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2015 | OriginalPaper | Buchkapitel

1. Similarity and Granulation

verfasst von : Lech Polkowski, Piotr Artiemjew

Erschienen in: Granular Computing in Decision Approximation

Verlag: Springer International Publishing

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Abstract

This chapter introduces into topics of similarity and granulation. We define similarity relations as tolerance and weak tolerance relations and give basic information on their structure. In preparation for theme of granulation, we extend notions of tolerance to graded tolerance and weak tolerance. We outline approaches to granulation and the notion of a granule.

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Literatur
1.
Zurück zum Zitat Albatineh, A.N., Niewiadomska-Bugaj, M., Mihalko, D.: On similarity indices and correction for chance agreement. J. Classif. 23, 301–313 (2006)CrossRefMathSciNet Albatineh, A.N., Niewiadomska-Bugaj, M., Mihalko, D.: On similarity indices and correction for chance agreement. J. Classif. 23, 301–313 (2006)CrossRefMathSciNet
2.
Zurück zum Zitat Bocheński, I.M.: Die Zeitg\(\ddot{{\rm o}}\)nossischen Denkmethoden. A. Francke AG, Bern (1954) Bocheński, I.M.: Die Zeitg\(\ddot{{\rm o}}\)nossischen Denkmethoden. A. Francke AG, Bern (1954)
3.
Zurück zum Zitat Casati, R., Varzi, A.C.: Parts and Places: The Structures of Spatial Representations. MIT Press, Cambridge (1999) Casati, R., Varzi, A.C.: Parts and Places: The Structures of Spatial Representations. MIT Press, Cambridge (1999)
4.
Zurück zum Zitat Gomolińska, A., Wolski, M.: Rough inclusion functions and similarity indices. In: Proceedings of CSP 2013 (22nd International Workshop on Concurrency, Specification and Programming), Warsaw University, September 2013. Białystok University of Technology, pp. 145–156 (2013). ISBN 978-83-62582-42-6 Gomolińska, A., Wolski, M.: Rough inclusion functions and similarity indices. In: Proceedings of CSP 2013 (22nd International Workshop on Concurrency, Specification and Programming), Warsaw University, September 2013. Białystok University of Technology, pp. 145–156 (2013). ISBN 978-83-62582-42-6
5.
Zurück zum Zitat Grzymala-Busse, J.W.: Data with missing attribute values: generalization of indiscernibility relation and rule induction. Transactions on Rough Sets I. Lecture Notes in Computer Science, vol. 3100, pp. 78–95. Springer, Berlin (2004) Grzymala-Busse, J.W.: Data with missing attribute values: generalization of indiscernibility relation and rule induction. Transactions on Rough Sets I. Lecture Notes in Computer Science, vol. 3100, pp. 78–95. Springer, Berlin (2004)
6.
Zurück zum Zitat Grzymala-Busse, J.W., Ming, H.: A comparison of several approaches to missing attribute values in data mining. Lecture Notes in Artificial Intelligence, vol. 2005, pp. 378–385. Springer, Berlin (2004) Grzymala-Busse, J.W., Ming, H.: A comparison of several approaches to missing attribute values in data mining. Lecture Notes in Artificial Intelligence, vol. 2005, pp. 378–385. Springer, Berlin (2004)
7.
Zurück zum Zitat Kuratowski, C., Mostowski, A.: Set Theory. Polish Scientific Publishers, Warszawa (1968)MATH Kuratowski, C., Mostowski, A.: Set Theory. Polish Scientific Publishers, Warszawa (1968)MATH
8.
Zurück zum Zitat Lin, T.Y.: Neighborhood systems and relational database. Abstract. In: Proceedings of CSC’88, p. 725 (1988) Lin, T.Y.: Neighborhood systems and relational database. Abstract. In: Proceedings of CSC’88, p. 725 (1988)
9.
Zurück zum Zitat Lin, T.Y.: Neighborhood systems and approximation in database and knowledge based systems. In: Proceedings of the 4th International Symposium on Methodologies for Intelligent Systems (ISMIS), pp. 75–86 (1989) Lin, T.Y.: Neighborhood systems and approximation in database and knowledge based systems. In: Proceedings of the 4th International Symposium on Methodologies for Intelligent Systems (ISMIS), pp. 75–86 (1989)
10.
