When Granules Are not Enough in a Theory of Granularities

  • Ricardo Almeida Silva
  • João Moura Pires
  • Maribel Yasmina Santos
Conference paper
Part of the Lecture Notes in Geoinformation and Cartography book series (LNGC)


Several approaches have been proposed to model spatiotemporal phenomena at multiple LoDs, in particularly, under the granular computing research area, where a granularities-based model was proposed. Such model stands out from the related literature, but has two major limitations. On one hand, it has difficulties for describing regions, intervals of time, among others complex descriptions, and on the other hand, the generalization process is the same whether it is generalizing spatial, temporal or other features of a phenomenon. These problems reduce its applicability. To overcome such limitations, this paper extends the granularities-based model by introducing the granular term concept. We apply this concept to represent time instants and intervals as well as cells and raster regions. For each granular term, generalization rules are defined so that a phenomenon can be expressed from one LoD to a coarser one in an automatic way. Changing a phenomenon’s LoD can simplify granular terms, transforming for instance a time interval into a time instant or a raster region into a cell. Our contributions are shown based on a real dataset about tornadoes in the USA. The results obtained show an enhancement of application scenarios from the extended granularities-based model to its ability of providing different phenomenon’s representations in each LoD, while keeping its original strengths.


Granule Granularity Granular computing 



This work has been supported by FCT—Fundação para a Ciência e Tecnologia MCTES, UID/CEC/04516/2013 (NOVA LINCS) and UID/CEC/00319/2013 (ALGORITMI), and COMPETE: POCI-01-0145-FEDER-007043 (ALGORITMI).


  1. Allen JF (1983) Maintaining knowledge about temporal intervals. Commun ACM 26(11):832–843CrossRefGoogle Scholar
  2. Andrienko G et al (2010) Space, time and visual analytics. Int J Geogr Inf Sci 24(10):1577–1600CrossRefGoogle Scholar
  3. Bettini C, Jajodia S, Wang S (2000) Time granularities in databases, data mining, and temporal reasoning. SpringerGoogle Scholar
  4. Brahim L, Okba K, Robert L (2015) Mathematical framework for topological relationships between ribbons and regions. J Vis Lang Comput 26:66–81CrossRefGoogle Scholar
  5. Bravo L, Rodríguez MA (2014) A multi-granular database model. In Foundations of information and knowledge systems. Springer, pp 344–360Google Scholar
  6. Camossi E, Bertolotto M, Bertino E (2006) A multigranular object-oriented framework supporting spatio-temporal granularity conversions. Int J Geogr Inf Sci 20(5):511–534CrossRefGoogle Scholar
  7. Egenhofer MJ, Sharma J, (1993) Topological relations between regions in ρ2 and ℤ2. In: Advances in spatial databases, pp 316–336Google Scholar
  8. Goodwin S et al (2016) Visualizing multiple variables across scale and geography. IEEE Trans Vis Comput Graph 22(1):599–608CrossRefGoogle Scholar
  9. Keet CM (2008) A formal theory of granularity. Free University of Bozen-BolzanoGoogle Scholar
  10. Keim D et al (2008) Visual analytics: definition, process, and challenges. In Kerren A et al (ed) Information visualization. Lecture notes in computer science. Springer, Berlin, pp 154–175Google Scholar
  11. Kong TY, Rosenfeld A (1989) Digital topology: introduction and survey. Comput Vis Graph Image Process 48(3):357–393CrossRefGoogle Scholar
  12. Laurini R (2014) A conceptual framework for geographic knowledge engineering. J Vis Lang Comput 25(1):2–19CrossRefGoogle Scholar
  13. Parent C et al (2009) Multiple representation modeling. In: Liu L, Özsu MT (eds) Encyclopedia of database systems. Springer, US, pp 1844–1849Google Scholar
  14. Pires JM, Silva RA, Santos MY (2014) Reasoning about space and time: moving towards a theory of granularities. In: Computational science and its applications–ICCSA 2014. Springer, pp 328–343Google Scholar
  15. Silva RA, Pires JM, Santos MY (2015a) A granularity theory for modelling spatio-temporal phenomena at multiple levels of detail. Int J Bus Intell Data Min 10(1):33CrossRefGoogle Scholar
  16. Silva RA, Pires JM, Santos MY (2015b) Aggregating spatio-temporal phenomena at multiple levels of detail. In: AGILE 2015. Springer Science Business Media, pp 291–308Google Scholar
  17. Silva RA et al (2016) Enhancing exploratory analysis by summarizing spatiotemporal events across multiple levels of detail. In: AGILE 2016Google Scholar
  18. Sips M et al (2012) A visual analytics approach to multiscale exploration of environmental time series. IEEE Trans Vis Comput Graph 18(12):2899–2907CrossRefGoogle Scholar
  19. Stell J, Worboys M (1998) Stratified map spaces: a formal basis for multi-resolution spatial databases. In: Proceedings 8th international symposium on spatial data handling. Department of Computer Science, Keele University, Staffordshire, UK ST5 5BG, pp. 180–189Google Scholar
  20. Vilain MB (1982) A system for reasoning about time. In: AAAI, pp 197–201Google Scholar
  21. Weibel R, Dutton G (1999) Generalising spatial data and dealing with multiple representations. Geogr Inf Syst 1:125–155Google Scholar
  22. Yao JT, Vasilakos AV, Pedrycz W (2013) Granular computing: perspectives and challenges. IEEE Trans Cybern 43(6):1977–1989CrossRefGoogle Scholar
  23. Zhou X et al (2004) Multiresolution spatial databases: making web-based spatial applications faster. In: Yu J et al (ed) Advanced web technologies and applications SE—5. Lecture notes in computer science. Springer, Berlin, pp 36–47Google Scholar

Copyright information

© Springer International Publishing AG 2017

Authors and Affiliations

  • Ricardo Almeida Silva
    • 1
  • João Moura Pires
    • 1
  • Maribel Yasmina Santos
    • 2
  1. 1.NOVA LINCS, DI, FCTUniversidade NOVA de LisboaLisbonPortugal
  2. 2.ALGORITMI Research CentreUniversity of MinhoBragaPortugal

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