Skip to main content

Fuzzy Logic in Computer Science

  • Chapter
  • First Online:

Abstract

Many researchers and practitioners in the field of artificial intelligence (and intelligent systems in particular) want to make computers smart. Unlike computers, human beings have great capacities to deal with ill-defined concepts, e.g., natural language. Even today, one wonders whether computers will ever be able to process vague information meaningfully. Fuzzy logic is such an approach to tackle this problem. In this chapter we therefore mainly introduce basic ideas and concepts of fuzzy logic. We discuss selected applications of fuzzy logic relevant to computer science and provide a list of references for further reading. The primary audience of the chapter are computer scientists and engineers.

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

Buying options

Chapter
USD   29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD   39.99
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD   54.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD   54.99
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

Learn about institutional subscriptions

References

  • Bezdek, J.C.: Fuzzy mathematics in pattern classification. PhD thesis, Cornell University, Itheca, NY, USA (1973)

    Google Scholar 

  • Bezdek, J.C.: Pattern Recognition with Fuzzy Objective Function Algorithms. Kluwer Academic Publishers, Norwell, MA, USA (1981)

    MATH  Google Scholar 

  • Bezdek, J.C., Keller, J., Krisnapuram, R., Pal, N.R.: Fuzzy Models and Algorithms for Pattern Recognition and Image Processing, The Handbooks of Fuzzy Sets, vol. 4. Kluwer Academic Publishers (1999)

    Google Scholar 

  • Boixader, D., Jacas, J.: Extensionality based approximate reasoning. International Journal of Approximate Reasoning 19(3–4), 221–230 (1998). DOI 10.1016/S0888-613X(98)00018-8

    Article  MATH  MathSciNet  Google Scholar 

  • Belohlavek, R.: Fuzzy Relational Systems: Foundations and Principles, IFSR International Series on Systems Science and Engineering, vol. 20. Kluwer Academic Publishers (2002)

    Google Scholar 

  • Belohlavek, R., Klir, G.J.: On Elkan’s theorems: Clarifying their meaning via simple proofs: Research articles. International Journal of Intelligent Systems 22, 203–207 (2007). DOI 10.1002/int.v22:2. ACM ID: 1190438

    Article  MATH  Google Scholar 

  • Belohlavek, R., Klir, G.J. (eds.): Concepts and Fuzzy Logic. MIT Press, Cambridge, MA, USA (2011)

    Google Scholar 

  • Belohlavek, R., Vychodil, V.: Fuzzy Equational Logic, Studies in Fuzziness and Soft Computing, vol. 186. Springer (2005)

    Google Scholar 

  • Belohlavek, R., Vychodil, V.: Attribute implications in a fuzzy setting. In: Formal Concept Analysis, Lecture Notes in Computer Science, vol. 3874, pp. 45–60. Springer-Verlag (2006)

    Google Scholar 

  • Cheeseman, P.: An inquiry into computer understanding. Computational Intelligence 4, 58–66 (1988)

    Article  Google Scholar 

  • Cheeseman, P.: Probabilistic versus fuzzy reasoning. In: L.N.K. Kanal, Lemmer (eds.) UAI ’85: Proceedings of the First Annual Conference on Uncertainty in Artificial Intelligence. Elsevier, New York, NY, USA (1988)

    Google Scholar 

  • Cignoli, R., Esteva, F., Godo, L., Torrens, A.: Basic fuzzy logic is the logic of continuous t-norms and their residua. Soft Computing 4(2), 106–112 (2000). DOI 10.1007/s005000000044

    Article  Google Scholar 

  • Cordón, O., del Jesus, M.J., Herrera, F.: A proposal on reasoning methods in fuzzy rule-based classification systems. International Journal of Approximate Reasoning 20(1), 21–45 (1999). DOI 10.1016/ S0888-613X(00)88942-2