Zurück zum Zitat Lin, T.Y.: Topological and fuzzy rough sets. In: Słowiński, R. (ed.) Intelligent Decision Support. Handbook of Applications and Advances of the Rough Sets Theory, pp. 287–304. Kluwer, Dordrecht (1992) Lin, T.Y.: Topological and fuzzy rough sets. In: Słowiński, R. (ed.) Intelligent Decision Support. Handbook of Applications and Advances of the Rough Sets Theory, pp. 287–304. Kluwer, Dordrecht (1992)
11.
Zurück zum Zitat Lin, T.Y.: From rough sets and neighborhood systems to information granulation and computing with words. In: Proceedings of the European Congress on Intelligent Techniques and Soft Computing, pp. 1602–1606 (1994) Lin, T.Y.: From rough sets and neighborhood systems to information granulation and computing with words. In: Proceedings of the European Congress on Intelligent Techniques and Soft Computing, pp. 1602–1606 (1994)
12.
Zurück zum Zitat Lin, T.Y.: Granular computing: fuzzy logic and rough sets. In: Zadeh, L.A., Kacprzyk, J. (eds.) Computing with Words in Information/Intelligent Systems, vol. 1, pp. 183–200. Physica Verlag, Heidelberg (1999)CrossRef Lin, T.Y.: Granular computing: fuzzy logic and rough sets. In: Zadeh, L.A., Kacprzyk, J. (eds.) Computing with Words in Information/Intelligent Systems, vol. 1, pp. 183–200. Physica Verlag, Heidelberg (1999)CrossRef
13.
Zurück zum Zitat Lin, T.Y.: Granular Computing. Lecture Notes in Computer Science, vol. 2639, pp. 16–24. Springer, Berlin (2003) Lin, T.Y.: Granular Computing. Lecture Notes in Computer Science, vol. 2639, pp. 16–24. Springer, Berlin (2003)
14.
Zurück zum Zitat Lin, T.Y.: Granular computing: examples, intuitions, and modeling. In: Proceedings of IEEE 2005 Conference on Granular Computing GrC05, pp. 40–44. IEEE Press, Beijing (2005) Lin, T.Y.: Granular computing: examples, intuitions, and modeling. In: Proceedings of IEEE 2005 Conference on Granular Computing GrC05, pp. 40–44. IEEE Press, Beijing (2005)
15.
Zurück zum Zitat Lin, T.Y.: A roadmap from rough set theory to granular computing. In: Proceedings RSKT 2006, 1st International Conference on Rough Sets and Knowledge Technology, Chongqing, China. Lecture Notes in Artificial Intelligence, vol. 4062, pp. 33–41. Springer, Berlin (2006) Lin, T.Y.: A roadmap from rough set theory to granular computing. In: Proceedings RSKT 2006, 1st International Conference on Rough Sets and Knowledge Technology, Chongqing, China. Lecture Notes in Artificial Intelligence, vol. 4062, pp. 33–41. Springer, Berlin (2006)
16.
Zurück zum Zitat Łukasiewicz, J.: Die Logischen Grundlagen der Wahrscheinlichtkeitsrechnung. Cracow (1913) Łukasiewicz, J.: Die Logischen Grundlagen der Wahrscheinlichtkeitsrechnung. Cracow (1913)
17.
Zurück zum Zitat Menger, K.: Statistical metrics. Proc. Natl. Acad. Sci. USA 28, 535–537 (1942) Menger, K.: Statistical metrics. Proc. Natl. Acad. Sci. USA 28, 535–537 (1942)
18.
Zurück zum Zitat Nguyen, S.H.: Regularity analysis and its applications in data mining. In: Polkowski, L., Tsumoto, S., Lin, T.Y. (eds.) Rough Set Methods and Applications. New Developments in Knowledge Discovery in Information Systems, pp. 289–378. Physica Verlag, Heidelberg (2000) Nguyen, S.H.: Regularity analysis and its applications in data mining. In: Polkowski, L., Tsumoto, S., Lin, T.Y. (eds.) Rough Set Methods and Applications. New Developments in Knowledge Discovery in Information Systems, pp. 289–378. Physica Verlag, Heidelberg (2000)
19.
