranking methods based on valued preference relations: a characterization of the net flow method. Eur J Oper Res 60:61–67
Bouyssou D, Vincke P (1997) Ranking alternatives on the basis of preference relations: a progress report with special emphasis on outranking relations. J Multi-Crit Decis Anal 6:77–85
Branke J, Deb K, Miettinen K, Słowiński R (eds) (2008) Multiobjective optimization: interactive and evolutionary approaches, vol 5252. Springer Science & Business Media, Berlin
Corrente S, Greco S, Matarazzo B, Słowiński R (2021) Explainable interactive evolutionary multiobjective optimization. Available at SSRN 3792994
Dembczyński K, Greco S, Słowiński R (2002) Methodology of rough-set-based classification and sorting with hierarchical structure of attributes and criteria. Control Cybernet 31:891–920
Dembczyński K, Greco S, Słowiński R (2003) Dominance-based rough set approach to multicriteria classification with interval evaluations and assignments. In: Proceedings of the third international conference on decision support for telecommunications and information society, Warsaw, pp 73–84
Dembczyński K, Greco S, Słowiński R (2005) Second-order rough approximations in multi-criteria classification with imprecise evaluations and assignments. In: Ślezak D, Wang G, Szczuka M, Düntsch I, Yao Y (eds) Rough sets, fuzzy sets, data mining, and granular computing. Lecture notes in artificial intelligence, vol 3641. Springer, New York, pp 54–63
Dembczyński K, Greco S, Słowiński R (2009) Rough set approach to multiple criteria classification with imprecise evaluations and assignments. Eur J Oper Res 198(2):626–636
Dimitras AI, Słowiński R, Susmaga R, Zopounidis C (1999) Business failure prediction using rough sets. Eur J Oper Res 114(2):263–280
Du WS, Hu BQ (2016) Dominance-based rough set approach to incomplete ordered information systems. Inf Sci 346–347:106–129
Dubois D, Prade H, Esteva F, Garcia P, Godo L, Lopez de Mantaras R (1998) Fuzzy set modelling in case-based reasoning. Int J Intell Syst 13:345–373
Dziecioł T, Szmyt D, Zimny M (2020) Platform for multi-criteria classification support based on decision-rule preference model. B. Sc. thesis, Poznan University of Technology, supervisor: Marcin Szeląg
Fandel G, Gál T, Hanne T (eds) (1997) Multiple criteria decision making. Springer, New York
Fortemps P, Greco S, Słowiński R (2008) Multicriteria decision support using rules that represent rough-graded preference relations. Eur J Oper Res 188(1):206–223
Fürnkranz J (1999) Separate-and-conquer rule learning. Artif Intell Rev 13:3–54
Fürnkranz J, Hüllermeier E (eds) (2010) Preference learning. Springer, Berlin
Gal T, Stewart T, Hanne T (eds) (2013) Multicriteria decision making: advances in MCDM models, algorithms, theory, and applications, vol 21. Springer Science & Business Media, Berlin
Greco S, Matarazzo B, Słowiński R (1995) Rough set approach to multi-attribute choice and ranking problems. ICS Research Report 38/95, ICS, Warsaw University of Technology
Greco S, Matarazzo B, Słowiński R (1996) Rough approximation of a preference relation by dominance relations. In: Tsumoto S, Kobayashi S, Yokomori T, Tanaka H, Nakamura A (eds) Proceedings of the fourth international workshop on rough sets, fuzzy sets and machine discovery (RSFD’96). Tokyo University Press, Tokyo, pp 125–130
Greco S, Matarazzo B, Słowiński R (1996) Rough approximation of preference relation by dominance relations. ICS Research Report 16/96, Warsaw University of Technology, Warsaw
