Skip to main content
SpringerLink
Log in

From Computing with Numbers to Computing with Words: From Manipulation of Measurements to Manipulation of Perceptions

  • Chapter
Book cover The Dynamics of Judicial Proof

Part of the book series: Studies in Fuzziness and Soft Computing ((STUDFUZZ,volume 94))

Abstract

Computing, in its usual sense, is centered on manipulation of numbers and symbols. In contrast, computing with words, or CW for short, is a methodology in which the objects of computation are words and propositions drawn from a natural language, e.g., small, large, far, heavy, not very likely,the price of gas is low and declining,Berkeley is near San Francisco, it is very unlikely that there will be a significant increase in the price of oil in the near future, etc. Computing with words is inspired by the remarkable human capability to perform a wide variety of physical and mental tasks without any measurements and any computations. Familiar examples of such tasks are parking a car, driving in heavy traffic, playing golf, riding a bicycle, understanding speech and summarizing a story. Underlying this remarkable capability is the brain’s crucial ability to manipulate perceptions — perceptions of distance, size, weight, color, speed, time, direction, force, number, truth, likelihood and other characteristics of physical and mental objects. Manipulation of perceptions plays a key role in human recognition, decision and execution processes. As a methodology, computing with words provides a foundation for a computational theory of perceptions — a theory which may have an important bearing on how humans make — and machines might make — perception-based rational decisions in an environment of imprecision, uncertainty and partial truth.

© 1999 IEEE. Reprinted, with permission, from IEEE Transactions on Circuits and Systems — I: Fubdanebtal Theory and Applications, vol. 45, no. 1, 105-119. Publisher Item Identifier S 1057-7122(99)00546-2.

To Professor Michio Sugeno, who has contributed so much and in so many ways to the development of fuzzy logic and its applications.

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

Access this chapter

Log in via an institution
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
Hardcover Book
USD 219.99
Price excludes VAT (USA)
  • Durable hardcover 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 and Related Publications

  1. H.R. Berenji, Fuzzy Reinforcement Learning and Dynamic Programming, in Fuzzy Logic in Artificial Intelligence, Proc. IJCAI 93 Workshop, ed. A.L. Ralescu, Berlin: Springer-Verlag, pp. 1 - 9, 1994.

    Google Scholar 

  2. M. Black, Reasoning with Loose Concepts, Dialog 2, pp. 1 - 12, 1963.

    Article  Google Scholar 

  3. P. Bosch, Vagueness, Ambiguity and All the Rest,in Sprachstruktur, Individuum und Gesselschaft, eds. M. Van de Velde and W. Vandeweghe, Tubingen: Niemeyer, 1978.

    Google Scholar 

  4. J. Bowen, R. Lai, and D. Bahler, Fuzzy Semantics and Fuzzy Constraint Networks, Proc. of the 1st IEEE Conf. on Fuzzy Systems, San Francisco, pp. 1009 - 1016, 1992.

    Google Scholar 

  5. J. Bowen, R. Lai, and D. Bahler,Lexical Imprecision in Fuzzy Constraint Networks, Proc. of the National Conf. on Artificial Intelligence, pp. 616620, 1992.

    Google Scholar 

  6. M.J. Cresswell, Logic and Languages, London: Methuen, 1973.

    Google Scholar 

  7. D. Dubois, H. Fargier, and H. Prade, Propagation and Satisfaction of Flexible Constraints, in Fuzzy Sets, Neural Networks, and Soft Computing, eds. R.R. Yager, L.A. Zadeh, New York: Von Nostrand Reinhold, pp. 166187, 1994.

    Google Scholar 

  8. D. Dubois, H. Fargier, and H. Prade, Possibility Theory in Constraint Satisfaction Problems: Handling Priority, Preference and Uncertainty, to appear in Applied Intelligence Journal.

    Google Scholar 

  9. D. Dubois, H. Fargier, and H. Prade, The Calculus of Fuzzy Restrictions as a Basis for Flexible Constraint Satisfaction, Proc. of the 2nd IEEE Int. Conf. on Fuzzy Systems, San Francisco, pp. 1131 - 1136, 1993.

    Google Scholar 

  10. E.C. Freuder and P. Snow, Improved Relaxation and Search Methods for Approximate Constraint Satisfaction with a Maximin Criterion, Proc. of the 8th Biennial Conf on the Canadian Society for Computational Studies of Intelligence, Ontario, pp. 227 - 230, 1990.

    Google Scholar 

  11. J.A. Goguen, The Logic of Inexact Concepts, Synthese 19, pp. 325 - 373, 1969.

    Article  Google Scholar 

  12. J.R. Hobbs, Making Computation Sense of Montagues Intensional Logic, Artificial Intelligence 9, pp. 287 - 306, 1978.

    Article  Google Scholar 

  13. O. Katai, S. Matsubara, H. Masuichi, M. Ida, et. al., Synergetic Computation for Constraint Satisfaction Problems Involving Continuous and Fuzzy Variables by Using Occam,in Transputer/Occam, Proc. of the 4th Transputer/Occam Int. Conf, eds. S. Noguchi and H. Umeo, Amsterdam: IOS Press, pp. 146 - 160, 1992.

