Skip to main content

From Computing with Numbers to Computing with Words — from Manipulation of Measurements to Manipulation of Perceptions

  • Chapter
Logic, Thought and Action

Part of the book series: Logic, Epistemology, and the Unity of Science ((LEUS,volume 2))

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 169.00
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 219.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  • Berenji H.R. (1994). “Fuzzy Reinforcement Learning and Dynamic Programming”, Fuzzy Logic in Artificial Intelligence (A.L. Ralescu, Ed.), Proc. IJCAI’93 Workshop, Berlin: Springer-Verlag, pp. 1–9.

    Google Scholar 

  • Black M. (1963). “Reasoning with Loose Concepts”, Dialog 2, pp. 1–12.

    Google Scholar 

  • Bosch P. (1978). Vagueness, Ambiguity and all the Rest, Sprachstruktur, Individuum und Gesselschaft (M. Van de Velde and W. Vandeweghe, Eds.). Tubingen: Niemeyer.

    Google Scholar 

  • Bowen J., Lai R. and Bahler D. (1992a). “Fuzzy semantics and fuzzy constraint networks”, Proceedings of the 1st IEEE Conference on Fuzzy Systems, San Francisco, pp. 1009–1016.

    Google Scholar 

  • Bowen J., Lai R. and Bahler D. (1992b). “Lexical imprecision in fuzzy constraint networks”, Proc. Nat. Conf. Artificial Intelligence, pp. 616–620.

    Google Scholar 

  • Cresswell M.J. (1973). Logic and Languages. London: Methuen.

    Google Scholar 

  • Dubois D., Fargier H. and Prade H. (1993). “The Calculus of Fuzzy Restrictions as a Basis for Flexible Constraint Satisfaction”, Proceedings of the 2nd IEEE International Conference on Fuzzy Systems. San Francisco, pp. 1131–1136.

    Google Scholar 

  • ____ (1994). Propagation and Satisfaction of Flexible Constraints, Fuzzy Sets, Neural Networks, and Soft Computing (R.R. Yager, L.A. Zadeh, Eds.) New York: Van Nostrand Reinhold, pp. 166–187.

    Google Scholar 

  • ____ (1996). “Possibility Theory in Constraint Satisfaction Problems: Handling Priority, Preference and Uncertainty”, Applied Intelligence 6:4, pp. 287–309.

    Google Scholar 

  • Freuder E.C. and Snow P. (1990). Improved Relaxation and Search Methods for Approximate Constraint Satisfaction with a Maximin Criterion, Proceedings of the 8th Biennial Conference of the Canadian Society for Computational Studies of Intelligence, Ontario, pp. 227–230.

    Google Scholar 

  • Goguen J.A. (1969). “The Logic of Inexact Concepts”, Synthese 19, pp. 325–373.

    Google Scholar 

  • Hobbs J.R. (1978). “Making Computation Sense of Montague’s Intensional Logic”, Artificial Intelligence, Vol. 9, pp. 287–306.

    Google Scholar 

  • Katai O., Matsubara S., Masuichi H., Ida M., et al. (1992). “Synergetic Computation for Constraint Satisfaction Problems Involving Continuous and Fuzzy Variables by Using Occam, Transputer/Occam”, (S. Noguchi and H. Umeo, Eds.), Proc. 4th Transputer/Occam Int. Conf., Amsterdam: IOS Press, pp. 146–160.

    Google Scholar 

  • Kaufmann A. and Gupta M.M. (1985). Introduction to Fuzzy Arithmetic: Theory and Applications, New York: Van Nostrand.

    Google Scholar 

  • Klir G. and Yuan B. (1995). Fuzzy Sets and Fuzzy Logic, New Jersey: Prentice Hall.

    Google Scholar 

  • Lano K. (1991). “A Constraint-Based Fuzzy Inference System”. Proc. 5th Portuguese Conf. Artificial Intelligence, EPIA’91 (P. Barahona, L.M. Pereira, and A. Porto, Eds.), Berlin: Springer-Verlag, pp. 45–59.

    Google Scholar 

  • Lodwick W.A. (1990). “Analysis of Structure in Fuzzy Linear Programs”, Fuzzy Sets Syst. 38:1, pp. 15–26.

