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Journal of Environmental Accounting and Management
António Mendes Lopes (editor), Jiazhong Zhang(editor)
António Mendes Lopes (editor)

University of Porto, Portugal

Email: aml@fe.up.pt

Jiazhong Zhang (editor)

School of Energy and Power Engineering, Xi'an Jiaotong University, Xi'an, Shaanxi Province 710049, China

Fax: +86 29 82668723 Email: jzzhang@mail.xjtu.edu.cn


Combination of Imperfect Data in Fuzzy and Probabilistic Extension Classes

Journal of Environmental Accounting and Management 3(2) (2015) 123--150 | DOI:10.5890/JEAM.2015.06.004

Jérôme Dantan$^{1}$,$^{2}$; Yann Pollet$^{2}$; Salima Taibi$^{1}$

$^{1}$ Esitpa, Agri’terr, Mont-Saint-Aignan, France

$^{2}$ CNAM, CEDRIC, Paris, France

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Abstract

In this article, we propose a uniform formal model able to handle uncertain data. The approach presented provides a formalism for both representing and manipulating rigorously quantities which may have a finite number of possible or probable values with their interdependencies. Then, we define an algebraic structure to operate chained computations on such quantities with properties similar to 兟 . Next, we provide a particular interpretation for mixing such quantities through the Dempster- Shafer theory. Finally, we provide an implementation of this approach into object oriented programming.