    Google Scholar 

  14. A. Kaufmann and M.M. Gupta, Introduction to Fuzzy Arithmetic: Theory and Applications, New York: Von Nostrand, 1985.

    Google Scholar 

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

    Google Scholar 

  16. K. Lano, A Constraint-Based Fuzzy Inference System, in EPIA 91, 5th Portuguese Conf. on Artificial Intelligence, eds. P. Barahona, L.M. Pereira, and A. Porto, Berlin: Springer-Verlag, pp. 45 - 59, 1991.

    Google Scholar 

  17. W.A. Lodwick, Analysis of Structure in Fuzzy Linear Programs, Fuzzy Sets and Systems, 38 (1), pp. 15 - 26, 1990.

    Article  Google Scholar 

  18. E.H. Mamdani and B.R. Gaines, Eds., Fuzzy Reasoning and its Applications, London, 1981.

    Google Scholar 

  19. M. Mares, Computation Over Fuzzy Quantities, Boca Raton: CRC Press, 1994.

    Google Scholar 

  20. V. Novak, Fuzzy Logic, Fuzzy Sets, and Natural Languages, Int. J. of General Systems 20 (1), pp. 83 - 97, 1991.

    Article  Google Scholar 

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

    Google Scholar 

  22. M.S. Oshan, O.M. Saad and A.G. Hassan, On the Solution of Fuzzy Mul- tiobjective Integer Linear Programming Problems with a Parametric Study, Advances in Modelling & Analysis A, 24(2), pp. 49 - 64, 1995.

    Google Scholar 

  23. B. Partee, Montague Grammar, New York: Academic Press, 1976.

    Google Scholar 

  24. W. Pedrycz and F. Gomide, Introduction to Fuzzy Sets, Cambridge: MIT Press, 1998.

    Google Scholar 

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

    Google Scholar 

  26. H. Rasiowa and M. Marek, On reaching consensus by groups of intelligent agents, in Z. W. Ras, (ed.): Methodologies for Intelligent Systems, Amsterdam: North-Holland, pp. 234 - 243, 1989.

    Google Scholar 

  27. A. Rosenfeld, R.A. Hummel and S.W. Zucker, Scene Labeling by Relaxation Operations, IEEE Trans. on Systems, Man and Cybernetics, 6, pp. 420 - 433, 1976.

    Article  Google Scholar 

  28. M. Sakawa, K. Sawada, and M. Inuiguchi, A Fuzzy Satisficing Method for Large-Scale Linear Programming Problems with Block Angular Structure, European Journal of Operational Research, 81(2), pp. 399 - 409, 1995.

    Google Scholar 

  29. G. Shafer, A Mathematical Theory of Evidence, Princeton: Princeton University Press, 1976.

    Google Scholar 

  30. S.C. Tong, Interval Number and Fuzzy Number Linear Programming, Advances in Modelling & Analysis A, 20 (2), pp. 51 - 56, 1994.

    Google Scholar 

  31. R. Vallee, Cognition et Systeme, Paris: lInterdisciplinaire Systeme(s), 1995.

    Google Scholar 

  32. R.R. Yager, Some extensions of constraint propagation of label setsInt. J. of Approximate Reasoning, 3, pp. 417 - 435, 1989.

    Article  Google Scholar 

  33. L.A. Zadeh, From circuit theory to system theory, Proc. IRE,50, pp. 856865, 1961.

    Google Scholar 

  34. L.A. Zadeh, Fuzzy Sets, Inf. Control, 8, pp. 338 - 353, 1965.

    Article  Google Scholar 

  35. L.A. Zadeh, "Probability measures of fuzzy events," Jour. Math. Analysis and Appl. 23, pp. 421 - 427, 1968.

    Article  Google Scholar 

  36. L.A. Zadeh, A fuzzy-set-theoretic interpretation of linguistic hedges, J. of Cybernetics 2, pp. 4 - 34, 1972.

    Article  Google Scholar 

  37. L.A. Zadeh, Outline of a New Approach to the Analysis of Complex System and Decision Processes, IEEE Trans. on Systems, Man, and Cybernetics, SMC-3, pp. 28 - 44, 1973.

    Google Scholar 

  38. L.A. Zadeh, On the Analysis of Large Scale Systems, Systems Approaches and Environment Problems, ed. H. Gottinger, Gottingen: Vandenhoeck and Ruprecht, pp. 23-37, 1974.

    Google Scholar 

  39. L.A. Zadeh, Calculus of Fuzzy Restrictions, in Fuzzy Sets and Their Applications to Cognitive and Decision Processes, eds. L.A. Zadeh, K.S. Fu, M. Shimura, New York: Academic Press, pp. 1 - 39, 1975.

