Granular Computing and Data Mining for Ordered Data: The Dominance-Based Rough Set Approach
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This article describes the dominance‐based rough set approach (DRSA) to granular computing and data mining. DRSA was first introduced asa generalization of the rough set approach for dealing with multicriteria decision analysis, where preference order is important. The ordering isalso important, however, in many other problems of data analysis. Even when the ordering seems absent, the presence or the absence of a property canbe represented in ordinal terms, because if two properties are related, the presence, rather than the absence, of one property should make more (or less)probable the presence of the other property. This is even more apparent when the presence or the absence of a property is graded or fuzzy, because inthis case, the more credible the presence of a property, the more (or less) probable the presence of the other property. Since the presence ofproperties, possibly fuzzy, is the basis of any granulation, DRSA can be seen as a general basis for...
Bibliography
- 1.Cattaneo G, Ciucci D (2004) Algebraic structures for rough sets. In: Transactionon rough sets II. LNCS, vol 3135. Springer, Berlin, pp 208–252Google Scholar
- 2.Cattaneo G, Giuntini R, Pilla R (1999) BZMVdM algebras and stonian MV‐algebras, (applications to fuzzy sets and rough approximations). Fuzzy Sets Syst108:201–222MathSciNetzbMATHGoogle Scholar
- 3.Dubois D, Prade H (1990) Rough fuzzy sets and fuzzy rough sets. Int J GeneralSyst 17:191–209zbMATHGoogle Scholar
- 4.Dubois D, Prade H (1992) Gradual inference rules in approximate reasoning. InfSci 61:103–122MathSciNetzbMATHGoogle Scholar
- 5.Dubois D, Prade H (1992) Putting rough sets and fuzzy sets together. In:Słowiński R (ed) Intelligent decision support – Handbook of applications and advances of the rough sets theory. Kluwer, Dordrechtpp 203–232Google Scholar
- 6.Dubois D, Prade H, Esteva F, Garcia P, Godo L, Lopez de Mantara R (1998) Fuzzyset modelling in case-based reasoning. Int J Intell Syst 13:345–373zbMATHGoogle Scholar
- 7.Dubois D, Grzymala‐Busse J, Inuiguchi M, Polkowski L (eds) (2004)Transations on rough sets II: Rough sets and fuzzy sets. LNCS, vol 3135. Springer, BerlinGoogle Scholar
- 8.Dyer J (2005) MAUT – Multiattribute utility theory, In:Figueira J, Greco S, Ehrgott M (eds) Multiple criteria decision analysis: State of the art surveys. Springer, Berlin,pp 266–294Google Scholar
- 9.Figueira J, Greco S, Ehrgott M (eds) (2005) Multiple criteria decision analysis:State of the art surveys. Springer, BerlinGoogle Scholar
- 10.Fodor J, Roubens M (1994) Fuzzy preference modelling and multicriteriadecision support. Kluwer, DordrechtzbMATHGoogle Scholar
- 11.Fortemps P, Greco S, Słowiński R (2008) Multicriteria decisionsupport using rules that represent rough‐graded preference relations. Eur J Operational Res 188:206–223Google Scholar
- 12.Gilboa I, Schmeidler D (2001) A theory of case-based decisions.Cambridge University Press, CabmridgezbMATHGoogle Scholar
- 13.Ginsburg S, Hull R (1983) Order dependency in the relational model. TheorComput Sci 26:149–195MathSciNetzbMATHGoogle Scholar
- 14.Greco S, Inuiguchi M, Słowiński R (2002) Dominance‐based roughset approach using possibility and necessity measures. In: Alpigini JJ, Peters JF, Skowron A, Zhong N (eds) Rough sets and current trends incomputing. LNAI, vol 2475. Springer, Berlin, pp 85–92Google Scholar
- 15.Greco S, Inuiguchi M, Słowiński R (2004) A new proposal forrough fuzzy approximations and decision rule representation. In: Dubois D, Grzymala‐Busse J, Inuiguchi M, Polkowski L (eds) Transations on roughsets II: Rough sets and fuzzy sets. LNCS, vol 3135. Springer, Berlin, pp 156–164Google Scholar
- 16.Greco S, Inuiguchi M, Słowiński R (2006) Fuzzy rough sets andmultiple‐premise gradual decision rules. Int J Approx Reason 41:179–211Google Scholar
- 17.Greco S, Matarazzo B, Słowiński R (1999) The use of rough sets andfuzzy sets in MCDM. In: Gal T, Stewart T, Hanne T (eds) Advances in multiple criteria decision making. Kluwer, Boston,pp 14.1–14.59Google Scholar
