×

Dominance-based rough set approach for group decisions. (English) Zbl 1346.91066

Summary: The objective of this paper is to propose an approach to support group multicriteria classification. The approach is composed of three phases. The first phase exploits the knowledge provided by each decision maker to individually approximate the decision classes using rough approximation. The second phase seeks to combine the outputs of individual approximation phase into a collective decision table by using an appropriate aggregation procedure. The third phase uses the collective decision table in order to infer a set of collective decision rules, which synthesize the judgements and perspectives of the different decision makers and to permit the classification of all decision objects. The proposed approach relies on the Dominance-based Rough Set Approach (DRSA), which is used at two different levels. First, the DRSA is used during the first phase to approximate the input data relative to each decision maker. Second, the DRSA is used during the third phase to approximate the collective decision table and generate the collective decision rules. This paper presents the theoretical foundation of the proposed approach, three case studies using real-world data and a comparative study of recent similar proposals.

MSC:

91B10 Group preferences
90C70 Fuzzy and other nonstochastic uncertainty mathematical programming

Software:

ELECTRE
PDFBibTeX XMLCite
Full Text: DOI Link

References:

[1] Abastante, F.; Bottero, M.; Greco, S.; Lami, I., Addressing the location of undesirable facilities through the dominance-based rough set approach, Journal of Multi-Criteria Decision Analysis, 21, 1-2, 3-23 (2014)
[2] Almeida-Dias, J.; Figueira, J.; Roy, B., Electre Tri-C: a multiple criteria sorting method based on characteristic reference actions, European Journal of Operational Research, 204, 3, 565-580 (2010) · Zbl 1181.90140
[3] Almeida-Dias, J.; Figueira, J.; Roy, B., A multiple criteria sorting method where each category is characterized by several reference actions: the Electre Tri-nC method, European Journal of Operational Research, 217, 3, 567-579 (2012) · Zbl 1244.90106
[4] Blasco, H.; Blaszczyński, J.; Billaut, J.; Nadal-Desbarats, L.; Pradat, P.; Devos, D.; Slowiński, R., Comparative analysis of targeted metabolomics: dominance-based rough set approach versus orthogonal partial least square-discriminant analysis, Journal of Biomedical Informatics, 53, 291-299 (2015)
[5] Blaszczyński, J.; Greco, S.; Slowiński, R., Multi-criteria classification - a new scheme for application of dominance-based decision rules, European Journal of Operational Research, 181, 3, 1030-1044 (2007) · Zbl 1121.90073
[6] Blaszczyński, J.; Greco, S.; Slowiński, R., Inductive discovery of laws using monotonic rules, Engineering Applications of Artificial Intelligence, 25, 2, 284-294 (2012)
[7] Blaszczyński, J.; Slowiński, R.; Szeląg, M., Induction of ordinal classification rules from incomplete data, (Yao, J.; Yang, Y.; Slowiński, R.; Greco, S.; Li, H.; Mitra, S.; Polkowski, L., Rough sets and current trends in computing. Rough sets and current trends in computing, Lecture Notes in Computer Science, vol. 7413 (2012), Springer: Springer Berlin Heidelberg), 56-65
[8] Bregar, A.; Györkös, J.; Jurič, M., Interactive aggregation/disaggregation dichotomic sorting procedure for group decision analysis based on the threshold model, Informatica, 19, 2, 161-190 (2008) · Zbl 1147.68702
[9] Brigui-Chtioui, I.; Saad, I., A multi-agent approach for collective decision making in knowledge management, Group Decision and Negotiation, 20, 1, 19-37 (2011)
[10] Cai, F.-L.; Liao, X.; Wang, K.-L., An interactive sorting approach based on the assignment examples of multiple decision makers with different priorities, Annals of Operations Research, 197, 87-108 (2012) · Zbl 1251.90215
[11] Chakhar, S.; Pusceddu, C., Decision tables aggregation in rough sets approximation, (Boonthum-Denecke, C.; Youngblood, G., Proceedings of the twenty-sixth international Florida artificial intelligence research society conference, FLAIRS 2013, St. Pete Beach, Florida. May 22-24, 2013 (2013), AAAI Press), 633-636
