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Type-2 Fuzzy Sets and Conceptual Spaces

Chapter
Part of the Studies in Fuzziness and Soft Computing book series (STUDFUZZ, volume 301)

Abstract

Conceptual spaces provide a rich interpretation for computing with words, offering additional structure to that provided by fuzzy set models alone. In fuzzy conceptual spaces, properties are type-2 fuzzy sets on domains, concepts are type-2 fuzzy sets on pairs of properties and an observation is a family of fuzzy sets on domains relevant to a context. These type-2 fuzzy set structures are derived and manipulated using subsethood. This chapter relates such a theory of conceptual spaces to conventional multivariate classification and computing with words (CWW), and illustrates its application to land use assessment tasks.

Keywords

Type-2 fuzzy sets Subsethood Context Concept Domains Applications Conceptual spaces Classification Land use Properties Linguistic variables Computing with words (CWW) Multivariate analysis Change assessment Observations Imprecision 

References

  1. 1.
    Gärdenfors, P.: Conceptual Spaces: the Geometry of Thought. MIT Press, Cambridge (2000)Google Scholar
  2. 2.
    Freund, M.: On the notion of concept. Art. Int. 172(4–5), 570–590 (2008)MathSciNetMATHCrossRefGoogle Scholar
  3. 3.
    Zadeh, L.A.: Fuzzy logic = computing with words. IEEE Trans. Fuzzy Syst. 4(2), 103–111 (1996)Google Scholar
  4. 4.
    Zadeh, L.A.: Is there a need for fuzzy logic? Inf. Sci. 178, 2751–2779 (2008)MathSciNetMATHCrossRefGoogle Scholar
  5. 5.
    Rickard, J.: A concept geometry for conceptual spaces. J. Fuzzy Optim. Decis. Mak. 5, 311–329 (2006)Google Scholar
  6. 6.
    Rickard, J., Aisbett, J., Gibbon, G.: Reformulation of the theory of conceptual spaces. Inf. Sci. 177, 4539–4565 (2007)MathSciNetMATHCrossRefGoogle Scholar
  7. 7.
    Ahlqvist, O.: A parameterized representation of uncertain conceptual spaces. Trans. GIS 8(4), 493–514 (2004)CrossRefGoogle Scholar
  8. 8.
    Ahlqvist, O.: Extending post classification change detection using semantic similarity metrics to overcome class heterogeneity: a study of 1992 and 2001 national land cover database changes. Remote Sens. Environ. 112(3), 1226–1241 (2008)CrossRefGoogle Scholar
  9. 9.
    Fisher, P., Cheng, T., Wood, J.: Higher order vagueness in geographical information. Geoinformatica 11, 311–330 (2007)CrossRefGoogle Scholar
  10. 10.
    Malczewski, J.: GIS-based land-use suitability analysis: a critical overview. Progress Plan. 62, 3–65 (2004)CrossRefGoogle Scholar
  11. 11.
    FAO: land use classification for agri-environmental statistics/indicators. Working paper No.13, Joint ECE/Eurostat work session on methodological issues of environment statistics, Statistics Division FAO (1999)Google Scholar
  12. 12.
    Triantafilis, J., Ward, W.T., Mcbratney, A.B.: Land suitability assessment in the lower Namoi valley of Australia. Aust. J. Soil Res. 39, 273–290 (2001)Google Scholar
  13. 13.
    Rickard, J., Aisbett, J., Gibbon G.: Type-2 fuzzy conceptual spaces. In: IEEE International Conference on Fuzzy Systems, 1–8 (2010)Google Scholar
  14. 14.
    Aisbett, J., Rickard, J.T., Morgenthaler, D.: Multivariate modeling and type-2 fuzzy sets. Fuzzy Sets Syst. 163, 78–95 (2011)MathSciNetMATHCrossRefGoogle Scholar
  15. 15.
    Halmos, P.: Measure Theory. Springer, New York (1974)Google Scholar
  16. 16.
    Wu, D., Mendel, J.M.: Efficient algorithms for computing a class of subsethood and similarity measures for interval type-2 fuzzy sets. In: IEEE International Conference on Fuzzy Systems, 1–7 (2010)Google Scholar
  17. 17.
    Schyns, P.G., Goldstone, R. L. Thibaut, J-P.: The development of features in object concepts. Behav. Brain Sci. 21, 1–54 (1998)Google Scholar
  18. 18.
    FAO: agro-ecological land resources assessment for agricultural development planning—a case study of Kenya. Technical report. Natural Resources Management and Environment Department, FAO (1991)Google Scholar
  19. 19.
    Soil Survey Staff NRCS: Natural Resources Conservation Service, United States Department of Agriculture. Web Soil Survey. http://websoilsurvey.nrcs.usda.gov/ (2008). Accessed 20 Jan 2008
  20. 20.
    Ochola, W.O., Kerkides, P.: An integrated indicator-based spatial decision support system for land quality assessment in Kenya. Comput. Electron. Ag 45, 3–26 (2004)CrossRefGoogle Scholar
  21. 21.
    Mendel, J.M.: Computing with words and its relationships with fuzzistics. Inf. Sci. 177, 985–1006 (2007)Google Scholar
  22. 22.
    Aisbett, J., Rickard, J.T., Morgenthaler, D.: Intersection and union of type-n fuzzy sets. IEEE International Conference on Fuzzy Systems, 1–8 (2010)Google Scholar
  23. 23.
    Finch, P.D.: Characteristics of interest and fuzzy subsets. Inf. Sci. 24, 121–134 (1981)Google Scholar
  24. 24.
    Lee, J.W.T.: Ordinal decomposability and fuzzy connectives. Fuzzy Sets Syst. 136, 237–249 (2003)Google Scholar
  25. 25.
    Nosofsky, R.: Attention, similarity and the identification-categorization relationship. J. Exp. Psych. Gen. 115(1), 39–57 (1986)CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media New York 2013

Authors and Affiliations

  1. 1.Faculty of Science and ITThe University of NewcastleNewcastleAustralia
  2. 2.Distributed Infinity, Inc.LarkspurUSA

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