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Abstract

A personal account of the emergence and development of generalized information theory (GIT) in the context of data-driven (inductive) systems modeling. In GIT, information is defined in terms of relevant uncertainty reduction. Main results regarding measures of uncertainty and uncertainty-based information in Dempster-Shafer theory of evidence and in generalized possibility theory are overviewed, and their role in three basic uncertainty principles is discussed: the principles of maximum uncertainty, minimum uncertainty, and uncertainty invariance. Finally, some open problems and undeveloped areas in GIT are examined.

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References

  1. Ashby, W. R. [1972] , “Systems and their informational measures.” In: Klir, G. J., ed., Trends in General Systems Theory. Wiley-Interscience, New York, pp. pp. 78–97.

    Google Scholar 

  2. Choquet, G. [1953–54] , “Theory of capacities.” Annales de L’Institut Fourier, 5, pp. 131–295.

    Article  MathSciNet  Google Scholar 

  3. Christensen, R. [1985] , “Entropy minimax multivariate statistical modeling — I: Theory.” Intern. J. of General Systems, 11(3), pp. 231–277.

    Article  Google Scholar 

  4. Christensen, R. [1986] , “Entropy minimax multivariate statistical modeling — II: Applications.” Intern. J. of General Systems, 12(3), pp. 227–305.

    Article  Google Scholar 

  5. Conant, R. [1976] , “Laws of information which govern systems.” IEEE Trans, on Systems, Man, and Cybernetics, SMC-6(4), pp. 240–255.

    MathSciNet  Google Scholar 

  6. De Cooman, G. [1997] , “Possibility theory.” Intern. J. of General Systems, 25(4), pp. 291–371.

    Article  MATH  Google Scholar 

  7. Dubois, D. and Prade, H. [1985] , “A note on measures of specificity for fuzzy sets.” Int. J. of General Systems, 10(4), pp. 279–283.

    Article  MathSciNet  MATH  Google Scholar 

  8. Dubois, D. and Prade, H. [1988] , Possibility Theory. Plenum Press, New York.

    Book  MATH  Google Scholar 

  9. Harmanec, D. and Klir G.J. [1997] , “On information-preserving transformations.” Intern. J. of General Systems, 26(3), pp. 265–290.

    Article  MathSciNet  MATH  Google Scholar 

  10. Hartley, R. V. L. [1928] , “Transmission of information.” The Bell System Technical., 7(3), pp. 535–563.

    Google Scholar 

  11. Higashi, M. and Klir, G. J. [1983] , “Measures of uncertainty and information based on possibility distributions.” Intern. J. of General Systems, 9(1), pp. 43–58.

    Article  MathSciNet  Google Scholar 

  12. Jaynes, E. T. [1979] , “Where do we stand on maximum entropy?” In: R.L.Levine and M.Tribus, (eds.), The Maximum Entropy Formalism. MIT Press, Cambridge, Mass., pp. 15–118.

    Google Scholar 

  13. Kapur, J. N. [1989] , Maximum Entropy Models in Science and Engineering. John Wiley, New York.

    MATH  Google Scholar 

  14. Klir, G. J. [1969] , An Approach to General Systems Theory. Van Nostrand Reinhold, New York.

    Google Scholar 

  15. Klir, G. J. [1975] , “On the representation of activity arrays.” Intern. J. of General Systems, 2(3), pp. 149–168.

    Article  Google Scholar 

  16. Klir, G. J. [1976] , “Identification of generative structures in empirical data.” Intern. J. of General Systems , 3(2), pp. 89–104.

    Article  Google Scholar 

  17. Klir, G. J. [1983] , “General systems framework for inductive modelling.” In: Oren, T. et al., eds., Simulation and Model-based Methodologies. Springer- Verlag, New York, pp. 69–90.

    Google Scholar 

  18. Klir G. J. [1985] , Architecture of Systems Problem Solving. Plenum Press, New York.

    Book  MATH  Google Scholar 

  19. Klir, G. J. [1989] , “Inductive systems modelling: An overview.” In: Zeigler, B. P. et al., eds., Modelling and Simulation Methodology. North-Holland, New York, pp. 55–75.

    Google Scholar 

  20. Klir, G. J. [1990] , “A principle of uncertainty and information invariance.” Intern. J. of General Systems, 17(2–3), pp. 249–275.

    Article  MATH  Google Scholar 

  21. Klir, G. J. [1991] , “Aspects of uncertainty in qualitative systems modeling.” In: P.A. Fishwick and P.A. Luker, (eds.), Qualitative Simulation Modeling and Analysis. Springer-Verlag, New York, pp. 24–50.