    Google Scholar 

  • Mamdani E.H. and Gaines B. R., Eds. (1981). Fuzzy Reasoning and its Applications. London: Academic Press.

    Google Scholar 

  • Mares M. (1994). Computation Over Fuzzy Quantities, Boca Raton: CRC Press.

    Google Scholar 

  • Novak V. (1991). “Fuzzy Logic, Fuzzy Sets, and Natural Languages”, International Journal of General Sysems 20:1, pp. 83–97.

    Google Scholar 

  • Novak V., Ramik M., Cerny M. and Nekola J., Eds. (1992). Fuzzy Approach to Reasoning and Decision-Making, Boston: Kluwer.

    Google Scholar 

  • Oshan M.S., Saad O.M. and Hassan A.G. (1995). “On the Solution of Fuzzy Multiobjective Integer Linear Programming Problems With a Parametric Study”, Adv. Modell. Anal. A, Vol. 24, No. 2, pp. 49–64.

    Google Scholar 

  • Partee B. (1976). Montague Grammar, New York: Academic Press.

    Google Scholar 

  • Pedrycz W. and Gomide F. (1998). Introduction to Fuzzy Sets, Cambridge: MIT Press, pp. 38–40.

    Google Scholar 

  • Qi G. and Friedrich G. (1992). “Extending Constraint Satisfaction Problem Solving in Structural Design”, 5th Int. Conf. Industrial and Engineering Applications of Artificial Intelligence and Expert Systems, IEA/AIE-92 (F. Belli and F.J. Radermacher, Eds.), Berlin: Springer-Verlag, pp. 341–350.

    Google Scholar 

  • Rasiowa H. and Marek M. (1989). “On Reaching Consensus by Groups of Intelligent Agents”, Methodologies for Intelligent Systems (Z.W. Ras, Ed.). Amsterdam: North-Holland, pp. 234–243.

    Google Scholar 

  • Rosenfeld A., Hummel R.A. and Zucker S.W. (1976). “Scene Labeling by Relaxation Operations”, IEEE Transactions on systems man and cybernetics, Vol. 6, pp. 420–433.

    Google Scholar 

  • Sakawa M., Sawada K. and Inuiguchi M. (1995). “A Fuzzy Satisficing Method for Large-Scale Linear Programming Problems with Block Angular Structure”, European Journal of Operational Research, Vol. 81, No. 2, pp. 399–409.

    Google Scholar 

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

    Google Scholar 

  • Tong S.C. (1994). “Interval Number and Fuzzy Number Linear Programming”, Adv. Modell. Anal. A, 20:2, pp. 51–56.

    Google Scholar 

  • Vallée R. (1995). Cognition et système. Paris: l’Interdisciplinaire Système(s).

    Google Scholar 

  • Yager R.R. (1989). “Some Extensions of Constraint Propagation of Label Sets”, International Journal of Approximate Reasoning 3, pp. 417–435.

    MathSciNet  Google Scholar 

  • Zadeh L.A. (1961). “From Circuit Theory to System Theory”, Proc. of the Institute of Radio Engineers 50, pp. 856–865.

    Google Scholar 

  • ____ (1965). Fuzzy sets, Information and Control 8, pp. 338–353.

    Google Scholar 

  • ____ (1968). “Probability Measures of Fuzzy Events”, Journal of Mathematical Analysis and Applications 23, pp. 421–427.

    Google Scholar 

  • ____ (1972). “A Fuzzy—Set-Theoretic Interpretation of Linguistic Hedges”, Journal of Cybernetics 2, pp. 4–34.

    Google Scholar 

  • ____ (1973). “Outline of a New Approach to the Analysis of Complex System and Decision Processes”, IEEE Transactions on systems man and cybernetics SMC-3, pp. 28–44.

    Google Scholar 

  • ____ (1974). On the Analysis of Large Scale Systems, Systems Approaches and Environment Problems (H. Gottinger, Ed.). Gottingen: Vandenhoeck and Ruprecht, pp. 23–37.

