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Part of the book series: Studies in Fuzziness and Soft Computing ((STUDFUZZ,volume 33))

Abstract

In order to be able to carry out the agenda of computing with words we need a formal knowledge representation and manipulation systems, approximate reasoning provides such a tool. In this work we introduce the basic ideas of approximate reasoning. We show the generality of this framework by indicating how some classical reasoning systems, such as binary propositional logic can be formulated within this framework

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References

  1. Zadeh, L. A., “Fuzzy logic = computing with words,” IEEE Transactions on Fuzzy Systems 4, 103–111, 1996.

    Article  Google Scholar 

  2. Yager, R. R., Ovchinnikov, S., Tong, R. and Nguyen, H., Fuzzy Sets and Applications: Selected Papers by L. A. Zadeh, John Wiley & Sons: New York, 1987.

    Google Scholar 

  3. Zadeh, L. A., “A theory of approximate reasoning,” in Machine Intelligence, Vol. 9, edited by Hayes, J., Michie, D. and Mikulich, L. I., Halstead Press: New York, 149–194, 1979.

    Google Scholar 

  4. Yager, R. R., “Deductive approximate reasoning systems,” IEEE Transactions on Knowledge and Data Engineering 3, 399–414, 1991.

    Article  MathSciNet  Google Scholar 

  5. Dubois, D. and Prade, H., “Fuzzy sets in approximate reasoning Part I: Inference with possibility distributions,” Fuzzy Sets and Systems 40,’143–202, 1991.

    Google Scholar 

  6. Dubois, D. and Prade, H., “Fuzzy sets in approximate reasoning Part 2: logical approaches,” Fuzzy Sets 40, 203–244, 1991.

    Article  MathSciNet  MATH  Google Scholar 

  7. Zadeh, L. A., “Toward a theory of fuzzy information granulation and its centrality in human reasoning and fuzzy logic,” Fuzzy Sets and Systems 90, 111–127, 1997.

    Article  MathSciNet  MATH  Google Scholar 

  8. Yager, R. R. and Filev, D. P., Essentials of Fuzzy Modeling and Control, John Wiley: New York, 1994.

    Google Scholar 

  9. Dubois, D. and Prade, H., “Necessity measures and the resolution principle,” IEEE Trnasactions on Systems, Man and Cybernetics 17, 474–478, 1987. [10].Dubois, D., Lang, J. and Prade, H., “Automated reasoning using possibilistic logic: semantics, belief revision and variable certainty weights,” IEEE Transactions on Knowledge and Data Engineering 6, 65–70, 1994.

    Google Scholar 

  10. ].Dubois, D., Lang, J. and Prade, H., “Possibilistic Logic,” in Handbook of Logic in Artificial Intelligence and Logic Programmling: Volume 3, edited by Gabbay, D. M., Hogger, C. J. and Robinson, J. A., Clarendon Press: Oxford, 439–513, 1994. [12].Benferhat, S., Dubois, D. and Prade, H., “Nonmonotonic reasoning, conditional objects and possibility theory,” Artificial Intelligence 92, 259–276, 1997.

    Google Scholar 

  11. Goguen, J. A., “L-fuzzy sets,” J. of Math. Analysis & Applications 18, 145174, 1967.

    Google Scholar 

  12. 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 

  13. Date, C. J., An Introduction to Database Systems, Addison Wesley: Reading, MA, 1986.

    Google Scholar 

  14. Hohle, U., “Probabilistic uniformization of fuzzy topologies,” Fuzzy Sets and Systems 1, 1978, 1978.

    Article  MathSciNet  Google Scholar 

  15. Zadeh, L. A., “Fuzzy sets,” Information and Control 8, 338–353, 1965.

    Article  MathSciNet  MATH  Google Scholar 

  16. Alsina, C., Trillas, E. and Valverde, L., “On some logical connectives for fuzzy set theory,” J. Math Anal. & Appl. 93, 15–26, 1983.

    Article  MathSciNet  MATH  Google Scholar 

  17. Klir, G. J. and Yuan, B., Fuzzy Sets, Fuzzy Logic and Fuzzy Systems: Selected Papers by Lotfi A. Zadeh, World Scientific: Singapore, 1996.

    Google Scholar 

  18. Kosko, B., Fuzzy Engineering, Prentice Hall: Upper Saddle River, NJ, 1997.

    MATH  Google Scholar 

  19. Yager, R. R., “Measuring tranquility and anxiety in decision making: An application of fuzzy sets,” Int. J. of General Systems 8, 139–146, 1982.

    Article  MathSciNet  MATH  Google Scholar 

  20. Yager, R. R., “On the specificity of a possibility distribution,” Fuzzy Sets and Systems 50, 279–292, 1992.

    Article  MathSciNet  MATH  Google Scholar 

  21. Yager, R. R., “On measures of specificity,” in Computational Intelligence: Soft Computing and Fuzzy-Neuro Integration with Applications, edited by Kaynak, O., Zadeh, L. A., Turksen, B. and Rudas, I. J., Springer-Verlag: Berlin, 94–113, 1998.

    Chapter  Google Scholar 

  22. Yager, R. R., “Fuzzy set methods for representing commonsense knowledge,” Journal of Intelligent and Fuzzy Systems, (To Appear).

    Google Scholar 

  23. Yager, R. R, “Fuzzy logics and artificial intelligence,” Fuzzy Sets and Systems 90, 193–198, 1997.

    Article  MathSciNet  Google Scholar 

  24. Zadeh, L. A., “A computational approach to fuzzy quantifiers in natural languages,” Computing and Mathematics with Applications 9, 149–184, 1983.

    Article  MathSciNet  MATH  Google Scholar 

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© 1999 Springer-Verlag Berlin Heidelberg

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Yager, R.R. (1999). Approximate Reasoning as a Basis for Computing with Words. In: Zadeh, L.A., Kacprzyk, J. (eds) Computing with Words in Information/Intelligent Systems 1. Studies in Fuzziness and Soft Computing, vol 33. Physica, Heidelberg. https://doi.org/10.1007/978-3-7908-1873-4_3

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  • DOI: https://doi.org/10.1007/978-3-7908-1873-4_3

  • Publisher Name: Physica, Heidelberg

  • Print ISBN: 978-3-662-11362-2

  • Online ISBN: 978-3-7908-1873-4

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