    Chapter  Google Scholar 

  22. Klir, G. J. [1991] , “Generalized information theory.” Fuzzy Sets and Systems, 40(1), pp. 127–142.

    Article  MathSciNet  MATH  Google Scholar 

  23. Klir, G. J. [1998] , “On fuzzy-set interpretation of possibility theory.” Fuzzy Sets and Systems, 108(3)

    Google Scholar 

  24. Klir, G. J. and Mariano, M. [1987] , “On the uniqueness of possibilistic measure of uncertainty and information.” Fuzzy Sets and Systems, 24(2), pp. 197–219.

    Article  MathSciNet  MATH  Google Scholar 

  25. Klir, G. J. and Wierman M.J. [1998] , Uncertainty-Based Information: Elements of Generalized Information Theory. Physica-Verlag/Springer-Verlag, Heidelberg and New York.

    MATH  Google Scholar 

  26. Klir, G. J. and Yuan, B. [1995] , Fuzzy Sets and Fuzzy Logic: Theory and Applications. Prentice Hall, PTR, Upper Saddle River, NJ.

    Google Scholar 

  27. Klir, G. J. and Yuan, B. [1995] , “On nonspecificity of fuzzy sets with continuous membership functions.” Proc. 1995 Intern. Conf. on Systems, Man, and Cybernetics, Vancouver.

    Google Scholar 

  28. Kyburg, H. E. [1987] , “Bayesian and non-Bayesian evidential updating.” Artifical Intelligence, 31, pp. pp.271–293.

    Article  MathSciNet  MATH  Google Scholar 

  29. Pan, Y. and Klir, G.J. [1997] , “Bayesian inference based on interval probabilities.” J. of Intelligent and Fuzzy Systems, 5(3), pp. 193–203.

    Google Scholar 

  30. Pan, Y. and B. Yuan [1997] , “Bayesian inference of fuzzy probabilites.” Intern.l J. of General Systems, 26(1–2), pp. 73–90.

    Article  MathSciNet  MATH  Google Scholar 

  31. Ramer, A. [1987] , “Uniqueness of information measure in the theory of evidence.” Fuzzy Sets and Systems, 24(2), pp. 183–196.

    Article  MathSciNet  MATH  Google Scholar 

  32. Shafer G. [1976] , A Mathematical Theory of Evidence. Princeton Univ. Press, Princeton, NJ.

    Google Scholar 

  33. Shannon, C. E. [1948] , “The mathematical theory of communication.” The Bell System Technical J., 27(3&4), pp. 379–423, 623–656.

    MathSciNet  MATH  Google Scholar 

  34. Walley, P. [1991] , Statistical Reasoning With Imprecise Probabilities. Chapman and Hall, London.

    MATH  Google Scholar 

  35. Wang, Z. and Klir, G. J. [1992] , Fuzzy Measure Theory. Plenum Press, New York.

    Book  MATH  Google Scholar 

  36. Zadeh, L. A. [1975] , “The concept of a linguistic variable and its application to approximate reasoning.” Information Sciences, 8&9, pp. 8, pp. 199–249, 301–357, 9, pp.43–80.

    Article  MathSciNet  MATH  Google Scholar 

  37. Zeigler, B. P. [1974] , “A conceptual basis for modelling and simulation.” Intern. J. of General Systems, 1(4), pp. 213–228.

    Article  MATH  Google Scholar 

  38. Zeigler, B. P. [1976] , Theory of Modelling and Simulation. John Wiley, New York.

    MATH  Google Scholar 

  39. Zeigler, B. P. [1984] , Multifaceted Modelling and Discrete Event Simulation. Academic Press, New York.

    Google Scholar 

  40. Zeigler, B. P. [1990] , Object-Oriented Simulation with Hierarchical Models. Academic Press, San Diego.

    MATH  Google Scholar 

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Klir, G.J. (2001). The Role of Uncertainty in Systems Modeling. In: Sarjoughian, H.S., Cellier, F.E. (eds) Discrete Event Modeling and Simulation Technologies. Springer, New York, NY. https://doi.org/10.1007/978-1-4757-3554-3_4

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  • DOI: https://doi.org/10.1007/978-1-4757-3554-3_4

  • Publisher Name: Springer, New York, NY

  • Print ISBN: 978-1-4419-2868-9

  • Online ISBN: 978-1-4757-3554-3

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