Greco S, Matarazzo B, Słowiński R (1997) Rough set approach to multi-attribute choice and ranking problems. In: Fandel G, Gal T (eds) Multiple criteria decision making. Proceedings of the twelfth international conference on multiple criteria decision making, June 19–23, 1995, Hagen. Springer, New York, pp 318–329
Greco S, Matarazzo B, Słowiński R (1998) Rough approximation of a preference relation in a pairwise comparison table. In: Lech P, et al (eds) Rough sets in knowledge discovery, vol 2, chap 2. Springer, Berlin, Heidelberg, pp 13–36
Greco S, Matarazzo B, Słowiński R, Tsoukiàs A (1998) Exploitation of a rough approximation of the outranking relation in multicriteria choice and ranking. In: Stewart TJ, van den Honert RC (eds) Trends in multicriteria decision making. Lecture notes in economics and mathematical systems, vol 465. Springer, Berlin, pp 45–60
Greco S, Matarazzo B, Słowiński R (1999) Handling missing values in rough set analysis of multi-attribute and multi-criteria decision problems. In: Rough sets, fuzzy sets, data mining, and granular computing, pp 146–157
Greco S, Matarazzo B, Słowiński R (1999) Rough approximation of a preference relation by dominance relations. Eur J Oper Res 117:63–83
Greco S, Matarazzo B, Słowiński R (1999) The use of rough sets and fuzzy sets in MCDM. In: Gal T, Stewart T, Hanne T (eds) Multicriteria decision making: advances in MCDM models, algorithms, theory, and applications. Springer, New York, pp 397–455
Greco S, Matarazzo B, Słowiński R (2000) Dealing with missing data in rough set analysis of multi-attribute and multi-criteria decision problems. In: Zanakis S, Doukidis G, Zopounidis C (eds) Decision making: recent developments and worldwide applications. Kluwer, Dordrecht, pp 295–316
Greco S, Matarazzo B, Słowiński R (2000) Extension of the rough set approach to multicriteria decision support. INFOR: Inf Syst Oper Res 38(3):161–195
Greco S, Matarazzo B, Słowiński R, Stefanowski J (2000) An algorithm for induction of decision rules consistent with the dominance principle. In: Ziarko W, Yao YY (eds) Rough sets and current trends in computing. Lecture notes in computer science, vol 2005. Springer, New York, pp 304–313
Greco S, Matarazzo B, Słowiński R, Stefanowski J (2000) Variable consistency model of dominance-based rough sets approach. In: Rough sets and current trends in computing, pp 170–181
Greco S, Matarazzo B, Słowiński R (2001) Rough set approach to decisions under risk. In: Ziarko W, YYao (eds) Rough sets and current trends in computing. Springer, Berlin, pp 160–169
Greco S, Matarazzo B, Słowiński R (2001) Rough sets theory for multicriteria decision analysis. Eur J Oper Res 129(1):1–47
Greco S, Słowiński R, Stefanowski J (2002) Mining association rules in preference-ordered data. In: International symposium on methodologies for intelligent systems. Springer, New York, pp 442–450
Greco S, Matarazzo B, Słowiński R (2005) Decision rule approach. In: Figueira J, Greco S, Ehrgott M (eds) Multiple criteria decision analysis: state of the art surveys, international series in operations research & management science, vol 78. Springer, New York, pp 507–561
Greco S, Matarazzo B, Słowiński R (2006) Dominance-based rough set approach to case-based reasoning. In: Torra V, Narukawa Y, Valls A, Domingo-Ferrer J (eds) Modelling decisions for artificial intelligence. Lecture notes in artificial intelligence, vol 3885. Springer, Berlin, Heidelberg, pp 7–18
Greco S, Słowiński R, Yao Y (2007) Bayesian decision theory for dominance-based rough set approach. In: Yao J, Lingras P, Wu W, Szczuka M, Cercone NJ, Ślezak D (eds) RSKT 2007, LNAI 4481. Springer, Berlin, Heidelberg, pp 131–141
