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The Membership of a Fuzzy Set as Coherent Conditional Probability

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On Fuzziness

Part of the book series: Studies in Fuzziness and Soft Computing ((STUDFUZZ,volume 299))

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Abstract

A well–known view supported by Zadeh concerns the inadequateness of probability to capture what is usually treated by fuzzy theory. In particular, in his 2002’s paper [15] he refers to PT – standard Probability Theory – as not being fit to offer solutions for many simple problems in which a key role is played by (what he calls) a “perception–based information”. I agree with Zadeh’s position, inasmuch he specifies that by PT he means “standard probability theory of the kind found in textbooks and taught in courses”.

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References

  1. Coletti, G., Scozzafava, R.: Conditional Subjective Probability and Fuzzy Theory. In: Proceedings of 18th NAFIPS International Conference, pp. 77–80. IEEE, New York (1999)

    Google Scholar 

  2. Coletti, G., Scozzafava, R.: Fuzzy Sets as Conditional Probabilities: Which Meaningful Operations can be Defined? In: Proceedings of 20th NAFIPS International Conference, pp. 1892–1895. IEEE, Vancouver (2001)

    Google Scholar 

  3. Coletti, G., Scozzafava, R.: Conditional Probability, Fuzzy Sets, and Possibility: A Unifying View. Fuzzy Sets and Systems 144, 227–249 (2004)

    Article  MathSciNet  MATH  Google Scholar 

  4. Coletti, G., Scozzafava, R.: Conditioning in a Coherent Setting: Theory and Applications. Fuzzy Sets and Systems 155, 26–49 (2005)

    Article  MathSciNet  MATH  Google Scholar 

  5. Coletti, G., Scozzafava, R.: Conditional Probability and Fuzzy Information. Computational Statistics & Data Analysis 51, 115–132 (2006)

    Article  MathSciNet  MATH  Google Scholar 

  6. Coletti, G., Scozzafava, R.: Probabilistic Logic in a Coherent Setting (Trends in logic nr. 15). Kluwer, Dordrecht (2002)

    Book  Google Scholar 

  7. Coletti, G., Scozzafava, R.: From Conditional Events to Conditional Measures: A New Axiomatic Approach. Annals of Mathematics and Artificial Intelligence 32, 373–392 (2001)

    Article  MathSciNet  Google Scholar 

  8. Coletti, G., Vantaggi, B.: Inference With Probabilistic and Fuzzy Information (in this issue)

    Google Scholar 

  9. de Finetti, B.: Sull’impostazione assiomatica del calcolo delle probabilità. Annali Triestini 19, 3–55 (1949); Engl. transl. In: Probability, Induction, Statistics, ch. 5. Wiley, London (1972)

    Google Scholar 

  10. de Finetti, B.: Teoria della probabilità, Einaudi, Torino (1970); Engl. transl.: Theory of Probability, vol. 1, 2. Wiley, Chichester (1974)

    Google Scholar 

  11. Dubins, L.E.: Finitely Additive Conditional Probabilities, Conglomerability and Disintegration. The Annals of Probability 3, 89–99 (1975)

    Article  MathSciNet  MATH  Google Scholar 

  12. Koopman, B.O.: The Axioms and Algebra of Intuitive Probability. Annals of Mathematics 41, 269–292 (1940)

    Article  MathSciNet  Google Scholar 

  13. Krauss, P.H.: Representation of Conditional Probability Measures on Boolean Algebras. Acta Mathematica Academiae Scientiarum Hungaricae 19, 229–241 (1968)

    Article  MathSciNet  MATH  Google Scholar 

  14. Zadeh, L.A.: Probability Measures of Fuzzy Events. Journal of Mathematical Analysis and Applications 23, 421–427 (1968)

    Article  MathSciNet  MATH  Google Scholar 

  15. Zadeh, L.A.: Toward a Perception-based Theory of Probabilistic Reasoning With Imprecise Probabilities. Journal of Statistical Planning and Inference 105, 233–264 (2002)

    Article  MathSciNet  MATH  Google Scholar 

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Scozzafava, R. (2013). The Membership of a Fuzzy Set as Coherent Conditional Probability. In: Seising, R., Trillas, E., Moraga, C., Termini, S. (eds) On Fuzziness. Studies in Fuzziness and Soft Computing, vol 299. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-35644-5_29

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  • DOI: https://doi.org/10.1007/978-3-642-35644-5_29

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