Zurück zum Zitat Nieminen, J.: Rough tolerance equality and tolerance black boxes. Fundamenta Informaticae 11, 289–296 (1988)MATHMathSciNet Nieminen, J.: Rough tolerance equality and tolerance black boxes. Fundamenta Informaticae 11, 289–296 (1988)MATHMathSciNet
20.
Zurück zum Zitat Pawlak, Z.: Rough Sets: Theoretical Aspects of Reasoning About Data. Kluwer, Dordrecht (1991)CrossRefMATH Pawlak, Z.: Rough Sets: Theoretical Aspects of Reasoning About Data. Kluwer, Dordrecht (1991)CrossRefMATH
21.
Zurück zum Zitat Poincaré, H.: La Science et l’Hypothèse. Flammarion, Paris (1902) Poincaré, H.: La Science et l’Hypothèse. Flammarion, Paris (1902)
22.
Zurück zum Zitat Polkowski, L., Skowron, A, Żytkow, J.: Tolerance based rough sets. In: Lin, T.Y., Wildberger, M. (eds.) Soft Computing: Rough Sets, Fuzzy Logic, Neural Networks, Uncertainty Management, Knowledge Discovery, pp. 55–58. Simulation Councils Inc., San Diego (1994) Polkowski, L., Skowron, A, Żytkow, J.: Tolerance based rough sets. In: Lin, T.Y., Wildberger, M. (eds.) Soft Computing: Rough Sets, Fuzzy Logic, Neural Networks, Uncertainty Management, Knowledge Discovery, pp. 55–58. Simulation Councils Inc., San Diego (1994)
23.
Zurück zum Zitat Polkowski, L.: A rough set paradigm for unifying rough set theory and fuzzy set theory. Fundamenta Informaticae 54, 67–88; also. In: Proceedings RSFDGrC03, Chongqing, China, 2003. Lecture Notes in Artificial Intelligence, vol. 2639, pp. 70–78. Springer, Berlin (2003) Polkowski, L.: A rough set paradigm for unifying rough set theory and fuzzy set theory. Fundamenta Informaticae 54, 67–88; also. In: Proceedings RSFDGrC03, Chongqing, China, 2003. Lecture Notes in Artificial Intelligence, vol. 2639, pp. 70–78. Springer, Berlin (2003)
24.
Zurück zum Zitat Polkowski, L.: A note on 3-valued rough logic accepting decision rules. Fundamenta Informaticae 61, 37–45 (2004)MATHMathSciNet Polkowski, L.: A note on 3-valued rough logic accepting decision rules. Fundamenta Informaticae 61, 37–45 (2004)MATHMathSciNet
25.
Zurück zum Zitat Polkowski, L.: Toward rough set foundations. Mereological approach. In: Proceedings RSCTC04, Uppsala, Sweden. Lecture Notes in Artificial Intelligence, vol. 3066, pp. 8–25. Springer, Berlin (2004) Polkowski, L.: Toward rough set foundations. Mereological approach. In: Proceedings RSCTC04, Uppsala, Sweden. Lecture Notes in Artificial Intelligence, vol. 3066, pp. 8–25. Springer, Berlin (2004)
26.
Zurück zum Zitat Polkowski, L.: A rough-neural computation model based on rough mereology. In: Pal, S.K., Polkowski, L., Skowron, A. (eds.) Rough-Neural Computing. Techniques for Computing with Words, pp. 85–108. Springer, Berlin (2004) Polkowski, L.: A rough-neural computation model based on rough mereology. In: Pal, S.K., Polkowski, L., Skowron, A. (eds.) Rough-Neural Computing. Techniques for Computing with Words, pp. 85–108. Springer, Berlin (2004)
27.
Zurück zum Zitat Polkowski, L.: Formal granular calculi based on rough inclusions. In: Proceedings of IEEE 2005 Conference on Granular Computing GrC05, pp. 57–62. IEEE Press, Beijing (2005) Polkowski, L.: Formal granular calculi based on rough inclusions. In: Proceedings of IEEE 2005 Conference on Granular Computing GrC05, pp. 57–62. IEEE Press, Beijing (2005)
28.
