Skip to main content
SpringerLink
Log in

Introduction to Fuzzy Sets and Logic

  • Chapter
  • First Online:
Neural Networks and Statistical Learning

  • 4345 Accesses

Abstract

In many soft sciences (e.g., psychology, sociology, ethology), scientists provide verbal descriptions and explanations of various phenomena based on observations. Fuzzy logic provides the most suitable tool for verbal computation. It is a paradigm for modeling the uncertainty in human reasoning, and is a basic tool for machine learning and expert systems. This chapter introduces fuzzy sets and logic. Some associated topics on reasoning and granular computing are also described.

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

Access this chapter

Log in via an institution
eBook
USD 16.99
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 109.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 159.99
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

References

  1. Aamodt, A., & Plaza, E. (1994). Case-based reasoning: Foundational issues, methodological variations, and system approaches. AI Communications, 7(1), 39–59.

    Google Scholar 

  2. Bede, B., & Rudas, I. J. (2011). Approximation properties of fuzzy transforms. Fuzzy Sets and Systems, 180(1), 20–40.

    Article  MathSciNet  MATH  Google Scholar 

  3. Buckley, J. J. (1989). Fuzzy complex numbers. Fuzzy Sets and Systems, 33, 333–345.

    Article  MathSciNet  MATH  Google Scholar 

  4. Buckley, J. J. (1993). Sugeno type controllers are universal controllers. Fuzzy Sets and Systems, 53, 299–304.

    Article  MathSciNet  MATH  Google Scholar 

  5. Buckley, J. J., Hayashi, Y., & Czogala, E. (1993). On the equivalence of neural nets and fuzzy expert systems. Fuzzy Sets and Systems, 53, 129–134.

    Article  MathSciNet  MATH  Google Scholar 

  6. Buckley, J. J., & Eslami, E. (2002). An introduction to fuzzy logic and fuzzy sets. Heidelberg: Physica-Verlag.

    Book  MATH  Google Scholar 

  7. Davis, J. G., & Ganeshan, S. (2009). Aversion to loss and information overload: An experimental investigation. In Proceedings of the International Conference on Information Systems (Paper no. 11). Phoenix, AZ.

    Google Scholar 

  8. Dick, S. (2005). Toward complex fuzzy logic. IEEE Transactions on Fuzzy Systems, 13(3), 405–414.

    Article  Google Scholar 

  9. Dubois, D., Esteva, F., Garcia, P., Godo, L., de Mantaras, R. L., & Prade, H. (1997). Fuzzy modelling of case-based reasoning and decision. In D. B. Leake & E. Plaza (Eds.), Case-based reasoning research and development (Vol. 1266, pp. 599–610). LNAI. Berlin: Springer.

    Google Scholar 

  10. Ferrari-Trecate, G., & Rovatti, R. (2002). Fuzzy systems with overlapping Gaussian concepts: Approximation properties in Sobolev norms. Fuzzy Sets and Systems, 130, 137–145.

    Article  MathSciNet  MATH  Google Scholar 

  11. Figueiredo, M., Gomides, F., Rocha, A., & Yager, R. (1993). Comparison of Yager’s level set method for fuzzy logic control with Mamdani and Larsen methods. IEEE Transactions on Fuzzy Systems, 2, 156–159.

    Article  Google Scholar 

  12. Finnie, G., & Sun, Z. (2003). A logical foundation for the case-based reasoning cycle. International Journal of Intelligent Systems, 18, 367–382.

    Article  MATH  Google Scholar 

  13. Jang, J. S. R., & Sun, C. I. (1993). Functional equivalence between radial basis function networks and fuzzy inference systems. IEEE Transactions on Neural Networks, 4(1), 156–159.

    Article  Google Scholar 

  14. Leake, D. (1996). Case-based reasoning: Experiences, lessons, and future direction (p. 420). Menlo Park: AAAI Press/MIT Press.

    Google Scholar 

  15. Li, H. X., & Chen, C. L. P. (2000). The equivalence between fuzzy logic systems and feedforward neural networks. IEEE Transactions on Neural Networks, 11(2), 356–365.

    Article  Google Scholar 

  16. Karnik, N. N., & Mendel, J. M. (1999). Type-2 fuzzy logic systems. IEEE Transactions on Fuzzy Systems, 7(6), 643–658.

    Article  MATH  Google Scholar 

  17. Kosko, B. (1992). Fuzzy system as universal approximators. In Proceedings of IEEE International Conference on Fuzzy Systems (pp. 1153–1162). San Diego, CA.

    Google Scholar 

  18. Kosko, B. (1997). Fuzzy engineering. Englewood Cliffs: Prentice Hall.

    MATH  Google Scholar 

  19. Kreinovich, V., Nguyen, H. T., & Yam, Y. (2000). Fuzzy systems are universal approximators for a smooth function and its derivatives. International Journal of Intelligent Systems, 15, 565–574.

    Article  MATH  Google Scholar 

  20. Mamdani, E. H. (1974). Application of fuzzy algorithms for control of a simple dynamic plant. Proceedings of the IEEE, 12(1), 1585–1588.

    Google Scholar 

  21. Mantas, C. J., & Puche, J. M. (2008). Artificial neural networks are zero-order TSK fuzzy systems. IEEE Transactions on Fuzzy Systems, 16(3), 630–643.

    Article  Google Scholar 

  22. Mas, M., Monserrat, M., Torrens, J., & Trillas, E. (2007). A survey on fuzzy implication functions. IEEE Transactions on Fuzzy Systems, 15(6), 1107–1121.

