Modeling Uncertainty in Knowledge Representation

  • Yi Cai
  • Ching-man Au Yeung
  • Ho-fung Leung


The classical view in cognitive psychology holds that an object is either an instance of a concept or it is not. In terms of mathematics, every concept is a crisp set. However, as we have discussed above, many concepts do not have clear boundaries or definitions. Different objects have different degrees of membership or typicality with respect to a certain concept. In this section, we give a review of studies that investigate how graded membership, vagueness and uncertainty are modeled. Several extensions to existing ontology models or description logics involves fuzzy sets, therefore we will start by briefly reviewing the basic notions of fuzzy set theory.


Membership Function Knowledge Representation Semantic Similarity Resource Description Framework Description Logic 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. [1]
    Zadeh L (1965) Fuzzy Sets. Inform Control, 8: 338–353.MathSciNetzbMATHCrossRefGoogle Scholar
  2. [2]
    Klir J, Yuan B (1995) Fuzzy Sets and Fuzzy Logic: Theory and Applications.,Prentice Hall, Upper Saddle River.zbMATHGoogle Scholar
  3. [3]
    Yamakawa T (1988) High-speed Fuzzy Controller Hardware System. Inform Sciences 45(2): 113–128.MathSciNetCrossRefGoogle Scholar
  4. [4]
    Yamakawa T (1989) Stabilization of an Inverted Pendulum by a High-speed Logic Controller Hardware System. Fuzzy Sets Syst, 326(2): 161–180.CrossRefGoogle Scholar
  5. [5]
    Bordogna G, Pasi G (2001) Modeling Vagueness in Information Retrieval. In: Agosti M, Crestani F, Pasi G (eds) Lectures on Information Retrieval, Lecture Notes in Computer Science, vol 1980. Springer, New York, pp 207–241.CrossRefGoogle Scholar
  6. [6]
    Bosc P, Pivert O (1994) Fuzzy Queries and Relational Databases. In: Proceedings of the 1994 ACM Symposium on Applied Computing, pp 170–174.Google Scholar
  7. [7]
    Chianese A, Picariello A, Sansone L et al (2004) Managing Uncertainties in Image Databases: A Fuzzy Approach. Multimedia Tools Appl 23(3): 237–252.CrossRefGoogle Scholar
  8. [8]
    Leung KS, Lam W (1988) Fuzzy Concepts in Expert Systems. Computer 21(9): 43–56.CrossRefGoogle Scholar
  9. [9]
    Sedbrook TA (1998) A Collaborative Fuzzy Expert System for the Web. SIGMIS Database 29(3): 19–30.CrossRefGoogle Scholar
  10. [10]
    Parry D (2004) A Fuzzy Ontology for Medical Document Retrieval. In: Hogan J, Montague P, Purvis M et al (eds) Proceedings of the Second Workshop on Australasian Information Security, Data Mining and Web Intelligence, and Software Internationalisation (ACSW Frontiers’ 04), vol 32. Australian Computer Society, Inc, Darlinghurst, Australia, pp 121–126.Google Scholar
  11. [11]
    Ding Z, Peng Y (2004) A Probabilistic Extension to Ontology Language OWL. In: Proceedings of the 37th Hawaii Int Conf on Sys Sci, p 10.Google Scholar
  12. [12]
    Stoilos G, Stamou G, Tzouvaras V et al (2005) Fuzzy Owl: Uncertainty and the Semantic Web. In: Proceedings of International Workshop of OWL: Experiences and Directions.Google Scholar
  13. [13]
    Dubois D, Prade H, Rossazza J (1991) Vagueness, Typicality, and Uncertainty in Class Hierarchies. Int J Intell Syst 6: 167–183.CrossRefGoogle Scholar
  14. [14]
    Tamma V, Bench-Capon T (2002) An Ontology Model to Facilitate Knowledge Sharing in Multi-agent Systems. Knowl Eng Rev 17(1): 41–60.CrossRefGoogle Scholar
  15. [15]
    Koller D, Levy A, Pfeffer A (1997) P-classic: A Tractable Probabilistic Description Logic. In: Proceedings of the Fourteenth National Conference on AI, pp 390–397.Google Scholar
  16. [16]
    Straccia U (1998) A Fuzzy Description Logic. In: Proceedings of the Fifteenth National Conference on Artificial Intelligence and the Tenth Annual Conference on Innovative Applications of Artificial Intelligence, pp 594–599.Google Scholar
  17. [17]
    Stoilos G, Stamou G, Tzouvaras V et al (2005) The Fuzzy Description Logic f-SHIN. In: Proceedings of the International Workshop on Uncertainty Reasoning for the Semantic Web.Google Scholar
  18. [18]
    Holldobler S, Khang TD, Storr HP (2004) A Fuzzy Description Logic With Hedges as Concept Modifiers. In: Proceedings of InTechVJFuzzy2002, pp 25–34.Google Scholar
  19. [19]
    Straccia U (2005) Towards a Fuzzy Description Logic for the Semantic Web. In: Proceedings of the Second European Semantic Web Conference, pp 167–181.Google Scholar
  20. [20]
    Zadeh LA (1988) Fuzzy Logic. Computer 21(4): 83–93.CrossRefGoogle Scholar
  21. [21]
    Klir GJ, Yuan B (1995) Fuzzy Sets and Fuzzy Logic: Theory and Applications. Prentice Hall, Upper Saddle River.zbMATHGoogle Scholar
  22. [22]
    Cross V, Voss CR (1999) Fuzzy Ontologies for Multilingual Document Exploitation. In: Proceedings of the 1999 Conference of NAFIPS, pp 392–397.Google Scholar
  23. [23]