Zurück zum Zitat Polkowski, L.: Rough-fuzzy-neurocomputing based on rough mereological calculus of granules. Int. J. Hybrid Intell. Syst. 2, 91–108 (2005)MATH Polkowski, L.: Rough-fuzzy-neurocomputing based on rough mereological calculus of granules. Int. J. Hybrid Intell. Syst. 2, 91–108 (2005)MATH
29.
Zurück zum Zitat Polkowski, L.: A model of granular computing with applications. In: Proceedings of IEEE 2006 Conference on Granular Computing GrC06, pp. 9–16. IEEE Press, Atlanta (2006) Polkowski, L.: A model of granular computing with applications. In: Proceedings of IEEE 2006 Conference on Granular Computing GrC06, pp. 9–16. IEEE Press, Atlanta (2006)
30.
Zurück zum Zitat Polkowski, L.: Granulation of knowledge in decision systems: the approach based on rough inclusions. The method and its applications. In: Proceedings RSEiSP’07 (in memory of Z. Pawlak). Lecture Notes in Artificial Intelligence, vol. 4585, pp. 69–79 (2007) Polkowski, L.: Granulation of knowledge in decision systems: the approach based on rough inclusions. The method and its applications. In: Proceedings RSEiSP’07 (in memory of Z. Pawlak). Lecture Notes in Artificial Intelligence, vol. 4585, pp. 69–79 (2007)
31.
Zurück zum Zitat Polkowski, L.: The paradigm of granular rough computing. In: Proceedings ICCI’07. 6th IEEE International Conference on Cognitive Informatics, pp. 145–163. IEEE Computer Society, Los Alamitos (2007) Polkowski, L.: The paradigm of granular rough computing. In: Proceedings ICCI’07. 6th IEEE International Conference on Cognitive Informatics, pp. 145–163. IEEE Computer Society, Los Alamitos (2007)
32.
Zurück zum Zitat Polkowski, L.: Rough mereology in analysis of vagueness. In: Proceedings RSKT 2008. Lecture Notes in Artificial Intelligence, vol. 5009, pp. 197–205. Springer, Berlin (2008) Polkowski, L.: Rough mereology in analysis of vagueness. In: Proceedings RSKT 2008. Lecture Notes in Artificial Intelligence, vol. 5009, pp. 197–205. Springer, Berlin (2008)
33.
Zurück zum Zitat Polkowski, L.: A unified approach to granulation of knowledge and granular computing based on rough mereology: a survey. In: Pedrycz, W., Skowron, A., Kreinovich, V. (eds.) Handbook of Granular Computing, pp. 375–400. Wiley, Chichester (2008) Polkowski, L.: A unified approach to granulation of knowledge and granular computing based on rough mereology: a survey. In: Pedrycz, W., Skowron, A., Kreinovich, V. (eds.) Handbook of Granular Computing, pp. 375–400. Wiley, Chichester (2008)
34.
Zurück zum Zitat Polkowski, L.: Granulation of knowledge: similarity based approach in information and decision systems. In: Meyers, R.A. (ed.) Springer Encyclopedia of Complexity and System Sciences. Springer, Berlin, article 00 788 (2009) Polkowski, L.: Granulation of knowledge: similarity based approach in information and decision systems. In: Meyers, R.A. (ed.) Springer Encyclopedia of Complexity and System Sciences. Springer, Berlin, article 00 788 (2009)
35.
Zurück zum Zitat Polkowski, L.: Approximate Reasoning by Parts. An Introduction to Rough Mereology. ISRL, vol. 20. Springer, Berlin (2011) Polkowski, L.: Approximate Reasoning by Parts. An Introduction to Rough Mereology. ISRL, vol. 20. Springer, Berlin (2011)
37.
Zurück zum Zitat Schreider, Yu.: Equality, Resemblance, and Order. Mir Publishers, Moscow (1975) Schreider, Yu.: Equality, Resemblance, and Order. Mir Publishers, Moscow (1975)
38.
Zurück zum Zitat Tarski, A.: Zur Grundlegung der Booleschen Algebra. I. Fundamenta Mathematicae 24, 177–198 (1935) Tarski, A.: Zur Grundlegung der Booleschen Algebra. I. Fundamenta Mathematicae 24, 177–198 (1935)
39.
