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.
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References
Adamo JM (1985) Fuzzy decision trees. Fuzzy Sets Syst 4:207–219
Altman D (1994) Fuzzy set theoretic approaches for handling imprecision in spatial analysis. Int J Geogr Inf Syst 8 3:271–290
Bortolan G, Degani R (1985) A review of some methods for ranking fuzzy subsets. Fuzzy Sets Syst 15:1–19
Burrough PA, McDonnell RA (1998) Principle of geographical information systems. Oxford University Press, New York
Chang W (1981) Ranking of fuzzy utilities with triangular membership functions. In: Proceedings of international conference in policy analysis and system, pp 263–272
Chen S (1985) Ranking fuzzy numbers with maximizing set and minimizing set. Fuzzy Sets Syst 17:113–129
Conolly J, Lake M (2006) Geographic information system in archaeology. Cambridge University Press, London
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 351–356
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, Enschede
Delgado M, Verdegay JL, Villa MA (1988) A procedure for ranking fuzzy numbers. Fuzzy Sets Syst 26:49–62
Detyniecki M, Yager RR (2001) Ranking fuzzy numbers using α-weighted valuations. Int J Uncertain Fuzziness Knowl Based Syst 8(5):563–593
Dixon B (2005) Groundwater vulnerability mapping: a gis and fuzzy rule based integrated tool. Appl Geogr 20:1–21
Dubois D, Prade H (1983) Ranking fuzzy numbers in the setting of possibility theory. Inf Sci 30:183–224
Facchinetti G, Pacchiarotti N (2005) Evaluations of fuzzy quantities. Fuzzy Sets Syst 157:892–903
Fortemps P, Roubens M (1996) Ranking fuzzy sets: a decision theoretic approach. Fuzzy Sets Syst 82:319–330
Jain R (1977) A procedure for multiple-aspect decision making using fuzzy set. Int J Syst Sci 8:1–7
Kerre E (1982) The use of fuzzy set theory in electrocardiological diagnostics. In: Gupta M, Sanchez E (eds) Approximate reasoning in decision-analysis, pp 277–282
Kim K, Park KS (1990) Ranking fuzzy numbers with index of optimism. Fuzzy Sets Syst 35:143–150
Mitra B, Scott HD, McKimmey JM (1998) Application of fuzzy logic to the prediction of soil erosion in a large watersheld. Geoderma 86:183–209
Ramik J, Rimanek J (1985) Inequality relation between fuzzy numbers and its use in fuzzy optimization. Fuzzy Sets Syst 16:123–138
Saade JJ, Schwarzlander H (1992) Ordering fuzzy sets over real line: an approach based on decision making under uncertainty. Fuzzy Sets Syst 50:237–246
Wang X, Kerre E (2001a) Reasonable properties for the ordering fuzzy quantities (i). Fuzzy Sets Syst 118:375–385
Wang X, Kerre E (2001b) Reasonable properties for the ordering fuzzy quantities (ii). Fuzzy Sets Syst 118:387–405
Yager RR, Detyniecki M, Bouchon-Meunier B (2001) A context-dependent method for ordering fuzzy numbers using probabilities. Inf Sci 138:237–255
Zadeh LA (1965) Fuzzy sets. Inf Control 8:338–353
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.
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de Runz, C., Desjardin, E., Piantoni, F. et al. Anteriority index for managing fuzzy dates in archæological GIS. Soft Comput 14, 339–344 (2010). https://doi.org/10.1007/s00500-009-0408-2
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DOI: https://doi.org/10.1007/s00500-009-0408-2