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Inference Regions for Fuzzy Propositions

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Advances in Fuzzy Sets, Possibility Theory, and Applications

Abstract

Ever since L. A. Zadeh’s introduction of fuzzy sets [1], a concerned body of literature has appeared on the appropriate interpretations of (i) the logical fuzzy connectives, (Bellman and Gertz [2], Hamacher [3], Gaines [4], Bellman and Zadeh [5], Rödder [6], Zimmerman, et. al. [7], Zimmerman [8], Oden [9], Hersh and Caramazza [10], Goguen [11], Yager [12]) and (ii) the structural semantics of fuzzy logic and fuzzy conditional inference, (Zadeh [13,14], Gottwald [15], Mamdani [16], Fukami-Mizumoto-Tanaka [18], Mizumoto-Fukami-Tanaka [19], Hisdal [20], Türksen [21], and Türksen and Yao [22]). Naturally, these two avenues of concern are not independent of each other.

Supported by the Natural Science and Engineering Council of Canada.

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References

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

    Article  MathSciNet  MATH  Google Scholar 

  2. R. E. Gellman and M. Gertz, On the analytic formalism of the theory of fuzzy sets, Information Science, 5 (1973), 149–156.

    Article  Google Scholar 

  3. H. Hammacher, On logical connectives of fuzzy statements and their affiliated truth functions, Third Europ. Meeting on Cybernetics and Systems Research, Vienna (April, 1976).

    Google Scholar 

  4. B. R. Gaines, Foundations of fuzzy reasoning, Int. J. Man-Machine Studies, 8 (1976), 623–668.

    Article  MathSciNet  MATH  Google Scholar 

  5. R. E. Bellman and L. A. Zadeh, Local and fuzzy logics, in: J. M. Dunn and D. Epstein, eds., “Modern Uses of Multiple Valued Logic” (D. Reidel, Dordrecht, 1977), 103–165.

    Google Scholar 

  6. R. Rödder, On “and” and “or” connectives in fuzzy logic, EURO I Brussels (January, 1975).

    Google Scholar 

  7. H. J. Zimmerman, Results of empirical studies in fuzzy set theory, Proc. Int. Conference on Applied General Systems Theory, Binghamton, N.Y. (1977).

    Google Scholar 

  8. H. J. Zimmerman, Theory and applications of fuzzy sets, in: K. B. Haley, ed., OR ’78, North Holland Publishing Company (1978), N18m, 1–17.

    Google Scholar 

  9. G. Oden, Integration of fuzzy logical information, J. ma. Psychol. 3 (1977), 565–575.

    MathSciNet  Google Scholar 

  10. H. M. Hersh and A. Caramazza, A fuzzy set approach to modifiers and vagueness in natural language, J. Exp. Psychol. (1975), 254–276.

    Google Scholar 

  11. J. A. Goguen, The logic of inexact concepts, Synthese 19 (1969), 325–375.

    Article  MATH  Google Scholar 

  12. R. R. Yager, On a general class of fuzzy connectives, Fuzzy Sets and Systems 4, (1980) 235–242.

    Article  MathSciNet  MATH  Google Scholar 

  13. L. A. Zadeh, Calculus of fuzzy restrictions, in: L. A. Zadeh and K. Tanaka, et. al., eds., “Fuzzy Sets and Their Applications to Cognitive and Decision Processes,” Academic Press, N.Y. (1975), 1–39.

    Google Scholar 

  14. L. A. Zadeh, The concept of linguistic variable and its application to approximate reasoning, I, II, III, Information Sci. 8 (1975), 199–251; 8 (1975), 301–357; 9 (1975), 43–80

    Article  MathSciNet  Google Scholar 

  15. S. Gottwald, Fuzzy propositional logics, Working Paper, Sktion Mathematik, Karl Marx Universitat, Leipzig, G.D.R. (1976).

    Google Scholar 

  16. E. H. Mamdani, Application of fuzzy logic to approximate reasoning using linguistic systems, IEEE Trans. Comp. C-26 (1977), 1182–1191.

    Article  Google Scholar 

  17. N. Rescher, Many Valued Logic, McGraw Hill, N.Y., (1969).

    MATH  Google Scholar 

  18. S. Fukami, M. Mizumoto, K. Tanaka, Some considerations on fuzzy conditional inference, Fuzzy Sets and Systems, 4 (1980), 243–273.

    Article  MathSciNet  MATH  Google Scholar 

  19. M. Mizumoto, S. Fukami, K. Tanaka, Some methods of fuzzy reasoning, in: M. M. Gupta, et. al., eds., “Advances in Fuzzy Set Theory and Applications,” North-Holland, Amsterdam (1979), 117–136.

    Google Scholar 

  20. E. Hisdal, Generalized fuzzy sets systems and particularization, Fuzzy Sets and Systems 4 (1980), 275–291.

    Article  MathSciNet  MATH  Google Scholar 

  21. I. B. Türksen, Lattices and groups of fuzzy propositions, Working Paper #80–006, Department of Industrial Engineering, University of Toronto, Toronto, Ontario, M5S 1A4, Canada.

    Google Scholar 

  22. I. B. Türksen and D. D. Yao, Normal forms of fuzzy relational propositions, their lattice structures and applications, Working Paper #81–022, Department of Industrial Engineering, University of Toronto, Toronto, Ontario, M5S 1A4, Canada.

    Google Scholar 

  23. A. M. Norwich and I. B. Türksen, Measurement and Scaling of Membership Functions, Proc. of Int. Conf. on Applied Systems Research and Cybernetics, Acapulco, Mexico, (Dec. 1980) (to appear).

    Google Scholar 

  24. I. B. Türksen and A. M. Norwich, Measurement of Fuzziness, Proc. of Int. Conf. on Policy Analysis and Information Systems, Tapei, Taiwan, (August, 1981), 745–754.

    Google Scholar 

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Authors and Affiliations

  1. Department of Industrial Engineering, University of Toronto, Toronto, Ontario, M5S 1A4, Canada

    I. B. Türksen

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  1. I. B. Türksen
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Editors and Affiliations

  1. Duke University, Durham, North Carolina, USA

    Paul P. Wang

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© 1983 Plenum Press, New York

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Türksen, I.B. (1983). Inference Regions for Fuzzy Propositions. In: Wang, P.P. (eds) Advances in Fuzzy Sets, Possibility Theory, and Applications. Springer, Boston, MA. https://doi.org/10.1007/978-1-4613-3754-6_11

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  • DOI: https://doi.org/10.1007/978-1-4613-3754-6_11

  • Publisher Name: Springer, Boston, MA

  • Print ISBN: 978-1-4613-3756-0

  • Online ISBN: 978-1-4613-3754-6

  • eBook Packages: Springer Book Archive

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