Zurück zum Zitat Wille, R.: Restructuring lattice theory: an approach based on hierarchies of concepts. In: Rival, I. (ed.) Ordered Sets, pp. 445–470. D. Reidel, Dordrecht (1982) Wille, R.: Restructuring lattice theory: an approach based on hierarchies of concepts. In: Rival, I. (ed.) Ordered Sets, pp. 445–470. D. Reidel, Dordrecht (1982)
40.
Zurück zum Zitat Yao, Y.Y.: Granular computing: basic issues and possible solutions. In: Proceedings of the 5th Joint Conference on Information Sciences, vol. 1, pp. 186–189. Association for Intelligent Machinery, Atlantic (2000) Yao, Y.Y.: Granular computing: basic issues and possible solutions. In: Proceedings of the 5th Joint Conference on Information Sciences, vol. 1, pp. 186–189. Association for Intelligent Machinery, Atlantic (2000)
41.
Zurück zum Zitat Yao, Y.Y.: Perspectives of granular computing. In: Proceedings of IEEE 2005 Conference on Granular Computing GrC05, pp. 85–90. IEEE Press, Beijing (2005) Yao, Y.Y.: Perspectives of granular computing. In: Proceedings of IEEE 2005 Conference on Granular Computing GrC05, pp. 85–90. IEEE Press, Beijing (2005)
44.
Zurück zum Zitat Zadeh, L.A.: Fuzzy sets and information granularity. In: Gupta, M., Ragade, R., Yager, R.R. (eds.) Advances in Fuzzy Set Theory and Applications, pp. 3–18. North-Holland, Amsterdam (1979) Zadeh, L.A.: Fuzzy sets and information granularity. In: Gupta, M., Ragade, R., Yager, R.R. (eds.) Advances in Fuzzy Set Theory and Applications, pp. 3–18. North-Holland, Amsterdam (1979)
45.
Zurück zum Zitat Zeeman, E.C.: The topology of the brain and the visual perception. In: Fort, K.M. (ed.) Topology of 3-manifolds and Selected Topics, pp. 240–256. Prentice Hall, Englewood Cliffs (1965) Zeeman, E.C.: The topology of the brain and the visual perception. In: Fort, K.M. (ed.) Topology of 3-manifolds and Selected Topics, pp. 240–256. Prentice Hall, Englewood Cliffs (1965)
46.
Zurück zum Zitat Bargiela, A., Pedrycz, W.: Granular Computing: An Introduction. Kluwer Academic Publishers, Dordrecht (2003)CrossRef Bargiela, A., Pedrycz, W.: Granular Computing: An Introduction. Kluwer Academic Publishers, Dordrecht (2003)CrossRef
47.
Zurück zum Zitat Kacprzyk, J., Nurmi, H., Zadrożny, S.: Towards a comprehensive similarity analysis of voting procedures using rough sets and similarity measures. In: Skowron, A., Suraj, Z. (eds.) Rough Sets and Intelligent Systems—Professor Zdzisław Pawlak in Memoriam, vol. 1. Springer, Heidelberg, ISRL vol. 42, pp. 359–380 (2013) Kacprzyk, J., Nurmi, H., Zadrożny, S.: Towards a comprehensive similarity analysis of voting procedures using rough sets and similarity measures. In: Skowron, A., Suraj, Z. (eds.) Rough Sets and Intelligent Systems—Professor Zdzisław Pawlak in Memoriam, vol. 1. Springer, Heidelberg, ISRL vol. 42, pp. 359–380 (2013)
48.
Zurück zum Zitat Pal, S.K., Polkowski, L., Skowron, A. (eds.): Rough-Neural Computing: Techniques for Computing with Words. Springer, Heidelberg (2004) Pal, S.K., Polkowski, L., Skowron, A. (eds.): Rough-Neural Computing: Techniques for Computing with Words. Springer, Heidelberg (2004)
49.
Zurück zum Zitat Pedrycz, W. (ed.): Granular Computing: An Emerging Paradigm. Physica Verlag, Heidelberg (2001) Pedrycz, W. (ed.): Granular Computing: An Emerging Paradigm. Physica Verlag, Heidelberg (2001)
50.