    Google Scholar 

  • Cordón, O., Gomide, F., Herrera, F., Hoffmann, F., Magdalena, L.: Ten years of genetic fuzzy systems: current framework and new trends. Fuzzy Sets and Systems 141(1), 5–31 (2004). DOI 10.1016/S0165-0114(03) 00111-8

    Article  MATH  MathSciNet  Google Scholar 

  • Dickerson, J.A., Kosko, B.: Fuzzy function approximation with ellipsoidal rules. IEEE Transactions on Systems, Man, and Cybernetics, Part B: Cybernetics 26(4), 542–560 (1996). DOI 10.1109/3477.517030

    Article  Google Scholar 

  • Dubois, D., Prade, H.: The generalized modus ponens under sup-min composition – a theoretical study. In: M.M. Gupta, A. Kandel, W. Bandler, J.B. Kiszka (eds.) Approximate Reasoning in Expert Systems, pp. 217–232. Elsevier Science Publisher B.V. (North-Holland), Amsterdam, Netherlands (1985)

    Google Scholar 

  • Dubois, D., Prade, H.: Possibility Theory: An Approach to Computerized Processing of Uncertainty. Plenum Press, New York, NY, USA (1988)

    MATH  Google Scholar 

  • Dubois, D., Prade, H.: Possibility theory as a basis for preference propagation in automated reasoning. In: 1992 IEEE International Conference on Fuzzy Systems, pp. 821–832. IEEE Press, New York, NY, USA (1992). DOI 10. 1109/FUZZY.1992.258765

    Google Scholar 

  • Duda, R.O., Hart, P.E.: Pattern Classification and Scene Analysis. John Wiley & Sons, Ltd., New York, NY, USA (1973)

    MATH  Google Scholar 

  • Elkan, C.: The paradoxical success of fuzzy logic. In: Proceedings of the 11th National Conference on Artificial Intelligence, pp. 698–703. AAAIPress/MIT Press, Cambridge, MA, USA (1993)

    Google Scholar 

  • Elkan, C.: The paradoxical success of fuzzy logic. IEEE Expert: Intelligent Systems and Their Applications 9, 3–8 (1994). DOI 10.1109/64.336150. ACM ID: 630036

    Google Scholar 

  • Gerla, G.: Fuzzy Logic: Mathematical Tools for Approximate Reasoning. Kluwer Academic Publishers, Dordrecht, Netherlands (2001)

    MATH  Google Scholar 

  • Goguen, J.A.: The logic of inexact concepts. Synthese 19(3–4), 325–373 (1968). DOI 10.1007/BF00485654

    Google Scholar 

  • Gottwald, S.: A Treatise on Many-Valued Logics, Studies in Logic and Computation, vol. 9. Research Studies Press, Baldock, Hertfordshire, England (2001)

    Google Scholar 

  • Hájek, P.: Metamathematics of Fuzzy Logic, Trends in Logic, vol. 4. Kluwer Academic Publishers, Boston, MA, USA (1998)

    Book  Google Scholar 

  • Hájek, P.: What is mathematical fuzzy logic. Fuzzy Sets and Systems 157(5), 597–603 (2006). DOI 10.1016/j.fss.2005.10.004

    Article  MATH  MathSciNet  Google Scholar 

  • Höppner, F., Klawonn, F., Kruse, R., Runkler, T.: Fuzzy Cluster Analysis: Methods for Classification, Data Analysis and Image Recognition. John Wiley & Sons, Ltd., New York, NY, USA (1999)

    MATH  Google Scholar 

  • Hühn, J.C., Hüllermeier, E.: FR3: a fuzzy rule learner for inducing reliable classifiers. IEEE Transactions on Fuzzy Systems 17(1), 138–149 (2009). DOI 10.1109/TFUZZ.2008.2005490

