Abstract
The present paper is concerned with rough set theory (RST) and a particular approach to human-like induction, namely similarity coverage model (SCM). It redefines basic concepts of RST – such like e.g. a decision rule, accuracy and coverage of decision rules – in the light of SCM and explains how RST may be viewed as a similarity-based model of human-like inductive reasoning. Furthermore, following the knowledge-based theory of induction, we enrich RST by the concept of an ontology and, in consequence, we present an RST-driven conceptualisation of SCM. The paper also discusses a topological representation of information systems in terms of non-Archimedean structures. It allows us to present an ontology-driven interpretation of finite non-Archimedean nearness spaces and, to some extent, to complete recent papers about RST and the topological concepts of nearness.
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References
Albatineh, A., Niewiadomska-Bugaj, M., Mihalko, D.: On Similarity Indices and Correction for Chance Agreement. Journal of Classification 23, 301–313 (2006)
Atran, S.: Classifying Nature Across Cultures. In: Osherson, D., Smith, E. (eds.) An Invitation to Cognitive Science. Thinking, pp. 131–174. MIT Press, Cambridge (1995)
Deses, D., Lowen-Colebunders, E.: On Completeness in a Non-Archimedean Setting via Firm Reflections. Bulletin of the Belgian Mathematical Society, Special volume: p-adic Numbers in Number Theory, Analytic Geometry and Functional Analysis, 49–61 (2002)
Deses, D.: Completeness and Zero-dimensionality Arising from the Duality Between Closures and Lattices, Ph.D. Thesis, Free University of Brussels (2003), http://homepages.vub.ac.be/~diddesen/phdthesis.pdf
Gomolińska, A.: On Three Closely Related Rough Inclusion Functions. In: Kryszkiewicz, M., Peters, J., Rybiński, H., Skowron, A. (eds.) RSEISP 2007. LNCS, vol. 4585, pp. 142–151. Springer, Heidelberg (2007)
Heit, E.: Properties of Inductive Reasoning. Psychonomic Bulletin & Review 7, 569–592 (2000)
Kloos, H., Sloutsky, V., Fisher, A.: Dissociation Between Categorization and Induction Early in Development: Evidence for Similarity-Based Induction. In: Proceedings of the XXVII Annual Conference of the Cognitive Science Society (2005)
Kulczyński, S.: Die Pflanzenassociationen der Pieninen. Bulletin International de L’Academie Polonaise des Sciences et des letters, classe des sciences mathematiques et naturelles, Serie B, Supplement II 2, 57–203 (1927)
Osherson, D.N., Smith, E.E., Wilkie, O., Lopez, A., Shafir, E.: Category-Based Induction. Psychological Review 97(2), 185–200 (1990)
Pawlak, Z.: Rough Sets. International Journal of Computer and Information Sciences 11, 341–356 (1982)
Peters, J., Skowron, A., Stepaniuk, J.: Nearness of Objects: Extension of Approximation Space Model. Fundamenta Informaticae 79, 497–512 (2007)
Pawlak, Z.: Rough Sets: Theoretical Aspects of Reasoning About Data. Kluwer Academic Publishers, Boston (1991)
Polkowski, L., Skowron, A.: Rough Mereology: A New Paradigm for Approximate Reasoning. Int. J. Approx. Reasoning 15(4), 333–365 (1996)
Skowron, A., Stepaniuk, J.: Tolerance Approximation Spaces. Fundamenta Informaticae 27, 245–253 (1996)
Sloman, S.A.: Feature-Based Induction. Cognitive Psychology 25, 231–280 (1993)
Tsumoto, S.: Extraction of Experts’ Decision Rules from Clinical Databases Using Rough Set Model. Intelligent Data Analysis 2(1-4), 215–227 (1998)
Wille, R.: Restructuring Lattice Theory: an Approach Based on Hierarchies of Concepts. In: Rival, I. (ed.) Ordered Sets, pp. 445–470. Reidel, Dordrecht-Boston (1982)
Wille, R.: Concept lattices and Conceptual Knowledge Systems. Computers & Mathematics with Applications 23, 493–515 (1992)
Wolski, M.: Approximation Spaces and Nearness Type Structures. Fundamenta Informaticae 79, 567–577 (2007)
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Wolski, M. (2008). Category-Based Inductive Reasoning: Rough Set Theoretic Approach. In: Peters, J.F., Skowron, A., Rybiński, H. (eds) Transactions on Rough Sets IX. Lecture Notes in Computer Science, vol 5390. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-89876-4_23
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DOI: https://doi.org/10.1007/978-3-540-89876-4_23
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