- 18.Greco S, Matarazzo B, Słowiński R (2000) Rough set processing ofvague information using fuzzy similarity relations. In: Calude C, Paun G (eds) From finite to infinite. Springer, Berlin,pp 149–173Google Scholar
- 19.Greco S, Matarazzo B, Słowiński R (2000) A fuzzy extension ofthe rough set approach to multicriteria and multiattribute sorting. In: Fodor J, De Baets B, Perny P (eds) Preferences and decisions under incompleteinformation. Physica, Heidelberg, pp 131–154Google Scholar
- 20.Greco S, Matarazzo B, Słowiński R (2001) Rough sets theory formulticriteria decision analysis. Eur J Operational Res 129:1–47Google Scholar
- 21.Greco S, Matarazzo B, Słowiński R (2001) Rough set approach todecisions under risk. In: Ziarko W, Yao Y (eds) Rough sets and current trends in computing. LNAI, vol 2005. Springer, Berlin,pp 160–169Google Scholar
- 22.Greco S, Matarazzo B, Słowiński R (2002) Preference representationby means of conjoint measurement and decision rule model. In: Bouyssou D, Jacquet‐Lagréze E, Perny P, Słowiński R, Vanderpooten D,Vincke P (eds) Aiding decisions with multiple criteria – Essays in Honor of Bernard Roy. Kluwer, Dordrecht,pp 263–313Google Scholar
- 23.Greco S, Matarazzo B, Słowiński R (2004) Axiomatic characterizationof a general utility function and its particular cases in terms of conjoint measurement and rough-set decision rules. Eur J Operational Res158:271–292Google Scholar
- 24.Greco S, Matarazzo B, Słowiński R (2004) Dominance‐based roughset approach to knowledge discovery (I) – General perspective. In: Zhong N, Liu J (eds) Intelligent technologies for information analysis.Springer, Berlin, pp 513–552Google Scholar
- 25.Greco S, Matarazzo B, Słowiński R (2004) Dominance‐based roughset approach to knowledge discovery (II) – Extensions and applications. In: Zhong N, Liu J (eds) Intelligent technologies for informationanalysis. Springer, Berlin, pp 553–612Google Scholar
- 26.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. Springer, Berlin,pp 507–563Google Scholar
- 27.Greco S, Matarazzo B, Słowiński R (2005) Generalizing rough settheory through dominance‐based rough set approach. In: Slezak D, Yao J, Peters J, Ziarko W, Hu X (eds) Rough sets, fuzzy sets, data mining, andgranular computing. LNAI, vol 3642. Springer, Berlin, pp 1–11Google Scholar
- 28.Greco S, Matarazzo B, Słowiński R (2006) Dominance‐based roughset approach to case-based reasoning. In: Torra V, Narukawa Y, Valls A, Domingo‐Ferrer J (eds) Modelling decisions for artificial intelligence.LNAI, vol 3885. Springer, Berlin, pp 7–18Google Scholar
- 29.Greco S, Matarazzo B, Słowiński R (2007) Dominance‐based roughset approach as a proper way of handling graduality in rough set theory. In: Transactions on rough sets VII. LNAI, vol 4400. Springer, Berlin,pp 36–52Google Scholar
- 30.Greco S, Matarazzo B, Słowiński R (2008) An algebraic structure fordominance‐based rough set approach. In: Proc. 3rd Int Conference on rough sets and knowledge technology (RSKT 2008), LNAI. Springer, Berlin,pp 252–259Google Scholar
- 31.Greco S, Matarazzo B, Słowiński R, Stefanowski J (2001) Variableconsistency model of dominance‐based rough set approach, In: Ziarko W, Yao Y (eds) Rough sets and current trends in computing. LNAI, vol 2005.Springer, Berlin, pp 170–181Google Scholar
- 32.Greco S, Predki B, Słowiński R (2002) Searching for an equivalencebetween decision rules and concordance‐discordance preference model in multicriteria choice problems. Control Cybern31:921–935Google Scholar
- 33.Hume D (1748) An enquiry concerning human understanding. Oxford, ClarendonPressGoogle Scholar
- 34.Klement EP, Mesiar R, Pap E (2000) Triangular norms. Kluwer,DordrechtzbMATHGoogle Scholar
- 35.Kolodner J (1993) Case-based reasoning. Morgan Kaufmann, SanMateoGoogle Scholar
- 36.Leake DB (1996) CBR in context: the present and future. In: Leake D (ed)Case-based reasoning: Experiences, lessons, and future directions. AAAI Press/MIT Press, Menlo Park, pp 1–30Google Scholar
- 37.Lin TY (1988) Neighborhood systems and relational databases. In: Proceedingsof the ACM Conference on Computer Science, Atlanta, p 725Google Scholar