    Parry D (2004) A Fuzzy Ontology for Medical Document Retrieval. In: The Australasian Workshop on DataMining and Web Intelligence, pp 121–126.Google Scholar
  24. [24]
    Giordano L, Gliozzi V, Olivetti N et al (2008) Alc+t: Reasoning About Typicality in Description Logics. In: Proceedings of 23rd Convegno Italiano di Logica Computazionale.Google Scholar
  25. [25]
    Giordano L, Gliozzi V, Olivetti N et al (2010) Preferential vs Rational Description Logics: Which One for Reasoning About Typicality? In: 19th European Conference on Artificial Intelligence, Lisbon, Portugal, 16–20 August 2010. IOS Press, Amsterdam, pp 1069–1070.Google Scholar
  26. [26]
    Cai Y, Leung HF (2010) A Fuzzy Description Logic with Automatic Object Membership Measurement. In: KSEM, pp 76–87.Google Scholar
  27. [27]
    Cross V (2004) Fuzzy Semantic Distance Measures Between Ontological Concepts. In: Proceedings of the 2004 Conference of North American Fuzzy Information Processing Society (NAFIPS), pp 392–397.Google Scholar
  28. [28]
    Doan A, Madhavan J, Dhamankar R et al (2003) Learning to Match Ontologies on the Semantic Web. The VLDB Journal 12(4): 303–319.CrossRefGoogle Scholar
  29. [29]
    Kalfoglou Y, Schorlemmer M (2003) Ontology Mapping: The State of the Art. Knowl Eng Rev 18(1): 1–31.CrossRefGoogle Scholar
  30. [30]
    Rodriguez MA, Egenhofer MJ (2003) Determining Semantic Similarity Among Entity Classes From Different Ontologies. IEEE Trans on Knowl and Data Eng 15(2): 442–456.CrossRefGoogle Scholar
  31. [31]
    Varelas G, Voutsakis E, Raftopoulou P et al (2005) Semantic Similarity Methods in Wordnet and Their Application to Information Retrieval on the Web. In: WIDM’ 05: Proceedings of the 7th Annual ACM International Workshop on Web Information and Data Management, ACM Press, New York, pp 10–16.CrossRefGoogle Scholar
  32. [32]
    Kong CY, Wang CL, Lau FCM (2004) Ontology Mapping in Pervasive Computing Environment. In: EUC, pp 1014–1023.Google Scholar
  33. [33]
    Lesot MJ (2005) Similarity, Typicality and Fuzzy Prototypes for Numerical Data. In: 6th European Congress on Systems Science, Workshop “Similarity and resemblance”.Google Scholar
  34. [34]
    Van Rijsbergen (1979) Information Retrieval. Butterworths, London.Google Scholar
  35. [35]
    Rada, Roy, Mili H, Bicknell E et al (1989) Development and Application of a Metric on Semantic Nets. IEEE T Sys Man Cyb 19: 17–30.CrossRefGoogle Scholar
  36. [36]
    Kim Y, Kim J (1990) A Model of Knowledge-based Information Retrieval With Hierarchical Concept Graph. J Doc 46: 113–116.CrossRefGoogle Scholar
  37. [37]
    Lee J, Kim M (1993) Information Retrieval Based on Conceptual Distance in a Is-a Hierarchy. J Doc 49: 188–207.CrossRefGoogle Scholar
  38. [38]
    Resnik P (1995) Using Information Content to Evaluate Semantic Similarity in a Taxonomy. In: Proceedings of the International Joint Conference on Artificial Intelligence, pp 448–453.Google Scholar
  39. [39]
    Tversky A (1977) Features of Similarity. Psychological Review 84(4): 327–352.CrossRefGoogle Scholar
  40. [40]
    McCarthy J (1986) Notes on Formalizing Contexts. In: Proceedings of the Fifth National Conference on Artificial Intelligence, pp 555–560.Google Scholar
  41. [41]
    Giunchiglia F (1993) Contextual Reasoning. In: Proceedings of the IJCAI’93 Workshop on Using Knowledge in Its Context, Chambert, France.Google Scholar
  42. [42]
    Akman V, Surav M (1996) Steps Toward Formalizing Context. AI Mag 17(3): 55–72.Google Scholar
  43. [43]
    Buvac S, Mason IA (1993) Propositional Logic of Context. In: Proceedings of the Eleventh National Conference on Artificial Intelligence, Washington DC, pp 412–419.Google Scholar
  44. [44]
    Obrst L, Nichols D (2005) Context and Ontologies: Contextual Indexing of Ontological Expressions. In: AAAI 2005 Workshop on Context and Ontologies.Google Scholar
  45. [45]
    Grossi D, Dignum F, Meyer JJC (2004) Contextual Taxonomies. In: Proceedings of Fifth InternationanalWorkshop on Computational Logic in Multi-Agent Systems.Google Scholar
  46. [46]
    Grossi D, Dignum F, Meyer JJC (2005) Context in Categorization. In: Workshop on Context Representation and Reasoning.Google Scholar
  47. [47]
    Khriyenko O, Terziyan V (2005) Context Description Framework for the Semantic Web. In: Proceedings of CRR-05.Google Scholar

Copyright information

© Higher Education Press, Beijing and Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  • Yi Cai
    • 1
  • Ching-man Au Yeung
    • 2
  • Ho-fung Leung
    • 3
  1. 1.School of Software EngineeringSouth China University of TechnologyGuangzhouChina
  2. 2.Hong Kong Applied Science and Technology Research InstituteHong KongChina
  3. 3.Department of Computer Science and EngineeringThe Chinese University of Hong KongHong KongChina

Personalised recommendations