Zurück zum Zitat Pedrycz, W., Skowron, A., Kreinovich, V. (eds.): Handbook of Granular Computing. Wiley, Chichester (2008) Pedrycz, W., Skowron, A., Kreinovich, V. (eds.): Handbook of Granular Computing. Wiley, Chichester (2008)
51.
Zurück zum Zitat Pawlak, Z.: Elementary rough set granules: Toward a rough set processor. In: Pal, S.K., Polkowski, L., Skowron, A. (eds.) Rough Neuro-Computing: Techniques for Computing with Words, pp. 5–14. Springer, Heidelberg (2013) Pawlak, Z.: Elementary rough set granules: Toward a rough set processor. In: Pal, S.K., Polkowski, L., Skowron, A. (eds.) Rough Neuro-Computing: Techniques for Computing with Words, pp. 5–14. Springer, Heidelberg (2013)
52.
Zurück zum Zitat Polkowski, L., Skowron, A.: Grammar systems for distributed synthesis of of approximate solutions extracted from experience. In: Paun, Gh., Salomaa, A. (eds.) Grammatical Models of Multi-Agent Systems, pp. 316–333. Gordon and Breach, Amsterdam (1999) Polkowski, L., Skowron, A.: Grammar systems for distributed synthesis of of approximate solutions extracted from experience. In: Paun, Gh., Salomaa, A. (eds.) Grammatical Models of Multi-Agent Systems, pp. 316–333. Gordon and Breach, Amsterdam (1999)
53.
Zurück zum Zitat Polkowski, L., Skowron, A.: Towards adaptive calculus of granules. In: Zadeh, L.A., Kacprzyk, J. (eds.) Computing with Words in Information/Intelligent Systems. Foundations, vol. 1. Physica Verlag, Heidelberg (1999) Polkowski, L., Skowron, A.: Towards adaptive calculus of granules. In: Zadeh, L.A., Kacprzyk, J. (eds.) Computing with Words in Information/Intelligent Systems. Foundations, vol. 1. Physica Verlag, Heidelberg (1999)
54.
Zurück zum Zitat Polkowski, L., Skowron, A.: Rough mereological calculi of granules: a rough set approach to computation. Comput. Intell. Int. J. 17(3), 472–492 (2001)MathSciNet Polkowski, L., Skowron, A.: Rough mereological calculi of granules: a rough set approach to computation. Comput. Intell. Int. J. 17(3), 472–492 (2001)MathSciNet
55.
Zurück zum Zitat Polkowski, L., Semeniuk-Polkowska, M.: On rough set logics based on similarity relations. Fundamenta Informaticae 64, 379–390 (2005)MATHMathSciNet Polkowski, L., Semeniuk-Polkowska, M.: On rough set logics based on similarity relations. Fundamenta Informaticae 64, 379–390 (2005)MATHMathSciNet
56.
Zurück zum Zitat Skowron, A., Stepaniuk, J.: Information granules: towards foundations of granular computing. Int. J. Intell. Syst. 16(1), 57–86 (2001)CrossRefMATH Skowron, A., Stepaniuk, J.: Information granules: towards foundations of granular computing. Int. J. Intell. Syst. 16(1), 57–86 (2001)CrossRefMATH
57.
Zurück zum Zitat Skowron, A., Suraj, Z. (eds.): Rough Sets and Intelligent Systems. Professor Zdzisław Pawlak in Memoriam, vol. 1. Springer, ISRL, vol. 42. Heidelberg (2013) Skowron, A., Suraj, Z. (eds.): Rough Sets and Intelligent Systems. Professor Zdzisław Pawlak in Memoriam, vol. 1. Springer, ISRL, vol. 42. Heidelberg (2013)
58.
Zurück zum Zitat Stepaniuk, J. (ed.): Rough-Granular Computing in Knowledge Discovery and Data Mining. Springer, Heidelberg (2008)MATH Stepaniuk, J. (ed.): Rough-Granular Computing in Knowledge Discovery and Data Mining. Springer, Heidelberg (2008)MATH
Metadaten
Titel
Similarity and Granulation
verfasst von
Lech Polkowski
Piotr Artiemjew
Copyright-Jahr
2015
DOI
https://doi.org/10.1007/978-3-319-12880-1_1