[12] Chakhar, S.; Pusceddu, C.; Saad, I., Evaluating post-accident nuclear risk by coupling GIS and rough sets theory, (Campagna, M.; Montis, A. D.; Isola, F.; Lai, S.; Pira, C.; Zoppi, C., Planning support tools: policy analysis, implementation and evaluation, proceedings of the seventh international conference on informatics and urban and regional planning (INPUT 2012). May 10-12, 2012 (2012)), 223-235
[13] Chakhar, S.; Saad, I., Dominance-based rough set approach for groups in multicriteria classification, Decision Support Systems, 54, 1, 372-380 (2012)
[14] Chakhar, S.; Saad, I., Incorporating stakeholders’ knowledge in group decision-making, Journal of Decision Systems, 23, 1, 113-126 (2014)
[15] Chen, Y.; Kilgour, D.; Hipel, K., A decision rule aggregation approach to multiple criteria-multiple participant sorting, Group Decision and Negotiation, 21, 727-745 (2012)
[16] Cook, W., Distance-based and ad hoc consensus model in ordinal preference ranking with intensity of preference, European Journal of Operational Research, 172, 2, 369-385 (2006) · Zbl 1120.91007
[17] Damart, S.; Dias, L.; Mousseau, V., Supporting groups in sorting decisions: Methodology and use of a multicriteria aggregation/disaggregation DSS, Decision Support Systems, 43, 4, 1464-1475 (2007)
[18] Dembczynski, K.; Greco, S.; Kotlowski, W.; Slowiński, R., Statistical model for rough set approach to multicriteria classification, (Kok, J.; Koronacki, J.; Lopez de Mantaras, R.; Matwin, S.; Mladenic, D.; Skowron, A., Knowledge discovery in databases: PKDD 2007. Knowledge discovery in databases: PKDD 2007, Lecture Notes in Computer Science, vol. 4702 (2007), Springer: Springer Berlin Heidelberg), 164-175
[19] Deng, W.; Hu., F.; Blaszczyński, J.; Slowiński, R.; Szeląg, M.; Wang, G., A novel method for elimination of inconsistencies in ordinal classification with monotonicity constraints, Fundamenta Informaticae, 126, 4, 377-395 (2013)
[20] Dias, L.; Mousseau, V.; Figueira, J.; Clímaco, J., An aggregation/disaggregation approach to obtain robust conclusions with ELECTRE TRI, European Journal of Operational Research, 138, 332-348 (2002) · Zbl 1003.90512
[21] Doumpos, M.; Zopounidis, C., Preference disaggregation and statistical learning for multicriteria decision support: a review, European Journal of Operational Research, 209, 3, 203-214 (2011) · Zbl 1205.90147
[22] Dubois, C.; Bergeron, O.; Potvin, A.; Adolphe, L., Adapting cities to climate change: heat and urban form, The 8th international conference on urban climates (ICUC 8) (2012)
[23] Figueira, J.; Mousseau, V.; Roy, B., Electre methods, (Figueira, J.; Greco, S.; Ehrgott, M., Multiple criteria decision analysis: State of the art surveys (2005), Springer-Verlag: Springer-Verlag New York), 133-162 · Zbl 1072.90531
[24] Greco, S.; Kadziński, M.; Mousseau, V.; Slowiński, R., Robust ordinal regression for multiple criteria group decision: \(UTA^{GMS}\)-GROUP and \(UTADIS^{GMS}\)-GROUP, Decision Support Systems, 52, 3, 549-561 (2012)
[25] Greco, S.; Matarazzo, B.; Slowiński, Dominance-based rough set approach to interactive multiobjective optimization, (Branke, J.; Deb, K.; Miettinen, K.; Slowiński, R., Multiobjective optimization. Multiobjective optimization, Lecture Notes in Computer Science, vol. 5252 (2008), Springer: Springer Berlin Heidelberg), 121-155
[26] Greco, S.; Matarazzo, B.; Slowiński, R., Advances in multiple criteria decision making, 14.1-14.59 (1999), Kluwer Academic Publishers: Kluwer Academic Publishers Dordrecht, Boston · Zbl 0948.90078
[27] Greco, S.; Matarazzo, B.; Slowiński, R., Rough sets theory for multicriteria decision analysis, European Journal of Operational Research, 129, 1, 1-47 (2001) · Zbl 1008.91016
[28] Greco, S.; Matarazzo, B.; Slowiński, R., Rough approximation by dominance relations, International Journal of Intelligent Systems, 17, 2, 153-171 (2002) · Zbl 0997.68135
[29] Greco, S.; Matarazzo, B.; Slowiński, R., Dominance-based rough set approach to decision involving multiple decision makers, (Greco, S.; Hata, Y.; Hirano, S.; Inuiguchi, M.; Miyamoto, S.; Nguyen, H.; Slowiński, R., Proceedings of the 5th international conference rough sets and current trends in computing (RSCTC 2006), Kobe, Japan, November 6-8. Proceedings of the 5th international conference rough sets and current trends in computing (RSCTC 2006), Kobe, Japan, November 6-8, Lecture Notes in Artificial Intelligence, vol. 4259 (2006), Springer-Verlag: Springer-Verlag Berlin Heidelberg), 306-317 · Zbl 1162.91332