Greco S, Matarazzo B, Słowiński R (2008) Case-based reasoning using gradual rules induced from dominance-based rough approximations. In: Wang G, Li T, Grzymała-Busse JW, Miao D, Skowron A, Yao YY (eds) Rough sets and knowledge technology (RSKT 2008). Lecture notes in artificial intelligence, vol 5009. Springer, Berlin, pp 268–275
Greco S, Matarazzo B, Słowiński R (2008) Dominance-based rough set approach to interactive multiobjective optimization. In: Branke J, Deb K, Miettinen K, Słowiński R (eds) Multiobjective optimization. Springer, New York, pp 121–155
Greco S, Matarazzo B, Słowiński R (2008) Granular computing for reasoning about ordered data: the dominance-based rough set approach. In: Pedrycz W, Skowron A, Kreinovich V (eds) Handbook of granular computing, chap 15. John Wiley and Sons, Chichester, pp 347–373
Greco S, Ehrgott M, Figueira JR (eds) (2016) Multiple criteria decision analysis: state of the art surveys. Springer Science+Business Media, Inc, New York
Grzymała-Busse JW (1992) LERS - a system for learning from examples based on rough sets. In: Słowiński R (ed) Intelligent decision support: Handbook of applications and advances of the rough sets theory. Kluwer Academic Publishers, Dordrecht, pp 3–18
Grzymała-Busse JW (2004) Data with missing attribute values: generalization of indiscernibility relation and rule induction. In: Peters JF, Skowron A, Grzymała-Busse JW, Kostek B, Świniarski RW, Szczuka MS (eds) Transactions on rough sets I. Springer, Berlin, Heidelberg, pp 78–95
Grzymała-Busse JW (2005) Characteristic relations for incomplete data: a generalization of the indiscernibility relation. In: Peters JF, Skowron A (eds) Transactions on rough sets IV. Springer, Berlin, Heidelberg, pp 58–68
Grzymała-Busse JW (2011) Mining incomplete data – a rough set approach. In: Yao J, Ramanna S, Wang G, Suraj Z (eds) Rough sets and knowledge technology. Springer, Berlin, Heidelberg, pp 1–7
Grzymała-Busse JW, Hu M (2001) A comparison of several approaches to missing attribute values in data mining. In: Ziarko W, Yao Y (eds) Rough sets and current trends in computing. Springer, Berlin, Heidelberg, pp 378–385
Han J, Kamber M (2006) Data mining: concepts and techniques. Morgan Kaufmann, Burlington
Hu ML, Liu SF (2007) A rough analysis method of multi-attribute decision making for handling decision system with incomplete information. In: Proceedings of 2007 IEEE international conference on grey systems and intelligent services, November 18–20, 2007, Nanjing
Inuiguchi M, Yoshioka Y (2006) Variable-precision dominance-based rough set approach. In: Greco S, Hata Y, Hirano S, Inuiguchi M, Miyamoto S, Nguyen HS, Slowinski R (eds) Rough sets and current trends in computing. Lecture notes in computer science, vol 4259. Springer, New York, pp 203–212
Jówko P (2018) Multicriteria ranking decision support system based on decision rules induced from decision examples. M. Sc. thesis, Poznan University of Technology, supervisor: Marcin Szeląg
Keeney R, Raiffa H (1976) Decisions with multiple objectives: preferences and value tradeoffs. John Wiley & Sons, New York, NY
Kolodner J (1993) Case-based reasoning. Morgan Kaufmann, San Mateo
Kotłowski W (2009) Statistical approach to ordinal classification with monotonicity constraints. PhD thesis, Poznań University of Technology
Kotłowski W, Słowiński R (2008) Statistical approach to ordinal classification with monotonicity constraints. In: Preference learning ECML/PKDD 2008 workshop
Kusunoki Y, Błaszczyński J, Inuiguchi M, Słowiński R (2021) Empirical risk minimization for dominance-based rough set approaches. Inf Sci 567:395–417.