    Article  Google Scholar 

  • Keller, A., Kruse, R.: Fuzzy rule generation for transfer passenger analysis. In: L. Wang, S.K. Halgamuge, X. Yao (eds.) Proceedings of the 1st International Conference on Fuzzy Systems and Knowledge Discovery (FSDK’02), pp. 667–671. Orchid Country Club, Singapore (2002)

    Google Scholar 

  • Klawonn, F., Castro, J.L.: Similarity in fuzzy reasoning. Mathware & Soft Computing 2(3), 197–228 (1995)

    MATH  MathSciNet  Google Scholar 

  • Klawonn, F., Gebhardt, J., Kruse, R.: Fuzzy control on the basis of equality relations with an example from idle speed control. IEEE Transactions on Fuzzy Systems 3(3), 336–350 (1995). DOI 10.1109/91.413237

    Article  Google Scholar 

  • Klawonn, F., Kruse, R.: Equality relations as a basis for fuzzy control. Fuzzy Sets and Systems 54(2), 147–156 (1993). DOI 10.1016/0165-0114(93) 90272-J

    Article  MATH  MathSciNet  Google Scholar 

  • Klawonn, F., Kruse, R.: Automatic generation of fuzzy controllers by fuzzy clustering. In: 1995 IEEE International Conference on Systems, Man, and Cybernetics: Intelligent Systems for the 21st Century, vol. 3, pp. 2040–2045. IEEE Press, Vancouver, BC, Canada (1995). DOI 10.1109/ ICSMC.1995.538079

    Google Scholar 

  • Klawonn, F., Kruse, R.: Constructing a fuzzy controller from data. Fuzzy Sets and Systems 85(2), 177–193 (1997). DOI 10.1016/0165-0114(95)00350-9

    Article  MathSciNet  Google Scholar 

  • Klawonn, F., Novák, V.: The relation between inference and interpolation in the framework of fuzzy systems. Fuzzy Sets and Systems 81(3), 331–354 (1996). DOI 10.1016/0165-0114(96)83710-9

    Article  MATH  MathSciNet  Google Scholar 

  • Klement, E.P., Mesiar, R., Pap, E.: Triangular Norms, Trends in Logic, vol. 8. Kluwer Academic Publishers, Dordrecht, Netherlands (2000)

    Google Scholar 

  • Klir, G.J.: Is there more to uncertainty than some probability theorists might have us belive? International Journal of General Systems 15(4), 347–378 (1989). DOI 10.1080/03081078908935057

    Article  MATH  Google Scholar 

  • Klir, G.J., Yuan, B.: Fuzzy Sets and Fuzzy Logic: Theory and Applications. Prentice Hall, Upper Saddle River, NJ, USA (1995)

    MATH  Google Scholar 

  • Kosko, B.: Fuzziness vs. probability. International Journal of General Systems 17(2), 211–240 (1990). DOI 10.1080/03081079008935108

    Google Scholar 

  • Kruse, R., Döring, C., Lesot, M.: Fundamentals of fuzzy clustering. In: J.V. de Oliveira, W. Pedrycz (eds.) Advances in Fuzzy Clustering and its Applications, pp. 3–30. John Wiley & Sons, Ltd., Chichester, UK (2007)

    Google Scholar 

  • Kruse, R., Gebhardt, J., Klawonn, F.: Foundations of Fuzzy Systems. John Wiley & Sons Ltd, Chichester, UK (1994)

    Google Scholar 

  • Kuncheva, L.I.: Fuzzy Classifier Design, Studies in Fuzziness and Soft Computing, vol. 49. Physica-Verlag, Heidelberg, New York (2000)

    Google Scholar 

  • Lindley, D.V.: The probability approach to the treatment of uncertainty in artificial intelligence and expert systems. Statistical Science 2(1), 17–24 (1987)

    Article  MATH  MathSciNet  Google Scholar 

  • Loginov, V.I.: Probability treatment of zadeh membership functions and their use in pattern recognition. Engineering Cybernetics 4(2), 68–69 (1966)

