Modeling Uncertainty in Ontologies using Rough Set

Full Text (PDF, 563KB), PP.49-59

Views: 0 Downloads: 0


Armand F. Donfack Kana 1,* Babatunde O. Akinkunmi 2

1. Ahmadu Bello University/ Department of Mathematics, Zaria, Nigeria

2. University of Ibadan/ Department of Computer Science, Ibadan, Nigeria

* Corresponding author.


Received: 24 Aug. 2015 / Revised: 10 Nov. 2015 / Accepted: 12 Jan. 2016 / Published: 8 Apr. 2016

Index Terms

Ontologies, Uncertainty, Rough set, Approximation


Modeling the uncertain aspect of the world in ontologies is attracting a lot of interests to ontologies builders especially in the World Wide Web community. This paper defines a way of handling uncertainty in description logic ontologies without remodeling existing ontologies or altering the syntax of existing ontologies modeling languages. We show that the source of vagueness in an ontology is from vague attributes and vague roles. Therefore, to have a clear separation between crisp concepts and vague concepts, the set of roles R is split into two distinct sets〖 R〗_c and R_v representing the set of crisp roles and the set of vague roles respectively. Similarly, the set of attributes A was split into two distinct sets A_c and A_v representing the set of crisp attributes and the set of vague attributes respectively. Concepts are therefore clearly classified as crisp concepts or vague concepts depending on whether vague attributes or vague roles are used in its conceptualization or not. The concept of rough set introduced by Pawlak is used to measure the degree of satisfiability of vague concepts as well as vague roles. In this approach, the cost of reengineering existing ontologies in order to cope with reasoning over the uncertain aspects of the world is minimal.

Cite This Paper

Armand F. Donfack Kana, Babatunde O. Akinkunmi, "Modeling Uncertainty in Ontologies using Rough Set", International Journal of Intelligent Systems and Applications(IJISA), Vol.8, No.4, pp.49-59, 2016. DOI:10.5815/ijisa.2016.04.06


