Abstract
We consider the issue on decision rules induction for multicriteria ranking. Multiple Criteria Decision Analysis (MCDA) aims at giving people the knowledge of recommendation concerning a finite set of objects evaluated with multiple preference-ordered attributes (known as criteria). Dominance-based Rough Set Approach (DRSA) is a powerful tool for MCDA via assigning objects to several predefined and preference-ordered decision classes. Most of previous strategies are to induce a minimal set of “if…then…” rules. In this paper, we provide strategies to induce a new rule set as the substitution for the classical minimal rule set. The main contributions include: (1) providing methods to induce certain rules in two situations respectively: multi-criteria and mix-attributes; (2) providing the concept of believe factor and its three measuring degrees for exploring valuable uncertain information within rough boundary regions; (3) providing the properties of believe factor with explanations from the viewpoint of class-based rough model; (4) proposing an extended Net Flow Score method in consideration of both partial and total orders in multicriteria ranking, via our proposed decision rules. A numerical example is used for illustration of overall problem-solving procedures and for a comparison with the existing representative proposals.
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An LP, Tong LY (2009) Learning rules from pairwise comparison table. In: artificial intelligence and computational intelligence. LNCS 5855:18–27
Baucells M, Heukamp FH (2006) Stochastic dominance and cumulative prospect theory. Decis Anal 52(9):1409–1423
Chai JY, Liu JNK (2011) Class-based rough approximation with dominance relations. In: Proceeding of international conference on granular computing (GrC), pp 77–82
Chai JY, Liu JNK (2012) A reliable system platform for group decision support under uncertain environments. Reliable knowledge discovery, Chapter 17, Springer, pp 291–306
Chai JY, Liu JNK, Xu ZS (2012) A new rule-based SIR approach to supplier selection under intuitionistic fuzzy environments. Int J Uncertain, Fuzziness, and Knowl Based Sys 20(3):451–471. doi:10.1142/S0218488512500237
Chai JY, Liu JNK, Li AM (2012) A new intuitionistic fuzzy rough set approach for decision supports. In: International conference on rough sets and knowledge technology (RSKT), LNAI 7414, Springer, Heidelberg, pp 71–80
Figueira J, Greco S, Ehrgott M (2005) Multiple criteria decision analysis: state of the art surveys. Springer-Verlag, London
Greco S, Matarazzo B, Slowinski R (1999) Rough approximation of a preference relation by dominance relations. Eur J Oper Res 117(1):63–83
Greco S, Matarazzo B, Slowinski R (2001) Rough sets theory for multicriteria decision analysis. Eur J Oper Res 129(1):1–47
Greco S, Matarazzo B, Slowinski R (2002) Rough sets methodology for sorting problems in presence of multiple attributes and criteria. Eur J Oper Res 138(2):247–259
Greco S, Matarazzo B, Slowinski R (2005) Decision rule approach, multiple criteria decision analysis: state of the art surveys. eds. J. Figueira, S. Greco, M. Ehrgott, Springer-Verlag, Berlin, pp 507–561.