    Google Scholar 

  40. L.A. Zadeh, The concept of a linguistic variable and its application to approximate reasoning, Part I: Inf. Sci. 8, pp. 199-249; Part II: Inf. Sci. 8, pp. 301-357; Part III: Inf. Sci. 9, pp. 43 - 80, 1975.

    Google Scholar 

  41. L.A. Zadeh, A fuzzy-algorithmic approach to the definition of complex or imprecise concepts, Int. Jour. Man-Machine Studies 8, pp. 249 - 291, 1976.

    Article  Google Scholar 

  42. L.A. Zadeh, Fuzzy sets as a basis for a theory of possibility, Fuzzy Sets and Systems 1, pp. 3 - 28, 1978.

    Article  Google Scholar 

  43. L.A. Zadeh, PRUF - a Meaning Representation Language for Natural Languages, Int. J. Man-Machines Studies, 10, pp. 395 - 460, 1978.

    Article  Google Scholar 

  44. L.A. Zadeh, Fuzzy Sets and Information Granularity, in Advances in Fuzzy Set Theory and Applications, eds. M. Gupta, R.Ragade and R. Yager, Amsterdam: North-Holland, pp. 3 - 18, 1979.

    Google Scholar 

  45. L.A. Zadeh, A Theory of Approximate Reasoning, Machine Intelligence 9, eds. J. Hayes, D. Michie, and L.I. Mikulich, New York: Halstead Press, pp. 149-194, 1979.

    Google Scholar 

  46. L.A. Zadeh, Test-Score Semantics for Natural Languages and Meaning Representation via PRUF, Empirical Semantics,ed. B. Rieger, W. Germany: Brockmeyer, pp. 281-349. Also Technical Report Memorandum 246,AI Center, SRI International, Menlo Park, CA, 1981.

    Google Scholar 

  47. L.A. Zadeh, Test-score semantics for natural languages, Proc. of the Ninth International Conference on Computational Linguistics,Prague, pp. 425-430, 1982.

    Google Scholar 

  48. L.A. Zadeh, Syllogistic reasoning in fuzzy logic and its application to reasoning with dispositions,Proceedings of the 1984 International Symposium on Multiple-Valued Logic,Winnipeg, Canada, pp. 148-153, 1984.

    Google Scholar 

  49. L.A. Zadeh, Outline of a Computational Approach to Meaning and Knowledge Representation Based on a Concept of a Generalized Assignment Statement, Proc. of the Int. Seminar on Artificial Intelligence and Man-Machine Systems, eds. M. Thoma and A. Wyner, Heidelberg: Springer-Verlag, pp. 198-211, 1986.

    Google Scholar 

  50. L.A. Zadeh, Fuzzy Logic, Neural Networks and Soft Computing,Communications of the ACM,37(3), pp. 77-84, 1994.

    Google Scholar 

  51. L.A. Zadeh, Fuzzy Logic and the Calculi of Fuzzy Rules and Fuzzy Graphs: A Precis, Multiple Valued Logic 1, Gordon and Breach Science Publishers, pp. 1 - 38, 1996.

    Google Scholar 

  52. L.A. Zadeh,Fuzzy Logic = Computing with Words,EEE Transactions on Fuzzy Systems,Vol. 4, pp. 103-111, 1996.

    Google Scholar 

  53. L.A. Zadeh, Toward a Theory of Fuzzy Information Granulation and its Centrality in Human Reasoning and Fuzzy Logic Fuzzy Sets and Systems 90,pp. 111-127, 1997.

    Google Scholar 

  54. L.A. Zadeh, Maximizing Sets and Fuzzy Markoff Algorithms, IEEE Transactions on Systems, Man, and Cybernetics-Part C: Applications and Reviews, Vol. 28, pp. 9 - 15, 1998.

    Article  Google Scholar 

  55. L.A. Zadeh, A New Direction in AI — Toward a Computational Theory of Perceptions,AI Magazine, Vol 22, No. 1, pp. 73 - 84, 2001.

    Google Scholar 

Download references

Authors
  1. Lotfi A. Zadeh
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. Faculty of Law, University of British Columbia, 1822 East Mall, V6T 1Z1, Vancouver, BC, Canada

    Marilyn MacCrimmon

  2. Cardozo School of Law, Yeshiva University, 55 Fifth Avenue, 10003, New York, NY, USA

    Peter Tillers

Rights and permissions

Reprints and permissions

Copyright information

© 2002 Physica-Verlag Heidelberg

About this chapter

Cite this chapter

Zadeh, L.A. (2002). From Computing with Numbers to Computing with Words: From Manipulation of Measurements to Manipulation of Perceptions. In: MacCrimmon, M., Tillers, P. (eds) The Dynamics of Judicial Proof. Studies in Fuzziness and Soft Computing, vol 94. Physica, Heidelberg. https://doi.org/10.1007/978-3-7908-1792-8_5

Download citation

  • DOI: https://doi.org/10.1007/978-3-7908-1792-8_5

  • Publisher Name: Physica, Heidelberg

  • Print ISBN: 978-3-662-00323-7

  • Online ISBN: 978-3-7908-1792-8

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics

Search

Navigation