Lewandowski M (2019) System for visualization and exploration of monotonous decision rules. M. Sc. thesis, Poznan University of Technology, supervisor: Marcin Szeląg
Liang D, Yang SX, Jiang C, Zheng X, Liu D (2010) A new extended dominance relation approach based on probabilistic rough set theory. In: Yu J, et al (eds) RSKT 2010. LNAI, vol 6401. Springer, New York, pp 175–180
Lichtenstein S, Slovic P (eds) (2006) The construction of preference. Cambridge University Press, Cambridge
Liu D, Liang D (2017) Three-way decisions in ordered decision system. Knowl-Based Syst 137:182–195
Michalski RS (1969) On the quasi-minimal solution of the covering problem. In: Proceedings of the 5th international symposium on information processing (FCIP-69), Bled, Yugoslavia, vol A3 (Switching Circuits), pp 125–128
Pagallo G, Haussler D (1990) Boolean feature discovery in empirical learning. Mach Learn 5(1):71–99
Pawlak Z (1982) Rough sets. Int J Inf Comput Sci 11:341–356
Pawlak Z (1991) Rough sets. Theoretical aspects of reasoning about data. Kluwer Academic Publishing, Dordrecht
Pawlak Z, Słowiński R (1994) Decision analysis using rough sets. Int Trans Oper Res 1(1):107–114
Pawlak Z, Słowiński R (1994) Rough set approach to multi-attribute decision analysis. Eur J Oper Res 72(3):443–459
Roy B (1985) Méthodologie multicritère d’aide à la décision. Economica, Paris
Roy B (1990) Wielokryterialne wspomaganie decyzji. Wydawnictwa Naukowo-Techniczne, translation into Polish by Roman Słowiński
Roy B (1991) The outranking approach and the foundations of ELECTRE methods. Theor Decis 31:49–73
Roy B, Bouyssou D (1993) Aide Multicritère à la Décision: Méthodes et Cas. Economica, Paris
Roy B, Vincke P (1984) Relational systems of preference with one or more pseudo-criteria: some new concepts and results. Manage Sci 30(11):1323–1335
Słowiński R (1992) A generalization of the indiscernibility relation for rough set analysis of quantitative information. Rivista di matematica per le scienze economiche e sociali 15(1):65–78
Słowiński R (ed) (1992) Intelligent decision support: handbook of applications and advances of the rough sets theory, vol 11. Springer, New York
Słowiński R, Stefanowski J (1993) Special issue on Rough Sets – state of the art and perspectives. Found Comput Decis Sci 18(3–4):155–396
Słowiński R, Vanderpooten D (2000) A generalized definition of rough approximations based on similarity. IEEE Transactions on Knowledge and Data Engineering 12(2):331–336
Słowiński K, Słowiński R, Stefanowski J (1988) Rough sets approach to analysis of data from peritoneal lavage in acute pancreatitis. Med Inf 13(3):143–159
Słowiński R, Greco S, Matarazzo B (2002) Mining decision-rule preference model from rough approximation of preference relation. In: Proceedings of the 26th IEEE annual international conference on computer software and applications (COMPSAC 2002). IEEE Computer Society Press, Los Alamitos, CA, pp 1129–1134
Słowiński R, Greco S, Matarazzo B (2005) Rough set based decision support. In: Burke EK, Kendall G (eds) Search methodologies: introductory tutorials in optimization and decision support techniques, chap 16. Springer, New York, pp 475–527
Słowiński R, Greco S, Matarazzo B (2009) Rough sets in decision making. In: Meyers R (ed) Encyclopedia of complexity and systems science. Springer, New York, pp 7753–7786
Słowiński R, Greco S, Matarazzo B (2014) Rough set based decision support. In: Burke EK, Kendall G (eds) Search methodologies: introductory tutorials in optimization and decision support techniques, 2nd edn, chap 19. Springer, New York, pp 557–609
Słowiński R, Greco S, Matarazzo B (2015) Rough set methodology for decision aiding. In: Kacprzyk J, Pedrycz W (eds) Springer handbook of computational intelligence. Springer, New York, pp 349–370