Greco S, Matarazzo B, Slowinski R, Stefanowski J (2001) Variable consistency model of dominance-based rough sets approach. In: Ziarko W, Yao Y (eds) Rough sets and current trends in computing (RSCTC), Springler-Verlag, Berlin, pp 170–181
Hu QH, Yu DR (2004) Variable precision dominance based rough set model and reduction algorithm for preference-ordered data. In: Proceeding of international conference on machine learning and cybernetics (ICMLC) 4 pp 2279–2284
Hu QH, Guo MZ, Yu DR, Liu JF (2010) Information entropy for ordinal classification. Sci Ch Inform Sci 53(6):1188–1200
Hu QH, Yu DR, Guo MZ (2010) Fuzzy preference based rough sets. Inf Sci 180(10):2003–2022
Inuiguchi M, Yoshioka Y, Kusunoki Y (2009) Variable-precision dominance-based rough set approach and attribute reduction. Int J Approx Reason 50(8):1199–1214
Kotlowski W, Dembczynski K, Greco S, Slowinski R (2008) Stochastic dominance-based rough set model for ordinal classification. Inf Sci 178(21):4019–4037
Li Y, Shiu SCK, Pal SK (2006) Combining feature reduction and case selection in building CBR classifiers. IEEE Trans Knowl Data Eng 18(3):415–429
Ma WM, Wang K, Liu ZP (2011) Mining potentially more interesting associating rules with fuzzy interest measure. Soft Comput 15(6):1173–1182
Mareschal B (1986) Stochastic multicriteria decision making and uncertainty. Eur J Oper Res 26(1):58–64
Pawlak Z (2002) Rough sets, decision algorithm and Bayes’ theorem. Eur J Oper Res 136(1):181–189
Pawlak Z, Skowron A (2007) Rudiments of rough sets. Inf Sci 177(1):3–27
Pedrycz W, Ekel P, Parreiras R (2011) Fuzzy multicriteria decision-making: models, methods and applications. Wiley, Chichester
Roy B (1996) Multicriteria methodology for decision aiding. Kluwer, Dordrecht
Slowinski R, Greco S, Matarazzo B (2009) Rough sets in decision making. Encyclopedia of Complexity and Systems Science, ed. R.A. Meyers, Springer, pp 7753–7787
Tervonen T, Figueira J (2008) A survey on stochastic multicriteria acceptability analysis methods. J Multi Criteria Decis Anal 15(1–2):1–14
Wang XZ, Zhai JH, Lu SX (2008) Induction of multiple fuzzy decision trees based on rough set technique. Inf Sci 178(16):3188–3202
Wang XZ, Dong CR (2009) Improving generalization of fuzzy IF-THEN rules by maximizing fuzzy entropy. IEEE Trans Fuzzy Syst 17(3):556–567
Wang XZ, Dong LC, Yan JH (2011) Maximum ambiguity based sample selection in fuzzy decision tree induction In: IEEE transactions on knowledge and data engineering. doi:10.1109/TKDE.2011.67
Xu XZ (2001) The SIR method: a superiority and inferiority ranking method for multiple criteria decision making. Eur J Oper Res 131:587–602
Xu XZ, Martel JM, Lamond BF (2001) A multiple criteria ranking procedure based on distance between partial preorders. Eur J Oper Res 133(3):69–80
Xu ZS (2007) Intuitionistic fuzzy aggregation operators. IEEE Trans Fuzzy Syst 15:1179–1187
Yang XB, Song XN, Chen ZH, Yang JY (2011) On multigranulation rough sets in incomplete information system. Int J Mach Learn Cybern. doi: 10.1007/s13042-011-0054-8.
Zahiri SH (2011) Classification rule discovery using learning automata. Int J Mach Learn Cybern. doi: 10.1007/s13042-011-0056-6
Zhu W, Wang SP (2011) Matroidal approaches to generalized rough sets based on relations. Int J Mach Learn Cybern 2(4):273–279
Ziarko W (1993) Variable precision rough set model. J Comput Syst Sci 46(1):39–59
Zopounidis C, Doumpos M (2002) Multi-criteria decision aid in financial decision making: methodologies and literature review. J Multi Criteria Decis Anal 11(4–5):167–186
Acknowledgments
The authors are very grateful to the Editor-in-Chief, Professor Xizhao Wang, and the five anonymous reviewers for their careful, insightful, and constructive comments that lead to the improved version of this paper.
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Chai, J., Liu, J.N.K. Dominance-based decision rule induction for multicriteria ranking. Int. J. Mach. Learn. & Cyber. 4, 427–444 (2013). https://doi.org/10.1007/s13042-012-0105-9
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DOI: https://doi.org/10.1007/s13042-012-0105-9