- 38.Lin TY (1989) Neighborhood systems and approximation in database and knowledgebase systems. In: Proceedings of the Fourth International Symposium on Methodologies of Intelligent Systems, Poster Session, October 12–15,pp 75–86Google Scholar
- 39.Lin TY (1992) Topological and fuzzy rough sets. In: Slowinski R (ed)Intelligent decision support – Handbook of application and advances of the rough sets theory. Kluwer, Dordrecht,pp 287–304Google Scholar
- 40.Lin TY (1997) Granular computing. Announcement of the BISC Special InterestGroup on Granular ComputingGoogle Scholar
- 41.Lin TY (1998) Granular computing on binary relations I: Data mining andneighborhood systems. In: Skowron A, Polkowski L (eds) Rough sets in knowledge discovery. Physica, Heidelberg,pp 107–121Google Scholar
- 42.Lin TY (1998) Granular computing on binary relations II: Rough setrepresentations and belief functions. In: Skowron A, Polkowski L (eds) Rough sets in knowledge discovery. Physica, Heidelberg,pp 121–140Google Scholar
- 43.Loemker L (ed and trans), Leibniz GW (1969) Philosophical papers and letters,2nd edn. Reidel, DordrechtGoogle Scholar
- 44.Nakamura A, Gao JM (1991) A logic for fuzzy data analysis. Fuzzy SetsSyst 39:127–132MathSciNetzbMATHGoogle Scholar
- 45.Pal SK, Skowron A (eds) (1999) Rough-fuzzy hybridization: A new trends indecision making. Springer, SingaporeGoogle Scholar
- 46.Pawlak Z (1982) Rough sets. Int J Comput Inf Sci11:341–356MathSciNetzbMATHGoogle Scholar
- 47.Pawlak Z (1991) Rough sets. Kluwer, DordrechtzbMATHGoogle Scholar
- 48.Pawlak Z (2001) Rough set theory. Künstliche Intelligenz 3:38–39Google Scholar
- 49.Peters JF, Skowron A, Dubois D, Grzymala‐Busse J, Inuiguchi M, PolkowskiL (eds) (2005) Rough sets and fuzzy sets, transaction on rough sets II. Springer, BerlinGoogle Scholar
- 50.Polkowski L (2002) Rough set: mathematical foundations. Physica,HeidelbergzbMATHGoogle Scholar
- 51.Radzikowska AM, Kerre EE (2002) A comparative study of fuzzy roughsets. Fuzzy Sets Syst 126:137–155MathSciNetzbMATHGoogle Scholar
- 52.Słowiński R, Greco S, Matarazzo B (2002) Axiomatization of utility,outranking and decision‐rule preference models for multiple‐criteria classification problems under partial inconsistency with the dominanceprinciple. Control Cybern 31:1005–1035Google Scholar
- 53.Słowiński R, Greco S, Matarazzo B (2002) Mining decision‐rulepreference model from rough approximation of preference relation. In: Proc. 26th IEEE Annual Int. Conference on Computer Software & Applications(COMPSAC 2002), Oxford, pp 1129–1134Google Scholar
- 54.Słowiński R, Greco S, Matarazzo B (2005) Rough set based decisionsupport. In: Burke EK, Kendall G (eds) Search methodologies: Introductory tutorials in optimization and decision support techniques. Springer, New York,pp 475–527Google Scholar
- 55.Stewart T (2005) Dealing with uncertainties in MCDA. In: Figueira J, Greco S,Ehrgott M (eds) Multiple criteria decision analysis: State of the art surveys. Springer, Berlin, pp 445–470Google Scholar
- 56.Zadeh LA (1965) Fuzzy sets. Inf Control8:338–353MathSciNetzbMATHGoogle Scholar
- 57.Zadeh LA (1979) Fuzzy sets and information granularity. In: Gupta M, RagadeRK, Yager RR (eds) Advances in fuzzy set theory and applications. North‐Holland, Amsterdam, pp 3–18Google Scholar
- 58.Zadeh LA (1996) Key roles of information granulation and fuzzy logic in humanreasoning, concept formulation and computing with words. In: Proceedings of the 5th IEEE International Conference on Fuzzy Systems, New Orleans,p 1Google Scholar
- 59.Zadeh LA (1997) Towards a theory of fuzzy information granulation and itscentrality in human reasoning and fuzzy logic. Fuzzy Sets Syst 90:111–127MathSciNetzbMATHGoogle Scholar
- 60.Zadeh LA (1999) From computing with numbers to computing withwords – from manipulation of measurements to manipulation of perception. IEEE Trans Circuits Syst – I: Fundament Theor Appl45:105–119Google Scholar
- 61.Ziarko W (1993) Variable precision rough sets model. J Comput Syst Sci46:39–59MathSciNetzbMATHGoogle Scholar
- 62.Ziarko W (1998) Rough sets as a methodology for data mining. In:Polkowski L, Skowron A (eds) Rough Sets in Knowledge Discovery, vol 1. Physica, Heidelberg, pp 554–576Google Scholar