    Google Scholar 

  • Mamdani, E.H., Assilian, S.: An experiment in linguistic synthesis with a fuzzy logic controller. International Journal of Man-Machine Studies 7(1), 1–13 (1975). DOI 10.1016/S0020-7373(75)80002-2

    Article  MATH  Google Scholar 

  • Moewes, C., Kruse, R.: Unification of fuzzy SVMs and rule extraction methods through imprecise domain knowledge. In: J.L. Verdegay, L. Magdalena, M. Ojeda-Aciego (eds.) Proceedings of the International Conference on Information Processing and Management of Uncertainty in Knowledge-Based Systems (IPMU-08), pp. 1527–1534. Torremolinos (Málaga) (2008)

    Google Scholar 

  • Nauck, D., Klawonn, F., Kruse, R.: Foundations of Neuro-Fuzzy Systems. John Wiley & Sons, Inc. (1997)

    Google Scholar 

  • Nauck, D., Kruse, R.: A neuro-fuzzy method to learn fuzzy classification rules from data. Fuzzy Sets and Systems 89(3), 277–288 (1997). DOI 10.1016/ S0165-0114(97)00009-2

    Article  MathSciNet  Google Scholar 

  • Nauck, D., Kruse, R.: Neuro-fuzzy systems for function approximation. Fuzzy Sets and Systems 101(2), 261–271 (1999). DOI 10.1016/S0165-0114(98) 00169-9

    Article  MATH  MathSciNet  Google Scholar 

  • Novák, V., Perfilieva, I., Močkoř, J.: Mathematical Principles of Fuzzy Logic. Kluwer Academic Publishers, Dordrecht, Netherlands (1999)

    Book  MATH  Google Scholar 

  • Olaru, C., Wehenkel, L.: A complete fuzzy decision tree technique. Fuzzy Sets and Systems 138(2), 221–254 (2003). DOI 10.1016/S0165-0114(03) 00089-7

    Article  MathSciNet  Google Scholar 

  • Pavelka, J.: On fuzzy logic i, II, III. Zeitschrift für Mathematische Logik und Grundlagen der Mathematik 25, 45–52, 119–134, 447–464 (1979)

    Google Scholar 

  • Schröder, M., Petersen, R., Klawonn, F., Kruse, R.: Two paradigms of automotive fuzzy logic applications. In: M. Jamshidi, A. Titli, L. Zadeh, S. Boverie (eds.) Applications of Fuzzy Logic: Towards High Machine Intelligence Quotient Systems, Environmental and Intelligent Manufacturing Systems Series, vol. 9, pp. 153–174. Prentice-Hall, Inc., Upper Saddle River, NJ, USA (1997)

    Google Scholar 

  • Smith, N.J.J.: Vagueness and Degrees of Truth. Oxford University Press, New York, NY, USA (2009)

    Google Scholar 

  • Stevens, S.S.: On the theory of scales of measurement. Science 103(2684), 677–680 (1946). DOI 10.1126/science.103.2684.677

    Article  MATH  Google Scholar 

  • Sudkamp, T.: Similarity, interpolation, and fuzzy rule construction. Fuzzy Sets and Systems 58(1), 73–86 (1993). DOI 10.1016/0165-0114(93) 90323-A

    Article  MathSciNet  Google Scholar 

  • Sugeno, M., Yasukawa, T.: A fuzzy-logic-based approach to qualitative modeling. IEEE Transactions on Fuzzy Systems 1(1), 7–31 (1993). DOI 10. 1109/TFUZZ.1993.390281

    Article  Google Scholar 

  • Takagi, T., Sugeno, M.: Fuzzy identification of systems and its applications to modeling and control. IEEE Transactions on Systems, Man, and Cybernetics 15(1), 116–132 (1985)

    MATH  Google Scholar 

  • van Deemter, K.: Not Exactly: In Praise of Vagueness. Oxford University Press, New York, NY, USA (2010)

