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.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
Similar content being viewed by others
References and Related Publications
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.
M. Black, Reasoning with Loose Concepts, Dialog 2, pp. 1 - 12, 1963.
P. Bosch, Vagueness, Ambiguity and All the Rest,in Sprachstruktur, Individuum und Gesselschaft, eds. M. Van de Velde and W. Vandeweghe, Tubingen: Niemeyer, 1978.
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.
J. Bowen, R. Lai, and D. Bahler,Lexical Imprecision in Fuzzy Constraint Networks, Proc. of the National Conf. on Artificial Intelligence, pp. 616620, 1992.
M.J. Cresswell, Logic and Languages, London: Methuen, 1973.
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.
D. Dubois, H. Fargier, and H. Prade, Possibility Theory in Constraint Satisfaction Problems: Handling Priority, Preference and Uncertainty, to appear in Applied Intelligence Journal.
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.
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.
J.A. Goguen, The Logic of Inexact Concepts, Synthese 19, pp. 325 - 373, 1969.
J.R. Hobbs, Making Computation Sense of Montagues Intensional Logic, Artificial Intelligence 9, pp. 287 - 306, 1978.
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.
A. Kaufmann and M.M. Gupta, Introduction to Fuzzy Arithmetic: Theory and Applications, New York: Von Nostrand, 1985.
G. Klir and B. Yuan, Fuzzy Sets and Fuzzy Logic, New Jersey: Prentice Hall, 1995.
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.
W.A. Lodwick, Analysis of Structure in Fuzzy Linear Programs, Fuzzy Sets and Systems, 38 (1), pp. 15 - 26, 1990.
E.H. Mamdani and B.R. Gaines, Eds., Fuzzy Reasoning and its Applications, London, 1981.
M. Mares, Computation Over Fuzzy Quantities, Boca Raton: CRC Press, 1994.
V. Novak, Fuzzy Logic, Fuzzy Sets, and Natural Languages, Int. J. of General Systems 20 (1), pp. 83 - 97, 1991.
V. Novak, M. Ramik, M. Cerny and J. Nekola, Eds., Fuzzy Approach to Reasoning and Decision-Making, Boston: Kluwer, 1992.
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.
B. Partee, Montague Grammar, New York: Academic Press, 1976.
W. Pedrycz and F. Gomide, Introduction to Fuzzy Sets, Cambridge: MIT Press, 1998.
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.
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.
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.
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.
G. Shafer, A Mathematical Theory of Evidence, Princeton: Princeton University Press, 1976.
S.C. Tong, Interval Number and Fuzzy Number Linear Programming, Advances in Modelling & Analysis A, 20 (2), pp. 51 - 56, 1994.
R. Vallee, Cognition et Systeme, Paris: lInterdisciplinaire Systeme(s), 1995.
R.R. Yager, Some extensions of constraint propagation of label setsInt. J. of Approximate Reasoning, 3, pp. 417 - 435, 1989.
L.A. Zadeh, From circuit theory to system theory, Proc. IRE,50, pp. 856865, 1961.
L.A. Zadeh, Fuzzy Sets, Inf. Control, 8, pp. 338 - 353, 1965.
L.A. Zadeh, "Probability measures of fuzzy events," Jour. Math. Analysis and Appl. 23, pp. 421 - 427, 1968.
L.A. Zadeh, A fuzzy-set-theoretic interpretation of linguistic hedges, J. of Cybernetics 2, pp. 4 - 34, 1972.
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.
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.
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.
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.
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.
L.A. Zadeh, Fuzzy sets as a basis for a theory of possibility, Fuzzy Sets and Systems 1, pp. 3 - 28, 1978.
L.A. Zadeh, PRUF - a Meaning Representation Language for Natural Languages, Int. J. Man-Machines Studies, 10, pp. 395 - 460, 1978.
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.
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.
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.
L.A. Zadeh, Test-score semantics for natural languages, Proc. of the Ninth International Conference on Computational Linguistics,Prague, pp. 425-430, 1982.
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.
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.
L.A. Zadeh, Fuzzy Logic, Neural Networks and Soft Computing,Communications of the ACM,37(3), pp. 77-84, 1994.
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.
L.A. Zadeh,Fuzzy Logic = Computing with Words,EEE Transactions on Fuzzy Systems,Vol. 4, pp. 103-111, 1996.
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.
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.
L.A. Zadeh, A New Direction in AI — Toward a Computational Theory of Perceptions,AI Magazine, Vol 22, No. 1, pp. 73 - 84, 2001.
Editor information
Editors and Affiliations
Rights 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