A Comparative Study of MGRSs and their Uncertainty Measures

• Autorzy: Ma Z.-M. , Mi J.-S.

Identyfikatory

DOI

10.3233/FI-2015-1289

• Języki publikacji: EN

Abstrakty

EN

Multi-granulation rough set(MGRS), as a kind of fusion mechanism of different information or data, is an useful development of Pawlak rough set theory. Firstly, this paper gives an introduction for various types of MGRS, their properties and axiomatization characterizations are studied. We show that, except for the optimistic one, each of the existing MGRS means a single granulation rough set. Then, we made a comparative analysis on the different uncertainty measures among the various multi-granulation approximation spaces. At the basis of investigating for the existing uncertainty measures, we discuss their limitations via some examples, and propose a total ordered relation among approximation spaces, even in the more general covering ones. It will be better than the original partial relation in revealing uncertainty, which conceal in the approximation space or covering one. Finally, based on the total ordered relation, we present improved information entropy, rough entropy, knowledge granulation and axiomatic definition of the knowledge granulation measures. It is proved that they are more reasonable than the original ones. Then, some novel uncertainty measures and improved fusion uncertainty measures about various granulations are also proposed. By employing these measures, granulation measures of various MGRSs are defined and studied.

Słowa kluczowe

EN

rough set; multigranulation; total ordered relation; uncertainty measure

• Wydawca: IOS Press
• Czasopismo: Fundamenta Informaticae
• Rocznik: 2015
• Tom: Vol. 142, nr 1-4
• Strony: 161--181
• Opis fizyczny: Bibliogr. 54 poz.

Twórcy

autor

Ma Z.-M.

• College of Mathematics and Information Science Hebei Normal University Shijiazhuang 050024 P.R. China

autor

Mi J.-S.

• College of Mathematics and Information Science Hebei Normal University Shijiazhuang 050024 P.R. China