References

  1. [1]  Coupland, S. and John, R. (2008), New geometric inference techniques for type-2 fuzzy sets, International Journal of Approximate Reasoning 1(49): 198-211.
  2. [2]  Dantan, J., Pollet, Y. and Taibi, S. (2014), Taking account of uncertain, imprecise and incomplete data in sustainability assessments in agriculture. In proceedings of Computational Science and Its Applications - ICCSA 2014 - 14th International Conference - Workshop CLASS 2014 - Computational algorithms for Sustainability Assessment - Part III, Lecture Notes in Computer Science LNCS 8581, ISBN 978-3-319-09149-5, pp. 625–639. Springer International Publishing Switzerland. Guimar?es, Portugal, June 30 - July 3, 2014.
  3. [3]  Dempster, A. (1967), Upper and lower probabilities induced by multivalued mapping, Annals of Mathematical Statistics AMS-38: 325-339.
  4. [4]  Destercke S., Dubois D. and Chojnacki E. (2007), On the relationships between random sets, possibility distributions, p-boxes and clouds. 28th Linz Seminar on fuzzy set theory, 2007, Linz, Austria.
  5. [5]  Destercke, S., Dubois, D. and Chojnacki, E. (2008), Unifying practical uncertainty representations – I: Generalized p-boxes, International Journal of Approximate Reasoning 3(49): 649-663.
  6. [6]  Destercke, S. and Dubois, D. (2009), The role of generalised p-boxes in imprecise probability models. In proceedings of 6. International Symposium on Imprecise Probability (p. 179-188). Presented at ISIPTA '09, Durham, GBR (2009-07-14 - 2009-07-18).
  7. [7]  Dubois, D., Foulloy, L., Mauris, G. and Prade, H. (2004), Probability-Possibility Transformations, Triangular Fuzzy Sets, and Probabilistic Inequalities, Reliable Computing 4(10): 273-297.
  8. [8]  Dubois, D. and Prade, H. (1988), Théorie des possibilités, Application à la représentation des connaissances en informatique. Masson 1988. (In French)
  9. [9]  Ferson, S., Kreinovich, V., Ginzburg, L., Myers, D.S. and Sentz, K. (2003), Constructing probability boxes and Dempster–Shafer structures, Sandia National Laboratories, Albuquerque, NM, SAND2002-4015, 2003. Available from http://www.sandia.gov/epistemic/Reports/SAND2002-4015.pdf.
  10. [10]  Gacôgne, L. (1997), Eléments de logique floue. CNAM, Institut d’informatique d’Entreprise, p. 47, may 1997. (In French)
  11. [11]  Gong, Y., Hu, N., Zhang, J., Liu, G. and Deng, J. (2015), Multi-attribute group decision making method based on geometric Bonferroni mean operator of trapezoidal interval type-2 fuzzy numbers, Computers & Industrial Engineering 81: 167-176.
  12. [12]  Gonzalez, C., Goncalves, M. and Tineo, L. (2009), A New Upgrade to SQLf: Towards a Standard in Fuzzy Databases. Database and Expert Systems Application. DEXA '09. 20th International Workshop on , vol., no., pp.442,446, Aug. 31 2009-Sept. 4 2009 doi: 10.1109/DEXA.2009.35.
  13. [13]  Klement, E.P., Puri, M.L. and Ralescu, D.A. (1986), Limit theorems for fuzzy random variables, Proceedings of The Royal Society of London 407: 171-182.
  14. [14]  Kruse, R. and Meyer, K.D. (1987), Statistics with Vague Data. D. Reidel Publishing Company, Dortrecht - Boston - Lancaster - Tokyo 1987.
  15. [15]  Kwakernaak, H. (1978), Fuzzy Random Variables—I. Definitions and Theorems, Information Sciences 15(1): 1-29.
  16. [16]  Kwakernaak, H. (1979), Fuzzy Random Variables—II. Algorithms and Examples for the Discrete Case, Information Sciences 17(3): 253-278.
  17. [17]  Liu, Y.K. and Liu, B. (2003), Fuzzy Random Variables: A Scalar Expected Value Operator, Fuzzy Optimization and Decision Making 2(2): 143-160.
  18. [18]  Mendel, J.M. and John, R.I. (2002), Type-2 Fuzzy Sets Made Simple, IEEE Trans. on Fuzzy Systems 10: 117-127.
  19. [19]  Liang, Q. and Mendel, J.M. (2000), Interval type-2 fuzzy logic systems: Theory and design, IEEE Trans. Fuzzy Syst. 5(8): 535-550.
  20. [20]  Pivert, O. and Prade, H. (2014), Skyline queries in an uncertain database model based on possibilistic certainty. 8th International Conference on Scalable Uncertainty Management (SUM'14), Sept 2014, Oxford, United Kingdom. Springer, 8720, pp.280-285, LNAI.
  21. [21]  Pollet, Y., Bregeault, L. and Bridon, Ph. (1993), Bases de Données pour les systèmes de fusion de données. Troisièmes journées nationales "Applications des Ensembles Flous", Nîmes, France. (In French)
  22. [22]  Pollet, Y. and Robidou, S. (1995), An approach for the Management of Multivalued Attributes in Fuzzy Databases, In proceedings of the FUZZ-IEEE/IFES’95 Workshop on Fuzzy Database Systems and Information Retrieval, Yokohama.
  23. [23]  Pollet, Y. and Robidou, S. (1997), SAGESSE: un modèle de représentation de données pour la Fusion de Données Symboliques. Workshop on dynamic scene recognition from sensor data. ONERA/CERT, Toulouse, France, June 1997. (In French).
  24. [24]  Puri, M.L. and Ralescu, D.A. (1986), Fuzzy random variables, Journal of Mathematical Analysis and Applications 114: 409-422.
  25. [25]  Sadri, F. (1994), Modeling Uncertainty in Object-Oriented Databases, In proceedings of Workshop Incompleteness and Uncertainty in Information Systems, Springer-Verlag.
  26. [26]  Shafer, G. (1976), A mathematical theory of evidence. Princeton University Press.
  27. [27]  Shapiro, A.F. (2012), Implementing Fuzzy Random Variables. In proceedings of ARCH 2013.1. Society of Actuaries. University of Manitoba, Winnipeg, MB, Canada, August 1-4, 2012.
  28. [28]  Smets, Ph. and Kennes, R. (1994), The transferable belief model, Artificial Intelligence 66: 191-234.
  29. [29]  Troffaes, M. and Destercke, S. (2011), Probability boxes on totally preordered spaces for multivariate modelling, International Journal of Approximate Reasoning 6(52): 767-791.
  30. [30]  Troffaes, M., Miranda, E. and Destercke, S. (2013), On the connection between probability boxes and possibility measures, Information Sciences 224: 88-108.
  31. [31]  Van-Gyseghem, N., De Caluwe, R. and Vandenberghe, R. (1993), UFO Uncertainty and Fuzziness in an Object-oriented Model, In proceedings of 2nd IEEE Int Conf on Fuzzy Systems.
  32. [32]  Zadeh, L.A. (1965), Fuzzy Sets, Information and Control 8: Academic Press.
  33. [33]  Zadeh, L.A. (1975), The Concept of a Linguistic Variable and Its Application to Approximate Reasoning–1, Information Sciences 8: 199-249.
  34. [34]  Zadeh, L.A. (1978), Fuzzy Sets as a basis for a Theory of Possibility, Fuzzy Sets and Systems, 1.
  35. [35]  Zicari, R. (1990), Incomplete Information in Object-Oriented Databases, SIGMOD RECORD 19.