Abstract
Approximation of sets is a fundamental notion of rough set theory (RST) proposed by Z. Pawlak. Each rough set can be characterized numerically by the coefficient called the accuracy of approximation. This coefficient determines quantitatively a degree of roughness. Such an approach does not take into consideration semantics of data. In the paper, we show that adding information on semantic relations between decision attribute values in the form of ontological graphs enables us to determine qualitatively the accuracy of approximation. The qualitative assessment of approximation should be treated as some additional characteristic of rough sets. The proposed approach enriches application of rough sets if decision attribute values classifying objects are symbolical (e.g., words, terms, linguistic concepts, etc.). The presented approach refers to a general trend in computations proposed by L. Zadeh and called “computing with words”.
This is a preview of subscription content, log in via an institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsReferences
The Wikisaurus Homepage: http://en.wiktionary.org/wiki/Wiktionary: Wikisaurus
Brachman, R.: What IS-A is and isn’t: an analysis of taxonomic links in semantic networks. Computer 16(10), 30–36 (1983)
Chaffin, R., Herrmann, D.J.: The nature of semantic relations: a comparison of two approaches. In: Evens, M. (ed.) Relational Models of the Lexicon: Representing Knowledge in Semantic Networks, pp. 289–334. Cambridge University Press, New York (1988)
Cruse, D.: Lexical Semantics. Cambridge University Press, Cambridge (1986)
Greco, S., Matarazzo, B., Słowiński, R.: Rough sets theory for multicriteria decision analysis. Eur. J. Oper. Res. 129(1), 1–47 (2001)
Gupta, M.M.: On fuzzy logic and cognitive computing: some perspectives. Scientia Iranica 18(3), 590–592 (2011)
Ishizu, S., Gehrmann, A., Nagai, Y., Inukai, Y.: Rough ontology: extension of ontologies by rough sets. In: Smith, M.J., Salvendy, G. (eds.) HCII 2007. LNCS, vol. 4557, pp. 456–462. Springer, Heidelberg (2007)
Köhler, J., Philippi, S., Specht, M., Rüegg, A.: Ontology based text indexing and querying for the semantic web. Knowl.-Based Syst. 19, 744–754 (2006)
Lukaszewski, T., Józefowska, J., Lawrynowicz, A.: Attribute value ontology - using semantics in data mining. In: Maciaszek, L.A., Cuzzocrea, A., Cordeiro, J. (eds.) Proceedings of the 14th International Conference on Enterprise Information Systems, pp. 329–334. Wroclaw, Poland (2012)
Midelfart, H., Komorowski, J.: A rough set framework for learning in a directed acyclic graph. In: Alpigini, J.J., Peters, J.F., Skowron, A., Zhong, N. (eds.) RSCTC 2002. LNCS (LNAI), vol. 2475, pp. 144–155. Springer, Heidelberg (2002)
Milstead, J.L.: Standards for relationships between subject indexing terms. In: Bean, C.A., Green, R. (eds.) Relationships in the organization of knowledge, pp. 53–66. Kluwer Academic Publishers, Dordrecht (2001)
Neches, R., Fikes, R., Finin, T., Gruber, T., Patil, R., Senator, T., Swartout, W.: Enabling technology for knowledge sharing. AI Mag. 12(3), 36–56 (1991)
Pancerz, K.: Dominance-based rough set approach for decision systems over ontological graphs. In: Ganzha, M., Maciaszek, L., Paprzycki, M. (eds.) Proceedings of the FedCSIS 2012, pp. 323–330. Wroclaw, Poland (2012)
Pancerz, K.: Toward information systems over ontological graphs. In: Yao, J.T., Yang, Y., Słowiński, R., Greco, S., Li, H., Mitra, S., Polkowski, L. (eds.) RSCTC 2012. LNCS, vol. 7413, pp. 243–248. Springer, Heidelberg (2012)
Pancerz, K.: Semantic relationships and approximations of sets: an ontological graph based approach. In: Proceedings of the HSI 2013, pp. 62–69. Sopot, Poland (2013)
Pawlak, Z.: Rough Sets: Theoretical Aspects of Reasoning about Data. Kluwer Academic Publishers, Dordrecht (1991)
Pawlak, Z., Skowron, A.: Rudiments of rough sets. Inf. Sci. 177, 3–27 (2007)
Storey, V.C.: Understanding semantic relationships. VLDB J. 2, 455–488 (1993)
Winston, M.E., Chaffin, R., Herrmann, D.: A taxonomy of part-whole relations. Cogn. Sci. 11(4), 417–444 (1987)
Zadeh, L.: The concept of a linguistic variable and its application to approximate reasoning - I. Inf. Sci. 8(3), 199–249 (1975)
Zadeh, L.: Fuzzy logic = computing with words. IEEE Trans. Fuzzy Syst. 4(2), 103–111 (1996)
Zadeh, L.: A new direction in AI: toward a computational theory of perceptions. AI Mag. 22(1), 73–84 (2001)
Zadeh, L.A.: Outline of a new approach to the analysis of complex systems and decision processes. IEEE Trans. Syst. Man Cybern. SMC 3(1), 28–44 (1973)
Acknowledgments
The author would like to thank the anonymous reviewers for their critical remarks and useful suggestions that greatly contributed to improving the final version of the paper.
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2015 Springer-Verlag Berlin Heidelberg
About this chapter
Cite this chapter
Pancerz, K. (2015). Toward Qualitative Assessment of Rough Sets in Terms of Decision Attribute Values in Simple Decision Systems over Ontological Graphs. In: Peters, J., Skowron, A., Ślȩzak, D., Nguyen, H., Bazan, J. (eds) Transactions on Rough Sets XIX. Lecture Notes in Computer Science(), vol 8988. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-47815-8_6
Download citation
DOI: https://doi.org/10.1007/978-3-662-47815-8_6
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-662-47814-1
Online ISBN: 978-3-662-47815-8
eBook Packages: Computer ScienceComputer Science (R0)