Fuzzy Set Theory — and Inference Mechanism

  • H.-J. Zinmermann
Part of the NATO ASI Series book series (volume 48)


Most of our traditional tools for formal modelling, reasoning, and computing are crisp, deterministic and precise in character. By crisp we mean dichotomous, that is, of yes-or-no-type rather than more-or-less type. In conventional dual logic, for instance, a statement can be true or false—and nothing in between. In set theory an element can either belong to a set or not, and in optimization a solution is either feasible or not. Precision assumes that the parameters of a model represent exactly either our perception of the phenomenon modelled or the features of the real system that has been modelled. Generally precision also implies that the model is unequivocal, that is , that it contains no ambiguities.


Membership Function Fuzzy Logic Fuzzy Number Linguistic Variable Truth Table 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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  1. Baldwin, J.F.: A New Approach to Approximate Reasoning Using a Fuzzy Logic, in: Fuzzy Sets and Systems 2 (1979), pp. 309–325.CrossRefMATHMathSciNetGoogle Scholar
  2. Baldwin, J.F., Guild, N.C.F.: Feasible Algorithms for Approxi-Approximate Reasoning Using Fuzzy Logic, in: Fuzzy Sets and Systems 3 (1980), pp. 225–251.CrossRefMATHMathSciNetGoogle Scholar
  3. Baldwin, J.F., Pilsworth, B.W.: Fuzzy Truth Definition of Possibility Measure for Decision Classifica tion, in: In. J. Man-Machine Studies I (1979), pp. 447–463.Google Scholar
  4. Bellman, R., Zadeh, L.A.: Decision Making in a Fuzzy Environment, in: Management Science 17 (1970), pp. B141–164.CrossRefMathSciNetGoogle Scholar
  5. Blockley, D.I.: The Nature of Structural Design and Safety. Chichester 1980.Google Scholar
  6. Brand, H.W.: The Fecundity of Mathematical Methods, Dordrecht 1961.Google Scholar
  7. Cao, H., Chen, G.: Some Applications of Fuzzy Sets to Meteorological Forecasting, in: Fuzzy Sets and Systems 9 (1983), pp. 1–12.CrossRefMathSciNetGoogle Scholar
  8. Giles, R.: A Formal System for Fuzzy Reasoning, in: Fuzzy Sets and Systems 2 (1979), pp. 233–257.CrossRefMATHMathSciNetGoogle Scholar
  9. Giles, R.: A Computer Program for Fuzzy Reasoning, in: Fuzzy Sets and Systems 4 (1980), pp. 221–234.CrossRefMATHMathSciNetGoogle Scholar
  10. Goguen, J.A.: L-Fuzzy Sets, in: JMAA 18 (1967), pp. 145–174.MATHMathSciNetGoogle Scholar
  11. Goguen, J.A.: The Logic of Inexact Concepts, Synthese 19 (1969), pp. 325–373.CrossRefMATHGoogle Scholar
  12. Mamdani, E.H.: Advances in the Linguistic Synthesis of Fuzzy Controllers, in: Mamdani, Gaines (eds.), 1981, pp. 325–334.Google Scholar
  13. Mamdani, E.H., Efstathiou, H.J.: A Comparative Study of Applied Logics, in: Fuzzy Sets and Systems (1984)Google Scholar
  14. Mizumoto, M., Fukami, S., Tanaka, K.: Some Methods of Fuzzy Reasoning, in: Guptaet al. (eds.), 1979, pp. 117–136.Google Scholar
  15. Mizumoto, M., Zimmermann, H.-J.: Comparison of Fuzzy Reasoning Methods, in: Fuzzy Sets and Systems 8 (1982), pp. 253–283.CrossRefMATHMathSciNetGoogle Scholar
  16. Schwartz, J.: The Pernicious Influence of Mathematics in Science, in: Nagel, E., Suppes, P., Traski, A. (eds.): Logic Methodology and Philisophy of Science, Stanford 1962.Google Scholar
  17. Tsukamoto, Y.: An Approach to Fuzzy Reasoning Method, in: Guppta et al. (eds.) 1979, pp. 137–149.Google Scholar
  18. Vila, M.A., Delgado, M.: On Mecial Diagnosis Using Possibility Measures, in: Fuzzy Sets and Systems 10 (1983), pp. 211–222.CrossRefMATHMathSciNetGoogle Scholar
  19. Werners, B.: Interaktive Entscheidungsunterstützung durch ein flexibles mathematisches Programmierungssystem, Dissertation, Aachen 1984.Google Scholar
  20. Zadeh, L.A.: Fuzzy Sets, in: Information and Control 8 (1965), pp. 338–353.CrossRefMATHMathSciNetGoogle Scholar
  21. Zadeh, L.A.: The Concept of a Linguistic Variable and Its Application to Approximate Reasoning Memorandum ERL-M 411, Berkeley, October 1973 (a).Google Scholar
  22. Zadeh, L.A.: Outline of a New Approach to the Analysis of Complex Systems and Decision Processes, in: IEEE IEEE Trans. Vol. SMC 3 (1973b), pp. 28–44.MATHMathSciNetGoogle Scholar
  23. Zadeh, L.A.: Test-Score: Semantics for Natural Languages and Meaning Representation via PRϋF, in: Techn. Note 247, SRI, 1981.Google Scholar
  24. Zadeh, L.A.: The Role of Fuzzy Logic in the Management of Uncertainty in Expert Systems, in: Fuzzy Sets and Systems 11 (1983), pp. 199–227.CrossRefMATHMathSciNetGoogle Scholar
  25. Zimmermann, H.-J.: Testability and Meaning of Mathematical Models in Social Sciences, in: Mathematical Modeling 1 (1980), pp. 123–139.CrossRefGoogle Scholar
  26. Zimmermann, H.-J., Zadeh, L.A., Gaines, B.R. (eds.): Fuzzy Sets and Decision Analysis, Amsterdam, New York Oxford 1984.Google Scholar
  27. Zimmermann, H-J., Zysno, P.: Decisions and Evaluations by Hierarchical Aggregation of Information, in: Fuzzy Sets and Systems 10 (1983), pp. 243–266.CrossRefMATHGoogle Scholar
  28. Zimermann, H.-J., Zysno, P.: Latent Connectives in Human Decision Making, in: Fuzzy Sets and Systems 4 (1980), pp. 37–51.CrossRefGoogle Scholar
  29. Zimmermann, H-J.: Fuzzy Set Theory—And Its Applications, Boston, Dordrecht, Lancaster 1985.Google Scholar
  30. Zimmermann, H.-J.: Fuzzy Sets, Decision Making and Expert Systems, Boston, Dordrecht, Lancaster 1987.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1988

Authors and Affiliations

  • H.-J. Zinmermann
    • 1
  1. 1.RWTH AachenAachenThe Federal of Republic

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