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On Fuzziness pp 455–458Cite as

On Fuzziness in Mathematics

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

Abstract

I received my Ph. D. in mathematics from Iowa State University in 1963. My specialty was in abstract algebra. That same year I obtained a position in the Mathematics Department at Creighton University. For the first 20 years or so, I carried out a research program in traditional mathematics. In an attempt to reach out to other disciplines, I began collaborating with members of the Health Sciences at Creighton. It was then that I began to feel that some form of mathematics (not probability) dealing with imprecision would be useful in the health sciences. I found a book on fuzzy logic in the library. It seemed to me that this was exactly what I was looking for. However, I did not pursue the matter further at this time. It was later that I more fully appreciated the importance of the ideas of Lotfi Zadeh regarding uncertainty [1].

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References

  1. Zadeh, L.A.: Fuzzy Sets. Information and Control 8, 338–353 (1965)

    Article  MathSciNet  MATH  Google Scholar 

  2. Sugeno, M.: Theory of Fuzzy Integrals and Its Applications. PhD dissertation, Tokyo Institute of Technology (1974)

    Google Scholar 

  3. Sugeno, M.: Fuzzy Measures and Fuzzy Integrals – A Survey. In: Gupta, M.M., Saridis, G.N., Gaines, B.R. (eds.) Fuzzy Automata and Decision Processes, pp. 89–102. North-Holland, New York (1977)

    Google Scholar 

  4. Choquet, G.: Theory of Capacities. Annales de l’Institut Fourier 5, 131–295 (1954)

    Article  MathSciNet  Google Scholar 

  5. Dempster, A.P.: Upper and lower Probabilities induced by Multi-valued Mappings. Annals of Mathematical Statistics 38, 325–329 (1967)

    Article  MathSciNet  MATH  Google Scholar 

  6. Shafer, G.: A Mathematical Theory of Evidence. Princeton University Press, Princeton (1976)

    MATH  Google Scholar 

  7. Zadeh, L.A.: Fuzzy Sets as a Basis for a Theory of Possibility. Fuzzy Sets and Systems 1, 3–28 (1978)

    Article  MathSciNet  MATH  Google Scholar 

  8. Kerre, E.E., Mordeson, J.N.: Historical Overview of Fuzzy Mathematics. New Mathematics and Natural Computation 1, 1–26 (2005)

    Article  MathSciNet  MATH  Google Scholar 

  9. Pawlak, Z.: Rough Sets. International Journal of Computer and Information Sciences 11, 341–356 (1982)

    Article  MathSciNet  MATH  Google Scholar 

  10. Atanassov, K.T.: Intuitionistic Fuzzy Sets. STUDFUZZ, vol. 35. Physica-Verlag, Heidelberg (1999)

    Google Scholar 

  11. Chang, C.L.: Fuzzy Topological Spaces. Journal of Mathematical Analysis and Applications 24, 182–190 (1980)

    Article  Google Scholar 

  12. Liu, Y.-M., Luo, M.-K.: Fuzzy Topology, Advances in Fuzzy Systems – Applications and Theory, vol. 9. World Scientific, Singapore (1997)

    Google Scholar 

  13. Rosenfeld, A.: Fuzzy Groups. Journal of Mathematical Analysis and Applications 35, 512–517 (1971)

    Article  MathSciNet  MATH  Google Scholar 

  14. Pearl, J.: Causality: Models, Reasoning, and Inference. Cambridge University Press, Cambridge (2000)

    MATH  Google Scholar 

  15. Kerre, E.E.: On the Evolution of the Mathematics of Fuzziness. In: Ruan, D. (ed.) Fuzzy Set Theory and Advanced Mathematical Applications, pp. 1–34. Kluwer Academic Publishers, Boston (1995)

    Google Scholar 

  16. Mordeson, J.N.: Zadeh’s Influence on Mathematics. Scientia Iranica, Transactions: Electrical and Computer Engineering (2011)

    Google Scholar 

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Mordeson, J.N. (2013). On Fuzziness in Mathematics. 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_4

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