[1]A. Bellenger and S. Gatepaille, "Uncertainty in Ontologies: Dempster-Shafer Theory for Data Fusion Applications," workshop on the Theory of Belief Functions, Brest, France CoRR abs/1106.3876, 2011.
[2]P. Maji, R. Bismas and A. R. Roy, "Soft set theory," Computers & Mathematics with Applications vol.45, pp. 555-562., 2010.
[3]J. Zhao, "Uncertainty and Rule Extensions to Description Logics and Semantic Web Ontologies," Advances in semantic computing. Vol.2, pp. 1-22, 2010.
[4]K. J. Laskey, K. B. Laskey, P. C. G. Costa, M. M. Kokar, T. Martin and T. Lukasiewicz, "Uncertainty Reasoning for the World Wide Web," W3c incubator group report., 2008.
[5]Z. Pawlak, "Rough sets," International Journal of Information and Computer Sciences 11, pp. 341-356, 1982.
[6]W. Xu, X. Zhang, Q. Wang and S. Sun, "On General Binary Relation Based Rough Set," Journal of Information and Computing Science 7(1), pp. 054-066, 2012.
[7]I. Masahiro and T. Tetsuzo, "Generalized rough sets and rule extraction.," in Rough Sets and Current Trends in Computing. Berlin: Springer Berlin/Heidelberg., pp. 105-112, 2002.
[8]Z. Pawlak and A. Skowron., " Rough sets: Some Extensions.," Information Sciences. 177(1), pp. 28-40, 2007.
[9]Z. Pawlak and A. Skowron., "Rough sets and Boolean Reasoning," Information Sciences. 177(1), pp. 41-73, 2007.
[10]Z. Pawlak and A. Skowron., "Rudiments of rough sets," Information Sciences. 177(1), pp. 3-27, 2007.
[11]R. Silvia and L.-T. Germano, "Rough Set Theory – Fundamental Concepts, Principals, Data Extraction, and Applications," in Julio Ponce and Adem Data Mining and Knowledge Discovery in Real Life Applications, Julio Ponce and Adem Karahoca (Ed.), ISBN: 978-3-902613-53-0, InTech, 2009.
[12]S. Thabet, "Application of Rough Set Theory in Data Mining," International journal of Computer Science & Network Solutions, 1(3), pp. 1-10, 2013.
[13]I. Horrocks, " Reasoning with expressive description logics: Theory and practice," Proceeding of the 19th International Conference on Automated Deduction (CADE 2002), number 2392 in Lecture Notes in Artificial Intelligence, pp. 1-15, 2002.
[14]M. Krötzsch, F. Simančík and I. Horrocks, "A Description Logic Primer," CoRR, abs/1201.4089, 2012.
[15]F. Baader and N. Werner, "Basic Description Logics.," in The Description Logics Handbook., Cambridge, Cambridge University Press,2003., 2003, pp. 43-95.
[16]S. Rudolph, "Foundations of description logics," In Axel Polleres, Claudia d’Amato, Marcelo Arenas, Siegfried Handschuh, Paula Kroner, Sascha Ossowski, and Peter F. PatelSchneider, editors, Reasoning Web. Semantic Technologies for the Web, 2011.
[17]Z. Pawlak, "Some Issues on Rough Sets," in Transactions on Rough Sets. James F. et all Eds. Volume 3100 of Lecture Notes in Computer Science, Springer, 2004.
[18]A. Donfack- Kana and B. Akinkunmi, "An Algebra of Ontologies Approximation under Uncertainty," International Journal of Intelligence Science, 4,, pp. 54-64, 2014.
[19]Z. Pawlak, "Rough Sets, Rough Relations and Rough Functions." Fundamenta Informaticae 27(2/3), pp. 103-108, 1996.
[20]Z. William, "Relationship between generalized rough sets based on binary relation and covering," Information Sciences. 179, pp. 210-225., 2009.
[21]Z. William and F. Wang, "Binary Relation Based Rough Sets." FSKD, LNAI. 4223, pp. 276-285, 2006.
[22]C. M. Keet, "On the feasibility of Description Logic knowledge bases," in Proc. 23rd Int. Workshop on Description Logics (DL2010), CEUR-WS 573, Waterloo, Canada, 2010.
[23]C.M. Keet, "Ontology engineering with rough concepts and instances.," in 17th International Conference on Knowledge Engineering and Knowledge Management (EKAW'10), P. Cimiano and H.S. Pinto (Eds.). 11-15 October 2010, Lisbon, Portugal. Springer LNAI 6317, 50.
[24]O. Udrea, V. Subrahmanian and Z. Majkic, " Probabilistic rdf.," in Proceedings IRI-2006, IEEE Systems, Man, and Cybernetics Society, 2006.
[25]P. C. G. Costa and K. B. Laskey, " PR-OWL: a framework for probabilistic ontologies.," Frontiers in Artificial Intelligence and Applications vol.150, pp. 237-249., 2006.
[26]Z. Ding, Y. Peng and R. Pan, "BayesOWL: Uncertainty Modelling in Semantic Web," Ontologies, Soft Computing in Ontologies and Semantic Web. volume 204 of Studies in Fuzziness and Soft Computing, 2005.
[27]Y. Yang and J. Calmet, " Ontobayes: An ontology-driven uncertainty model.," Computational Intelligence for Modelling, Control and Automation., pp. 457-463, 2005.
[28]P. Klinov, "Pronto: a Non-Monotonic Proba-bilistic Description Logic Reasoner," in European Semantic Web Conference, 2008.
[29]P. Klinov and P. Bijan, " Pronto: A Practical Probabilistic Description Logic Reasoner," Uncertainty Reasoning For The Semantic Web II. Lecture Notes in Computer Science vol.7123, pp. 59-79, 2013.
[30]G. Stoilos, G. Stamou, P. J. Z., V. Tzouvaras and I. Horrocks, " Reasoning with Very Expressive Fuzzy Description Logics," Journal of Artificial Intelligence Research, 30(8), pp. 273-320, 2007.
[31]F. Bobillo and U. Straccia, " fuzzyDL: An Expressive Fuzzy Description Logic Reasoner, Fuzzy Systems," in 17th IEEE International Conference on Fuzzy Systems, 2008.
[32]B. Liu, J. Li and Y. Zhao, "A Query-specific Reasoning Method for Inconsistent and Uncertain Ontology," in International Multi-Conference of Engineers and Computer scientists , Hong Kong, 2011.
[33]G. Qi, Q. Ji, J. Pan and J. Du, "Extending descrip-tion logics with uncertainty reasoning in possibilistic logic," International Journal of Intelligent Systems 26(4), p. 353–381, 2011.
[34]J. Zhu, G. Qi and B. Suntisrivaraporn, "Tableaux Algorithms for Expressive Possibilistic Description Logics," in IEEE/WIC/ACM International Joint Conferences on Web Intelligence (WI) and Intelligent Agent Technologies, 2013.