Bibliografia

• [1] F. Angiulli, C. Pizzuti, Outlier mining in large high-dimensional data sets. IEEE Transactions on Knowledge and Data Engineering 17 (2) (2005) 203–215.
• [2] W. Bartol, J. Miro, K. Pioro, F. Rossello, On the coverings by tolerance classes. Information Sciences 166 (1–4) (2004) 193–211.
• [3] T. Beaubouef, F.E. Petry, G. Arora, Information-theoretic measures of uncertainty for rough sets and rough relational databases. Information Sciences 109 (1998) 185–195.
• [4] J.K. Chen, J.J. Lin, Y.J. Lin, Computing connected components of simple undirected graphs based on generalized rough sets. Knowledge-Based Systems 37 (2013) 80–85.
• [5] J.K. Chen, J.J. Lin, An application of rough sets to graph theory. Information Sciences 201 (2012) 114–127.
• [6] C. Cornelis,M.D. Cock, E.E. Kerre, Intuitionistic fuzzy rough sets: at the crossroads of imperfect knowledge. Expert Systems 20 (2003) 260–270.
• [7] I. Duntsch, G. Gediga, Uncertainty measures of rough set prediction. Artificial Intelligence 106 (1998) 109–137.
• [8] I. Duntsch, G. Gediga, Roughian: Rough information analysis. International Journal of General Systems 16 (2001) 121–147.
• [9] T. Feng, S.P. Zhang, J.S. Mi, Intuitionistic Fuzzy Rough Sets and Intuitionistic Fuzzy Topology Spaces. Information: An International Interdisciplinary Journal 14 (8) (2011) 2553–2562.
• [10] M. Hall, G. Holmes, Benchmarking attribute selection techniques for discrete class data mining. IEEE Transactions on Knowledge and Data Engineering 15 (6) (2003) 1437–1447.
• [11] J. Järvinen, Approximations and rough sets based on tolerances. in: W. Ziarko, Y. Yao (Eds.), Lecture Notes in Artifical Intelligence 2475(RSCTC 2002), Springer, Berlin, 2002, pp. 123–130.
• [12] R. Jensen, Q. Shen, Semantics-preserving dimensionality reduction: rough and fuzzy-rough-based approaches. IEEE Transactions on Knowledge and Data Engineering 16 (12) (2004) 1457–1471.
• [13] Y. Leung, W.Z. Wu, W.X. Zhang, Knowledge acquisition in incomplete information systems: A rough set approach. European Journal of Operational Research 168 (2006) 164–180.
• [14] J.Y. Liang, Z.Z. Shi, The information entropy, rough entropy and knowledge granulation in rough set theory. International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems 12(1) (2004) 37–46.
• [15] J.Y. Liang, Z.Z. Shi, D.Y. Li, Information entropy, rough entropy and knowledge granulation in incomplete information systems. International Journal of General Systems 35 (6) (2006) 641–654.
• [16] J.Y. Liang, J.H. Wang, Y.H. Qian, A new measure of uncertainty based on knowledge granulation for rough sets. Information Sciences 179 (2009) 458–470.
• [17] G.P. Lin, J.Y. Liang, Y.H. Qian, Uncertainty measures for multigranulation approximation space. International Journal of Uncertianty, Fuzziness and Knowledge-Based Systems 2014 (In Press).
• [18] G.P. Lin, Y.H. Qian, J.J. Lin, NMGRS: Neighborhood-basedmultigranulation rough sets. International Journal of Approximate Reasoning 53(7) (2012) 1080–1093.
• [19] Y.J. Lin, J.J. Li, P.R. Lin, G.P. Lin, J.K. Chen, Feature selection via neighborhood multi-granulation fusion. Knowledge-Based Systems 67 (2014) 162–168.
• [20] Y.J. Lin, J.J. Li, M.L. Lin, J.K. Chen, A new nearest neighbor classifier via fusing neighborhood information. Neurocomputing 143(2) (2014) 164–169.
• [21] G.L. Liu, W. Zhu, The algebraic structures of generalized rough set theory. Information Sciences 178 (2008) 4105–4113.
• [22] J.S.Mi, Y. Leung,W.Z.Wu, An uncertaintymeasure in partition-based fuzzy rough sets. International Journal of General Systems 34 (2005) 77–90.
• [23] J.S. Mi, Y. Leung, W.Z. Wu, Dependence-space-based attribute reduction in consistent decision tables. Soft Computing 15(2) (2011) 261–268.
• [24] J.S. Mi, W.X. Zhang, An axiomatic characterization of a fuzzy generalization of rough sets. Information Sciences 160 (2004) 235–249.
• [25] J. Nieminen, Rough tolerance equality. Fundamenta Informaticae 11 (3) (1988) 289–296.
• [26] Z. Pawlak, Rough sets. International Journal of Computer and Information Sciences 5 (1982) 341–356.
• [27] Z. Pawlak, A. Skowron, Rudiments of rough sets. Information Sciences 177 (2007) 3–27.
• [28] Z. Pawlak, A. Skowron, Rough sets: Some extensions. Information Sciences 177 (2007) 28–40.
• [29] Z. Pawlak, Rough Sets: Theoretical Aspects of Reasoning about Data. Kluwer Academic Publishers, Dordrecht, 1991.
• [30] L. Polkowski, A. Skowron (Eds.), Rough sets in knowledge discovery, vol.1, Physica-Verlag, Heidelberg, 1998.
• [31] L. Polkowski, S. Tsumoto, T.Y. Lin, Rough set methods and applications. Physica-Verlag, Heidelberg, 2000.
• [32] J.A. Pomykala, About tolerance and similarity relations in information systems. in: J.J. Alpigini, J.F. Peters, A. Skowron, N. Zhong (Eds.), Lecture Notes in Artificial Intelligence 2475 (RSCTC 2002) Springer, Berlin, 2002, pp. 175–182.
• [33] Y.H. Qian, J.Y. Liang, Combination entropy and combination granulation in rough set theory, International Journal of Uncertainty. Fuzziness and Knowledge-Based systems 16 (2) (2008) 179–193.
• [34] Y.H. Qian, J.Y. Liang, W. Wei, Pessimistic rough decision. In: Second international workshop on rough sets theory (2010) 19–21.
• [35] Y.H. Qian, J.Y. Liang, Y.Y.Yao, C.Y. Dang, MGRS: a mulit-granulation rough set. Information Sciences 180 (2010) 949–970.
• [36] Y.H. Qian, J.Y. Liang, Knowledge structure, knowledge granulation and knowledge distance in a knowledge base. International Journal of Approximation and Reasoning 50 (2009) 174–188.
• [37] C.E. Shannon, The mathematical theory of communication. The Bell System Technical Journal 27 (3 and 4) (1948) 373–423 (see also 623–656).
• [38] A. Skowron, J. Stepaniuk, Tolerance approximation spaces. Fundamenta Informaticae 27 (1996) 245–253.
• [39] A. Skowron, D. Vanderpooten, A generalized definition of rough approximations based on similarity. IEEE Transactions on Knowledge and Data Engineering 12 (2000) 331–336.
• [40] M.J.Wierman,Measuring uncertainty in rough set theory, International Journal of General Systems 28 (1999) 283–297.
• [41] W.Z. Wu, W.X. Zhang, H.Z. Li, Knowledge acquisition in incomplete fuzzy information systems via rough set approach. Expert Systems 20 (5) (2003) 280–286.
• [42] W.Z. Wu, J.S. Mi, W.X. Zhang, Generalized fuzzy rough sets. Information Sciences 151 (2003) 263–282.
• [43] W.Z. Wu, M. Zhang, H.Z. Li, J.S. Mi, Knowledge reduction in random information systems via Dempster-Shafer theory of evidence. Information Sciences 174 (2005) 143–164.
• [44] W.Z. Wu, Y. Leung, J.S. Mi, On characterizations of (I,T)-fuzzy rough approximation operators. Fuzzy Sets and Systems 154 (1) (2005) 76–102.
• [45] Y.Y. Yao, Probabilistic approaches to rough sets. Expert Systems 20(5) (2003) 287–297.
• [46] Y.Y. Yao, Two views of the theory of rough sets in finite universe. International Journal of Approximation and Reasoning 15 (4) (1996) 291–317.
• [47] Y.Y. Yao, Constructive and algebraic methods of the theory of rough sets. Information Sciences 109 (1998) 21–47.
• [48] Y.Y. Yao, On generalized Pawlak approximation operators. Rough Sets and Current Trends in Computing, LNAI 1424 (1998) 298–307.
• [49] L.A. Zadeh, Fuzzy sets and information granularity, in: M. Gupta, R. Ragade, R. Yager (Eds.), Advances in Fuzzy Set Theory and Application, North-Holland, Amsterdam, 1979, pp. 3–18.
• [50] Y.L. Zhang, J.J. Li, W.Z. Wu, On axiomatic characterizations of three pairs of covering based approximation operators. Information Sciences 180 (2010) 274–287.
• [51] L. Zhou, W.Z. Wu, W.X. Zhang, On intuitionistic fuzzy rough sets and their topological structures. International Journal of General Systems 38 (6) (2009) 589–616.
• [52] W. Zhu, Generalized rough sets based on relations. Information Sciences 177 (2007) 4997–5011.
• [53] W. Zhu, Relationship between generalized rough sets based on binary relation and covering. Information Sciences 179 (2009) 210–225.
• [54] W. Zhu, F.Y. Wang, On three types of covering rough sets. IEEE Transactions on Knowledge and Data Engineering 19 (8) (2007) 1131–1144.