By Jerzy W. Grzymala-Busse (auth.), James F. Peters, Andrzej Skowron, Sheela Ramanna, Zbigniew Suraj, Xin Wang (eds.)
The LNCS magazine Transactions on tough units is dedicated to the total spectrum of tough units similar concerns, from logical and mathematical foundations, via all elements of tough set conception and its functions, akin to information mining, wisdom discovery, and clever details processing, to kinfolk among tough units and different techniques to uncertainty, vagueness, and incompleteness, comparable to fuzzy units and conception of proof. quantity XVI contains extensions of papers from the tough units and information expertise convention which used to be held in Banff, Canada, in October 2011. furthermore this e-book encompasses a lengthy paper in response to a PhD thesis. The papers conceal either idea and purposes of tough, fuzzy and close to units. they give a continuation of a few study streams that have grown out of the seminal paintings by way of Zdzislaw Pawlak throughout the first decade of the twenty first century.
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313–319. IEEE Computer Society (2003) 9. : Algorithms for Clustering Data. Prentice-Hall, Englewood Cliffs (1988) 10. : Data clustering: a review. ACM Computing Surveys (CSUR) 31(3), 264–323 (1999) 11. : Clustering sequences with hidden markov models. Advances in Neural Information Processing Systems, 648–654 (1997) 12. : Deterministic annealing for clustering, compression, classification, regression, and related optimization problems. Proceedings of the IEEE 86(11), 2210– 2239 (1998) 13. : Rough sets: theoretical aspects of reasoning about data.
The smaller this value, the better the performance. This criterion aims at the optimal performance comparison. 1 (d) Haberman data set Fig. 4. Performance comparison based on Nb The results of criterion 1 is depicted in Fig. 4. One can see that: 1. 10). 005. 2. 10). 06). 3. 10). 07). 005. 4. 10). 03). 04. 28 F. Li and Q. Liu Obviously, although RCM outperforms ERCM on few values of ε, ERCM shows better performance than RCM for the four tested data sets. Table 3. 224E-6 The statistical results of DB index are shown in Table 3.
A generalized definition of rough approximations based on similarity. IEEE Transactions on Knowledge and Data Engineering 12(2), 331–336 (2000) 22. : Constructive and algebraic methods of theory of rough sets. Information Sciences 109, 21–47 (1998) 23. : Decision-Theoretic Rough Set Models. , Wu, ´ ezak, D. ) RSKT 2007. , Sl¸ vol. 4481, pp. 1–12. Springer, Heidelberg (2007) 24. : Three-way decisions with probabilistic rough sets. Information Sciences 180(3), 341–353 (2010) 25. : Case generation using rough sets with fuzzy representation.