Advertisement

Soft Computing

, 14:339 | Cite as

Anteriority index for managing fuzzy dates in archæological GIS

  • Cyril de RunzEmail author
  • E. Desjardin
  • F. Piantoni
  • M. Herbin
Original Paper

Abstract

During the exploitation of an archæological geographical information system, experts need to evaluate the anteriority in pairs of dates which are uncertain and inaccurate, and consequently represented by fuzzy numbers. To build their hypotheses, they need to have an assessment, taking value in [0, 1], of the relation “lower than” between two FNs. We answer the experts’ need of evaluation by constructing an anteriority index based on the Kerre index. Two applications, which constitute a step in the evaluation of the evolution of Reims during the domination of the Roman Empire, illustrate the use of the anteriority index.

Keywords

Fuzzy numbers Fuzzy comparison GIS Archæology 

Notes

Acknowledgments

The authors would like to thank the Champagne-Ardenne Regional Service in Archæology and the National Institute of Research in Preventive Archæology in Reims for their data as well as expert knowledge, and Dominique Pargny (GEGENA laboratory at the University of Reims Champagne Ardenne) for his contribution to the SIGRem project.

References

  1. Adamo JM (1985) Fuzzy decision trees. Fuzzy Sets Syst 4:207–219CrossRefMathSciNetGoogle Scholar
  2. Altman D (1994) Fuzzy set theoretic approaches for handling imprecision in spatial analysis. Int J Geogr Inf Syst 8 3:271–290CrossRefGoogle Scholar
  3. Bortolan G, Degani R (1985) A review of some methods for ranking fuzzy subsets. Fuzzy Sets Syst 15:1–19zbMATHCrossRefMathSciNetGoogle Scholar
  4. Burrough PA, McDonnell RA (1998) Principle of geographical information systems. Oxford University Press, New YorkGoogle Scholar
  5. Chang W (1981) Ranking of fuzzy utilities with triangular membership functions. In: Proceedings of international conference in policy analysis and system, pp 263–272Google Scholar
  6. Chen S (1985) Ranking fuzzy numbers with maximizing set and minimizing set. Fuzzy Sets Syst 17:113–129zbMATHCrossRefGoogle Scholar
  7. Conolly J, Lake M (2006) Geographic information system in archaeology. Cambridge University Press, LondonGoogle Scholar
  8. de Runz C, Desjardin E, Piantoni F, Herbin M (2007a) Management of multi-modal data using the fuzzy hough transform: application to archaeological simulation. In: Ouarzazate M, Rolland C, Pastor O, Cavarero J-L (eds) First international conference on research challenges in information science, pp 351–356Google Scholar
  9. de Runz C, Desjardin E, Piantoni F, Herbin M (2007b) Using fuzzy logic to manage uncertain multi-modal data in an archaeological gis. In: Proceedings of the international symposium on spatial data quality, Pays-Bas, EnschedeGoogle Scholar
  10. Delgado M, Verdegay JL, Villa MA (1988) A procedure for ranking fuzzy numbers. Fuzzy Sets Syst 26:49–62zbMATHCrossRefGoogle Scholar
  11. Detyniecki M, Yager RR (2001) Ranking fuzzy numbers using α-weighted valuations. Int J Uncertain Fuzziness Knowl Based Syst 8(5):563–593MathSciNetGoogle Scholar
  12. Dixon B (2005) Groundwater vulnerability mapping: a gis and fuzzy rule based integrated tool. Appl Geogr 20:1–21Google Scholar
  13. Dubois D, Prade H (1983) Ranking fuzzy numbers in the setting of possibility theory. Inf Sci 30:183–224zbMATHCrossRefMathSciNetGoogle Scholar
  14. Facchinetti G, Pacchiarotti N (2005) Evaluations of fuzzy quantities. Fuzzy Sets Syst 157:892–903CrossRefMathSciNetGoogle Scholar
  15. Fortemps P, Roubens M (1996) Ranking fuzzy sets: a decision theoretic approach. Fuzzy Sets Syst 82:319–330zbMATHCrossRefMathSciNetGoogle Scholar
  16. Jain R (1977) A procedure for multiple-aspect decision making using fuzzy set. Int J Syst Sci 8:1–7zbMATHCrossRefGoogle Scholar
  17. Kerre E (1982) The use of fuzzy set theory in electrocardiological diagnostics. In: Gupta M, Sanchez E (eds) Approximate reasoning in decision-analysis, pp 277–282Google Scholar
  18. Kim K, Park KS (1990) Ranking fuzzy numbers with index of optimism. Fuzzy Sets Syst 35:143–150CrossRefGoogle Scholar
  19. Mitra B, Scott HD, McKimmey JM (1998) Application of fuzzy logic to the prediction of soil erosion in a large watersheld. Geoderma 86:183–209CrossRefGoogle Scholar
  20. Ramik J, Rimanek J (1985) Inequality relation between fuzzy numbers and its use in fuzzy optimization. Fuzzy Sets Syst 16:123–138zbMATHCrossRefMathSciNetGoogle Scholar
  21. Saade JJ, Schwarzlander H (1992) Ordering fuzzy sets over real line: an approach based on decision making under uncertainty. Fuzzy Sets Syst 50:237–246CrossRefMathSciNetGoogle Scholar
  22. Wang X, Kerre E (2001a) Reasonable properties for the ordering fuzzy quantities (i). Fuzzy Sets Syst 118:375–385zbMATHCrossRefMathSciNetGoogle Scholar
  23. Wang X, Kerre E (2001b) Reasonable properties for the ordering fuzzy quantities (ii). Fuzzy Sets Syst 118:387–405zbMATHCrossRefMathSciNetGoogle Scholar
  24. Yager RR, Detyniecki M, Bouchon-Meunier B (2001) A context-dependent method for ordering fuzzy numbers using probabilities. Inf Sci 138:237–255zbMATHCrossRefMathSciNetGoogle Scholar
  25. Zadeh LA (1965) Fuzzy sets. Inf Control 8:338–353zbMATHCrossRefMathSciNetGoogle Scholar

Copyright information

© Springer-Verlag 2009

Authors and Affiliations

  • Cyril de Runz
    • 1
    • 2
    Email author
  • E. Desjardin
    • 1
  • F. Piantoni
    • 2
  • M. Herbin
    • 1
  1. 1.CReSTIC EA-3804, IUT Reims Chalons CharlevilleReims Cedex 2France
  2. 2.HABITER EA-2076, URCAReims CedexFrance

Personalised recommendations