    Google Scholar 

  • Wang, L., Mendel, J.M.: Generating fuzzy rules by learning from examples. IEEE Transactions on Systems, Man, and Cybernetics 22(6), 1414–1427 (1992). DOI 10.1109/21.199466

    Article  MathSciNet  Google Scholar 

  • Zadeh, L.A.: Fuzzy sets. Information and Control 8(3), 338–353 (1965). DOI 10.1016/S0019-9958(65)90241-X

    Article  MATH  MathSciNet  Google Scholar 

  • Zadeh, L.A.: Probability measures of fuzzy events. Journal of Mathematical Analysis and Applications 23(2), 421–427 (1968). DOI 10.1016/ 0022-247X(68)90078-4

    Article  MATH  MathSciNet  Google Scholar 

  • Zadeh, L.A.: Outline of a new approach to the analysis of complex systems and decision processes. IEEE Transactions on Systems, Man, and Cybernetics 3(1), 28–44 (1973)

    Article  MATH  MathSciNet  Google Scholar 

  • Zadeh, L.A.: Fuzzy logic and approximate reasoning. Synthese 30(3-4), 407–428 (1975). DOI 10.1007/BF00485052

    Article  MATH  Google Scholar 

  • Zadeh, L.A.: Fuzzy sets as a basis for a theory of possibility. Fuzzy Sets and Systems 1(1), 3–28 (1978). DOI 10.1016/0165-0114(78)90029-5. (Reprinted in Fuzzy Sets and Systems 100 (Supplement 1), 9-34, (1999))

    Article  MATH  MathSciNet  Google Scholar 

  • Zadeh, L.A.: A theory of approximate reasoning. In: J.E. Hayes, D. Michie, L.I. Mikulich (eds.) Proceedings of the Ninth Machine Intelligence Workshop, no. 9 in Machine Intelligence, pp. 149–194. John Wiley & Sons, Ltd., New York, NY, USA (1979)

    Google Scholar 

  • Zadeh, L.A.: The role of fuzzy logic in the management of uncertainty in expert systems. Fuzzy Sets and Systems 11(1–3), 197–198 (1983). DOI 10.1016/S0165-0114(83)80081-5

    Article  MathSciNet  Google Scholar 

  • Zadeh, L.A.: Toward a perception-based theory of probabilistic reasoning with imprecise probabilities. Journal of Statistical Planning and Inference 105(1), 233–264 (2002). DOI 10.1016/S0378-3758(01)00212-9

    Article  MATH  MathSciNet  Google Scholar 

  • Zadeh, L.A.: Generalized theory of uncertainty (GTU)-principal concepts and ideas. Computational Statistics & Data Analysis 51(1), 15–46 (2006). DOI 10.1016/j.csda.2006.04.029

    Article  MATH  MathSciNet  Google Scholar 

  • Zadeh, L.: Toward human level machine intelligence - is it achievable? the need for a paradigm shift. IEEE Computational Intelligence Magazine 3(3), 11–22 (2008). DOI 10.1109/MCI.2008.926583

    Article  Google Scholar 

Download references

Acknowledgment

R. Belohlavek was supported by the ESF project No. CZ.1.07/2.3.00/20.0059 (co-financed by the European Social Fund and the state budget of the Czech Republic).

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Radim Belohlavek .

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2011 Springer Science+Business Media, LLC

About this chapter

Cite this chapter

Belohlavek, R., Kruse, R., Moewes, C. (2011). Fuzzy Logic in Computer Science. In: Blum, E., Aho, A. (eds) Computer Science. Springer, New York, NY. https://doi.org/10.1007/978-1-4614-1168-0_16

Download citation

  • DOI: https://doi.org/10.1007/978-1-4614-1168-0_16

  • Published:

  • Publisher Name: Springer, New York, NY

  • Print ISBN: 978-1-4614-1167-3

  • Online ISBN: 978-1-4614-1168-0

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics