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Non-additive Measures by Interval Probability Functions

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New Frontiers in Artificial Intelligence (JSAI 2001)

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 2253))

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Abstract

Probability measures are well-defined ones that satisfy additivity. However, it is slightly tight because of its condition of additivity. Fuzzy measures that do not satisfy additivity have been proposed as the substitute measures. The only belief function involves a density function among them. In this paper, we propose two density functions by extending values of probability functions to interval values, which do not satisfy additivity. According to the definition of interval probability functions, lower and upper probabilities are defined, respectively. A combination rule and a conditional probability can be defined well. The properties of the proposed measure are clarified.

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References

  1. K.T. Atanassov (1986): Intuitionistic fuzzy sets, Int. J. of Fuzzy Sets and Systems, 20, 87–96.

    Article  MATH  MathSciNet  Google Scholar 

  2. L.M. De Campos, M.T. Lamata and S. Moral (1990): The concept of conditional fuzzy measure, Int. J. of Intelligent Systems, 5, 58–67.

    Google Scholar 

  3. L.M. De Campos, J.F. Huets and S. Moral (1994): Probability interval; A tool for uncertain reasoning, Int. J. of Uncertainty, Fuzziness and Knowledge-Based Systems, 2, 167–196.

    Article  Google Scholar 

  4. C. Choquet (1953): Theory of capacities, Ann. Inst. Fourier, 5, 131–295.

    MathSciNet  Google Scholar 

  5. D. Coker (1998): Fuzzy rough sets are intuitionistic L-fuzzy sets, Int. J. of Fuzzy Sets and Systems, 96, 381–383.

    Article  MATH  MathSciNet  Google Scholar 

  6. A.P. Dempster (1967): Upper and lower probabilities induced by a multivalued mapping, Ann. Math. Stat., 38, 325–339.

    Article  MathSciNet  MATH  Google Scholar 

  7. D. Dubois and H. Prade (1986): A set-theoritic view of belief functions, Int. J. of General Systems, 12, 193–226.

    Article  MathSciNet  Google Scholar 

  8. J.F. Lemmer and H.E. Kyburg (1991): Conditions for the existence of belief functions corresponding to intervals of belief, Proc. 9th. National Conference on AI, 488–493.

    Google Scholar 

  9. Y. Pan and G.J. Klir (1997): Baysian inference based on interval valued prior distributions and likelihood, J. of Intelligent and Fuzzy Systems, 5, 193–203.

    Google Scholar 

  10. G. Shafer (1976): The Mathematical Theory of Evidence, Princeton Univ. Press.

    Google Scholar 

  11. M. Sugeno (1977): Fuzzy measures and fuzzy integrals; A survey, In M.M. Gupta, G.N. Saridis and B.R. Gaines(eds.), Fuzzy Automata and Decision Processes, 89–102.

    Google Scholar 

  12. K. Sugihara and H. Tanaka: Interval Evaluation in the Analytic Hierarchy Process by Possibility Analysis, J. of Computational Intelligence (to appear).

    Google Scholar 

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Author information

Authors and Affiliations

  1. Graduate School of Management and Information Science, Toyohashi Sozo College, 20-1 Matsushita, 440-8511, Ushikawacho, Toyohashi, Japan

    Hideo Tanaka

  2. Course of Applied Physics, Graduate School of Engineering Osaka University, Yamadaoka 2-1, 565-0871, Suita, Osaka, Japan

    Kazutomi Sugihara

  3. Department of Industrial Engineering, College of Engineering Osaka Prefecture University, Gakuencho 1-1, 590-8531, Sakai, Osaka, Japan

    Yutaka Maeda

Authors
  1. Hideo Tanaka
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  2. Kazutomi Sugihara
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  3. Yutaka Maeda
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Editor information

Editors and Affiliations

  1. Graduate School of Business Science, The University of Tsukuba, Tokyo

    Takao Terano  & Yukio Ohsawa  & 

  2. School of Engineering, The University of Tokyo, Tokyo

    Toyoaki Nishida

  3. Dept.of Computer Science, National Defense Academy, Japan

    Akira Namatame

  4. School of Medicines, Shimane Medical University, Japan

    Syusaku Tsumoto

  5. The Institute of Scientific and Industrial Research, Osaka University, Osaka

    Takashi Washio

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© 2001 Springer-Verlag Berlin Heidelberg

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Tanaka, H., Sugihara, K., Maeda, Y. (2001). Non-additive Measures by Interval Probability Functions. In: Terano, T., Ohsawa, Y., Nishida, T., Namatame, A., Tsumoto, S., Washio, T. (eds) New Frontiers in Artificial Intelligence. JSAI 2001. Lecture Notes in Computer Science(), vol 2253. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-45548-5_39

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  • DOI: https://doi.org/10.1007/3-540-45548-5_39

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-43070-4

  • Online ISBN: 978-3-540-45548-6

  • eBook Packages: Springer Book Archive

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