Stefanowski J, Tsoukias A (2001) Incomplete information tables and rough classification. Comput Intell 17(3):545–566
Szeląg M (2015) Application of the dominance-based rough set approach to ranking and similarity-based classification problems. PhD thesis, Poznań University of Technology, http://www.cs.put.poznan.pl/mszelag/Research/MSzPhD.pdf, supervisor: prof. R. Słowiński
Szeląg M, Greco S, Błaszczyński J, Słowiński R (2011) Case-based reasoning using dominance-based decision rules. In: Yao J, Ramanna S, Wang G, Suraj Z (eds) Rough sets and knowledge technology 2011. Lecture notes in computer science, vol 6954. Springer, Heidelberg, pp 404–413
Szeląg M, Greco S, Słowiński R (2013) Rule-based approach to multicriteria ranking. In: Doumpos M, Grigoroudis E (eds) Multicriteria decision aid and artificial intelligence: links, theory and applications. Wiley, Chichester, pp 127–160
Szeląg M, Greco S, Słowiński R (2014) Variable consistency dominance-based rough set approach to preference learning in multicriteria ranking. Inf Sci 277:525–552
Szeląg M, Greco S, Słowiński R (2016) Similarity-based classification with dominance-based decision rules. In: Flores V, et al (eds) Rough sets, international joint conference, IJCRS 2016. Santiago de Chile, October 7–11, 2016, proceedings. Lecture notes in artificial intelligence. Springer, New York, pp 355–364
Szeląg M, Błaszczyński J, Słowiński R (2017) Rough set analysis of classification data with missing values. In: Polkowski L, et al (eds) Rough sets, international joint conference, IJCRS 2017, Olsztyn, July 3–7, 2017, proceedings, Part I. LNAI, vol 10313. Springer, New York, pp 552–565
Tsoukias A, Vincke P (1995) A new axiomatic foundation of partial comparability. Theor Decis 39:79–114
Tsoukias A, Vincke P (1997) Extended preference structures in MCDA. In: Climaco J (ed) Multicriteria analysis. Springer, Berlin, pp 37–50
Yang X, Yang J, Wu C, Yu D (2008) Dominance-based rough set approach and knowledge reductions in incomplete ordered information system. Inf Sci 178(4):1219–1234
Yang X, Yu D, Yang J, Wei L (2009) Dominance-based rough set approach to incomplete interval-valued information system. Data Knowl Eng 68(11):1331–1347
Yao Y (2008) Probabilistic rough set approximations. Int J Approx Reason 49:255–271
Yao Y, Zhou B (2016) Two Bayesian approaches to rough sets. Eur J Oper Res 251(3):904–917
Zadeh L (1965) Fuzzy sets. Inf Control 8(3):338–353
Zopounidis C (1998) Operational tools in the management of financial risks. Springer Science & Business Media, Berlin
Acknowledgements
This research was partially supported by TAILOR, a project funded by EU Horizon 2020 research and innovation programme under GA No. 952215. Salvatore Greco wishes to acknowledge the support of the Ministero dell’Istruzione, dell’Universitá e della Ricerca (MIUR)—PRIN 2017, project “Multiple Criteria Decision Analysis and Multiple Criteria Decision Theory,” grant 2017CY2NCA and the research project “Data analytics for entrepreneurial ecosystems, sustainable development and well being indices” of the Department of Economics and Business of the University of Catania.
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2022 The Author(s), under exclusive license to Springer Nature Switzerland AG
About this chapter
Cite this chapter
Błaszczyński, J., Greco, S., Matarazzo, B., Szeląg, M. (2022). Dominance-Based Rough Set Approach: Basic Ideas and Main Trends. In: Greco, S., Mousseau, V., Stefanowski, J., Zopounidis, C. (eds) Intelligent Decision Support Systems . Multiple Criteria Decision Making. Springer, Cham. https://doi.org/10.1007/978-3-030-96318-7_18
Download citation
DOI: https://doi.org/10.1007/978-3-030-96318-7_18
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-030-96317-0
Online ISBN: 978-3-030-96318-7
eBook Packages: Business and ManagementBusiness and Management (R0)