[30] Greco, S.; Matarazzo, B.; Slowiński, R., Customer satisfaction analysis based on rough set approach, Zeitschrift fur Betriebswirtschaft, 77, 3, 325-339 (2007)
[31] Greco, S.; Matarazzo, B.; Slowinski, R.; Stefanowski, J., An algorithm for induction of decision rules consistent with the dominance principle, (Ziarko, W.; Yao, Y., Rough sets and current trends in computing. Rough sets and current trends in computing, Lecture Notes in Computer Science, vol. 2005 (2001), Springer: Springer Berlin Heidelberg), 304-313 · Zbl 1014.68545
[32] Greco, S.; Matarazzo, B.; Slowiński, R.; Stefanowski, J., Variable consistency model of dominance-based rough sets approach, (Ziarko, W.; Yao, Y., Rough sets and current trends in computing. Rough sets and current trends in computing, Lecture Notes in Computer Science, vol. 2005 (2001), Springer: Springer Berlin/Heidelberg), 170-181 · Zbl 1014.68544
[33] Guay, G.; Joerin, F.; Chakhar, S.; Villeneuve, P.; Lavoie, C., FLORAIDE, a new decision-making tool for weed species, The 2nd world conference on biological invasions and ecosystem functioning group, Mar del Plata, Argentina (2011)
[34] Herowati, E.; Ciptomulyono, U.; Parung, J., Expertise-based experts importance weights in adverse judgment, ARPN Journal of Engineering and Applied Sciences, 9, 9, 1428-1435 (2014)
[35] Ishizaka, A.; Labib, A., Selection of new production facilities with the group analytic hierarchy process ordering method, Expert Systems With Applications, 38, 6, 7317-7325 (2011)
[36] Ishizaka, A.; Nemery, P., Multi-criteria decision analysis: methods and software (2013), Wiley
[37] Ishizaka, A.; Nemery, P., A multi-criteria group decision framework for partner grouping when sharing facilitiese, Group Decision and Negotiation, 22, 4, 773-799 (2013)
[38] Jabeur, K.; Martel, J.-M., An ordinal sorting method for group decision-making, European Journal of Operational Research, 180, 1272-1289 (2007) · Zbl 1121.90356
[39] Kadziński, M.; Slowiński, R.; Greco, S., Multiple criteria ranking and choice with all compatible minimal cover sets of decision rules, Knowledge-Based Systems, 89, 569-583 (2015)
[40] Kadziński, M.; Greco, S.; Slowiński, R., Robust ordinal regression for dominance-based rough set approach to multiple criteria sorting, Information Sciences, 283, 211-228 (2014) · Zbl 1355.91029
[41] Kadziński, M.; Slowiński, R., DIS-CARD: a new method of multiple criteria sorting to classes with desired cardinality, Journal of Global Optimization, 56, 3, 1143-1166 (2013) · Zbl 1272.90072
[42] Labib, A.; Read, M.; Gladstone-Millar, C.; Tonge, R.; Smith, D., Formulation of higher education institutional strategy using operational research approaches, Studies in Higher Education, 39, 5, 885-904 (2014)
[43] Legay, C.; Cloutier, G.; Chakhar, S.; Joerin, F.; Rodriguez, M., Estimation of urban water supply issues at the local scale: a participatory approach, Climatic Change, 130, 4, 491-503 (2015)
[44] Leyva-López, J.; Fernández-González, E., A new method for group decision support based on ELECTRE III methodology, European Journal of Operational Research, 148, 1, 14-27 (2003) · Zbl 1037.90540
[45] Li, S.; Li, T., Incremental update of approximations in dominance-based rough sets approach under the variation of attribute values, Information Sciences, 294, 348-361 (2015) · Zbl 1360.68840
[46] Liou, J.; Tang, C.-H.; Yeh, W.-C.; Tsai, C.-Y., A decision rules approach for improvement of airport service quality, Expert Systems with Applications, 38, 11, 13723-13730 (2011)
[47] Liu, J.; Liao, X.; Yang, J., A group decision-making approach based on evidential reasoning for multiple criteria sorting problem with uncertainty, European Journal of Operational Research, 246, 3, 858-873 (2015) · Zbl 1346.91055
[48] Lolli, F.; Ishizaka, A.; Gamberini, R.; Rimini, B.; Messori, M., FlowSort-GDSS - a novel group multi-criteria decision support system for sorting problems with application to FMEA, Expert Systems with Applications, 42, 17-18, 6342-6349 (2015)