    Article  Google Scholar 

  23. Mendel, J. M., Liu, F., & Zhai, D. (2009). \(\alpha \)-plane representation for type-2 fuzzy sets: Theory and applications. IEEE Transactions on Fuzzy Systems, 17(5), 1189–1207.

    Google Scholar 

  24. Mitra, S., & Hayashi, Y. (2000). Neuro-fuzzy rule generation: Survey in soft computing framework. IEEE Transactions on Neural Networks, 11(3), 748–768.

    Article  Google Scholar 

  25. Molodtsov, D. (1999). Soft set theory–first results. Computers & Mathematics with Applications, 37, 19–31.

    Article  MathSciNet  MATH  Google Scholar 

  26. Mondal, B., & Raha, S. (2011). Similarity-based inverse approximate reasoning. IEEE Transactions on Fuzzy Systems, 19(6), 1058–1071.

    Article  Google Scholar 

  27. Pawlak, Z. (1982). Rough sets. International Journal of Computer and Information Sciences, 11, 341–356.

    Article  MathSciNet  MATH  Google Scholar 

  28. Pawlak, Z. (1991). Rough sets–Theoretical aspects of reasoning about data. Dordrecht: Kluwer.

    MATH  Google Scholar 

  29. Pedrycz, W. (1998). Shadowed sets: Representing and processing fuzzy sets. IEEE Transactions on Systems, Man, and Cybernetics, Part B, 28, 103–109.

    Article  Google Scholar 

  30. Pedrycz, W. (2009). From fuzzy sets to shadowed sets: Interpretation and computing. International Journal of Intelligent Systems, 24, 48–61.

    Article  MATH  Google Scholar 

  31. Perfilieva, I. (2006). Fuzzy transforms: Theory and applications. Fuzzy Sets and Systems, 157, 993–1023.

    Article  MathSciNet  MATH  Google Scholar 

  32. Peters, G. (2011). Granular box regression. IEEE Transactions on Fuzzy Systems, 19(6), 1141–1152.

    Article  Google Scholar 

  33. Plaza, E., Esteva, F., Garcia, P., Godo, L., & de Mantaras, R. L. (1996). A logical approach to case-based reasoning using fuzzy similarity relations. Information Sciences, 106, 105–122.

    Article  MathSciNet  MATH  Google Scholar 

  34. Ramot, D., Friedman, M., Langholz, G., & Kandel, A. (2003). Complex fuzzy logic. IEEE Transactions on Fuzzy Systems, 11(4), 450–461.

    Article  Google Scholar 

  35. Ramot, D., Milo, R., Friedman, M., & Kandel, A. (2002). Complex fuzzy sets. IEEE Transactions on Fuzzy Systems, 10(2), 171–186.

    Article  Google Scholar 

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

    Article  MATH  Google Scholar 

  37. Tanaka, H. (1987). Fuzzy data analysis by possibilistic linear models. Fuzzy Sets and Systems, 24, 363–375.

    Article  MathSciNet  MATH  Google Scholar 

  38. Tanaka, K., & Sugeno, M. (1992). Stability analysis and design of fuzzy control systems. Fuzzy Sets and Systems, 45, 135–150.

    Article  MathSciNet  MATH  Google Scholar 

  39. Tsang, E. C. C., Chen, D., Yeung, D. S., Wang, X.-Z., & Lee, J. W. T. (2008). Attributes reduction using fuzzy rough sets. IEEE Transactions on Fuzzy Systems, 16(5), 1130–1141.

    Article  Google Scholar 

  40. Wagner, C., & Hagras, H. (2010). Toward general type-2 fuzzy logic systems based on \(z\)Slices. IEEE Transactions on Fuzzy Systems, 18(4), 637–660.

    Google Scholar 

  41. Wang, L. X. (1992). Fuzzy systems are universal approximators. In Proceedings of IEEE International Conference on Fuzzy Systems (pp. 1163–1170). San Diego, CA.

    Google Scholar 

  42. Wang, S., & Lu, H. (2003). Fuzzy system and CMAC network with B-spline membership/basis functions are smooth approximators. Soft Computing, 7, 566–573.

    Article  MATH  Google Scholar 

  43. Yen, J. (1999). Fuzzy logic–A modern perspective. IEEE Transactions on Knowledge and Data Engineering, 11(1), 153–165.

    Article  Google Scholar 

  44. Zadeh, L. A. (1965). Fuzzy sets. Information and Control, 8, 338–353.

    Article  MathSciNet  MATH  Google Scholar 

  45. Zadeh, L. A. (1975). The concept of a linguistic variable and its application to approximate reasoning–I, II, III. Information Sciences, 8, 199–249, 301–357; 9, 43–80.

    Article  MathSciNet  MATH  Google Scholar 

  46. Zadeh, L. A. (1978). Fuzzy sets as a basis for theory of possibility. Fuzzy Sets and Systems, 1, 3–28.

    Article  MathSciNet  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Electrical and Computer Engineering, Concordia University, Montreal, QC, Canada

    Ke-Lin Du & M. N. S. Swamy

  2. Xonlink Inc., Hangzhou, China

    Ke-Lin Du

Authors
  1. Ke-Lin Du
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. M. N. S. Swamy
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Ke-Lin Du .

Rights and permissions

Reprints and permissions

Copyright information

© 2019 Springer-Verlag London Ltd., part of Springer Nature

About this chapter

Check for updates. Verify currency and authenticity via CrossMark

Cite this chapter

Du, KL., Swamy, M.N.S. (2019). Introduction to Fuzzy Sets and Logic. In: Neural Networks and Statistical Learning. Springer, London. https://doi.org/10.1007/978-1-4471-7452-3_26

Download citation

Publish with us

Policies and ethics

Search

Navigation