    Google Scholar 

  • ____ (1975a). Calculus of Fuzzy Restrictions, Fuzzy Sets and Their Applications to Cognitive and Decision Processes, (L.A. Zadeh, K.S. Fu, M. Shimura, Eds.). New York: Academic Press, pp. 1–39.

    Google Scholar 

  • ____ (1975b). “The Concept of a Linguistic Variable and its Application to Approximate Reasoning”, Part I: Information Sciences 8, pp. 199–249; Part II: Inf. Sci. 8, pp. 301–357; Part III: Inf. Sci. 9, pp. 43–80.

    Google Scholar 

  • ____ (1976). “A Fuzzy-Algorithmic Approach to the Definition of Complex or Imprecise Concepts”, International Journal of Man-Machine Studies 8, pp. 249–291.

    Google Scholar 

  • ____ (1978a). “Fuzzy Sets as a Basis for a Theory of Possibility”, Fuzzy Sets and Systems 1, pp. 3–28.

    Google Scholar 

  • ____ (1978b). “PRUF — A Meaning Representation Language for Natural Languages”, International Journal of Man-Machine Studies 10, pp. 395–460.

    Google Scholar 

  • ____ (1979a). Fuzzy Sets and Information Granularity, Advances in Fuzzy Set Theory and Applications (M. Gupta, R. Ragade and R. Yager, Eds.). Amsterdam: North-Holland, pp. 3–18.

    Google Scholar 

  • ____ (1979b). “A Theory of Approximate Reasoning”, Machine Intelligence 9 (J. Hayes, D. Michie and L.I. Mikulich, Eds.). New York: Halstead Press, pp. 149–194.

    Google Scholar 

  • ____ (1981). Test-Score Semantics for Natural Languages and Meaning Representation via PRUF, Empirical Semantics (B. Rieger, W. Germany, Eds.), Brockmeyer, pp. 281–349. Also Technical Report Memorandum 246, AI Center, SRI International, Menlo Park, CA.

    Google Scholar 

  • ____ (1982). “Test-Score Semantics for Natural Languages”, Proc. 9-th Int. Conf. Computational Linguistics, Prague, pp. 425–430.

    Google Scholar 

  • ____ (1984). “Syllogistic Reasoning in Fuzzy Logic and its Application to Reasoning with Dispositions”, Proc. Int. Symp. Multiple-Valued Logic, Winnipeg, Canada, pp. 148–153.

    Google Scholar 

  • ____ (1986). “Outline of a Computational Approach to Meaning and Knowledge Representation Based on a Concept of a Generalized Assignment Statement”. Proc. International Seminar on Artificial Intelligence and Man-Machine Systems (M. Thoma and A. Wyner, Eds.) Heidelberg: Springer-Verlag, pp. 198–211.

    Google Scholar 

  • ____ (1994). “Fuzzy Logic, Neural Networks and Soft Computing”, Communications of the ACM 37:3, pp. 77–84.

    Google Scholar 

  • ____ (1996a). Fuzzy Logic and the Calculi of Fuzzy Rules and Fuzzy Graphs: A Precise, Multiple Valued Logic 1, Gordon and Breach Science Publishers, pp. 1–38.

    Google Scholar 

  • ____ (1996b). “Fuzzy Logic = Computing with Words”, IEEE Transactions on Fuzzy Systems 4, pp. 103–111.

    Google Scholar 

  • ____ (1997). “Toward a Theory of Fuzzy Information Granulation and its Centrality in Human Reasoning and Fuzzy Logic”, Fuzzy Sets and Systems 90, pp. 111–127.

    Google Scholar 

  • ____ (1998). “Maximizing Sets and Fuzzy Markoff Algorithms”, IEEE Transactions on systems man and cybernetics Part C — Applications and Reviews 28, pp. 9–15.

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 1999 IEEE

About this chapter

Cite this chapter

Zadeh, L. (1999). From Computing with Numbers to Computing with Words — from Manipulation of Measurements to Manipulation of Perceptions. In: Vanderveken, D. (eds) Logic, Thought and Action. Logic, Epistemology, and the Unity of Science, vol 2. Springer, Dordrecht. https://doi.org/10.1007/1-4020-3167-X_23

Download citation

Publish with us

Policies and ethics