[49] Mercat-Rommens, C.; Chakhar, S.; Chojnacki, E.; Mousseau, V., Coupling GIS and multi-criteria modeling to support post-accident nuclear risk evaluation, (Bisdorff, R.; Dias, L.; Meyer, P.; Mousseau, V.; Pirlot, M., Evaluation and decision models with multiple criteria. Evaluation and decision models with multiple criteria, International Handbooks on Information Systems (2015), Springer: Springer Berlin Heidelberg), 401-428
[50] Paolotti, L.; Greco, S.; Boggia, A., Multiobjective strategies for farms, using the dominance-based rough set approach, Aestimum, 65, 95-115 (2015)
[51] Pawlak, Z., Rough set. Theoretical aspects of reasoning about data (1991), Kluwer Academic Publishers: Kluwer Academic Publishers Dordrecht · Zbl 0758.68054
[52] Pawlak, Z., Some remarks on conflict analysis, European Journal of Operational Research, 166, 3, 649-654 (2005) · Zbl 1097.91010
[53] Saad, I.; Chakhar, S., A decision support for identifying crucial knowledge requiring capitalizing operation, European Journal of Operational Research, 195, 3, 889-904 (2009) · Zbl 1159.90428
[54] Saad, I.; Chakhar, S., Multi-criteria methodology based on majority principle for collective identification of firm’s valuable knowledge, Knowledge Management Research & Practice, 10, 4, 380-391 (2012)
[55] Shanteau, J.; Weiss, D.; Thomas, R.; Pounds, J., Performance-based assessment of expertise: How to decide if someone is an expert or not, European Journal of Operational Research, 136, 2, 253-263 (2002) · Zbl 1091.90524
[56] Slowiński, R.; Greco, S.; Matarazzo, B., Rough set analysis of preference-ordered data, (Alpigini, J.; Peters, J.; Skowron, A.; Zhong, N., Rough sets and current trends in computing. Rough sets and current trends in computing, Lecture Notes in Artificial Intelligence, vol. 2475 (2002), Springer: Springer Berlin Heidelberg), 44-59 · Zbl 1013.68599
[57] Slowiński, R.; Kadziński, M.; Greco, S., Robust ordinal regression for dominance-based rough set approach under uncertainty, (Kryszkiewicz, M.; Cornelis, C.; Ciucci, D.; Medina-Moreno, J.; Motoda, H.; Raś, Z., Rough sets and intelligent systems paradigms. Rough sets and intelligent systems paradigms, Lecture Notes in Computer Science, vol. 8537 (2014), Springer International Publishing), 77-87
[58] Slowiński, R.; Stefanowski, J.; Greco, S.; Matarazzo, B., Rough sets based processing of inconsistent information in decision analysis, Control and Cybernetics, 29, 1, 379-404 (2000) · Zbl 1030.90045
[60] Sun, B.; Ma, W., Rough approximation of a preference relation by multi-decision dominance for a multi-agent conflict analysis problem, Information Sciences, 315, 39-53 (2015) · Zbl 1388.91089
[61] Susmaga, R.; Slowiński, Generation of rough sets reducts and constructs based on inter-class and intra-class information, Fuzzy Sets and Systems, 274, 124-142 (2015) · Zbl 1373.68405
[62] Waegeman, W.; De Baets, B.; Boullart, L., Kernel-based learning methods for preference aggregation, 4OR, 7, 2, 169-189 (2009) · Zbl 1175.91058
[63] Wang, H.; Zhou, M.; She, K., Induction of ordinal classification rules from decision tables with unknown monotonicity, European Journal of Operational Research, 242, 1, 172-181 (2015) · Zbl 1341.91046
[64] Weiss, D.; Shanteau, J., Empirical assessment of expertise, Human Factors, 45, 1, 104-116 (2003)
[65] Wen-Jie, B.; Xiao-Hong, C., An extended dominance-based rough set approach to group sorting decision making, International conference on management science and engineering (ICMSE 2007), 339-344 (2007), IEEE
[67] Yang, X.; Qi, Y.; Yu, D.-J.; Yu, H.; Yang, J., \(α\)-dominance relation and rough sets in interval-valued information systems, Information Sciences, 294, 334-347 (2015) · Zbl 1360.68853
[68] Yue, Z., A method for group decision-making based on determining weights of decision makers using TOPSIS, Applied Mathematical Modelling, 35, 4, 1926-1936 (2011) · Zbl 1217.91046
[69] Zhang, F.; Ignatius, J.; Lim, C.; Goh, M., A two-stage dynamic group decision making method for processing ordinal information, Knowledge-Based Systems, 70, 189-202 (2014)
[70] Zopounidis, C.; Doumpos, M., Multicriteria classification and sorting methods: a literature review, European Journal of Operational Research, 138, 2, 229-246 (2002) · Zbl 1010.90032
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.