Skip to main content

Summary

  • Chapter
  • First Online:
  • 240 Accesses

Part of the book series: Studies in Fuzziness and Soft Computing ((STUDFUZZ,volume 378))

Abstract

This monograph presents theory concerning interval-valued fuzzy calculus, especially aggregation operators among which there are placed recently introduced pos-aggregation functions and nec-aggregation functions. Moreover, applications of interval-valued fuzzy methods (and more generally interval modeling), especially mentioned so far interval-valued aggregation functions in classification are provided. The presented algorithms may support decision processes for example in medical diagnosis. It was shown that applying interval-valued methods make it possible to improve classification results in situation when there is a large number of missing values or there is a large number of attributes in the considered data sets. The mentioned methods were applied in a few experiments, involving machine learning methods, whose results are presented in this monograph. The obtained results of the described algorithms confirm their usefulness. They allow effective classification in the case of uncertainty (imprecise or incomplete information). The source codes of the presented classification algorithms (from Chaps. 4 and 5) are available at [1].

I love the fact that I get something new to do almost every day and have new challenges.

Jim Lee

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   84.99
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   109.99
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

  1. http://diagres.ur.edu.pl/~fuzzydataminer/

  2. Bentkowska, U.: New types of aggregation functions for interval-valued fuzzy setting and preservation of pos-B and nec-B-transitivity in decision making problems. Inf. Sci. 424, 385–399 (2018)

    Article  MathSciNet  Google Scholar 

  3. Luengo, J., Herrera, F.: An automatic extraction method of the domains of competence for learning classifiers using data complexity measures. Knowl. Inf. Syst. 42, 147–180 (2015)

    Article  Google Scholar 

  4. Lucca, G., Sanz, J.A., Dimuro, G.P., Bedregal, B., Bustince, H.: Analyzing the behavior of aggregation and pre-aggregation functions in fuzzy rule-based classification systems with data complexity measures. In: Kacprzyk, J., et al. (eds.) Advances in Intelligent Systems and Computing, vol. 642, pp. 443–455. Springer AG, Cham (2018)

    Google Scholar 

  5. Beliakov, G.: How to build aggregation operators from data. Int. J. Intell. Syst. 18, 903–923 (2003)

    Article  Google Scholar 

  6. Beliakov, G., Gomez, D., James, J., Montero, J., Rodriguez, J.T.: Approaches to learning strictly-stable weights for data with missing values. Fuzzy Sets Syst. 325, 97–113 (2017)

    Article  MathSciNet  Google Scholar 

  7. Bartoszuk, M., Beliakov, G., Gagolewski, M., James, S.: Fitting aggregation functions to data: part I linearization and regularization. In: Carvalho, J.P., et al. (eds.) Information Processing and Management of Uncertainty in Knowledge-Based Systems, Part II, CCIS 611, IPMU 2016, Eindhoven, Netherlands, 2016, pp. 767–779. Springer International Publishing, Switzerland (2016)

    Google Scholar 

  8. Bartoszuk, M., Beliakov, G., Gagolewski, M., James, S.: Fitting aggregation functions to data: part II idempotization. In: Carvalho, J.P., et al. (eds.) Information Processing and Management of Uncertainty in Knowledge-Based Systems, Part II, CCIS 611, IPMU 2016, Eindhoven, Netherlands, 2016, pp. 780–789. Springer International Publishing, Switzerland (2016)

    Google Scholar 

  9. Beliakov, G.: Construction of aggregation functions from data using linear programming. Fuzzy Sets Syst. 160, 65–75 (2009)

    Article  MathSciNet  Google Scholar 

  10. Kaymak, U. Van Nauta Lemke, H.R.: Selecting an aggregation operator for fuzzy decision making. In: Proceedings of the 1994 IEEE 3rd International Fuzzy Systems Conference, vol. 2, pp. 1418–1422. Orlando, FL (1994)

    Google Scholar 

  11. Beliakov, G., Calvo, T.: Constructions of aggregation operators that preserve ordering of the data. In: Štěpnička, M., Novák, V., Bodenhofer, U. (eds.) New Dimensions in Fuzzy Logic and Related Technologies. Proceedings of the 5th EUSFLAT Conference, Ostrava, Czech Republic, 11–14 Sept 2007, pp. 61–66. Universitas Ostraviensis, Ostrava (2007)

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Urszula Bentkowska .

Rights and permissions

Reprints and permissions

Copyright information

© 2020 Springer Nature Switzerland AG

About this chapter

Check for updates. Verify currency and authenticity via CrossMark

Cite this chapter

Bentkowska, U. (2020). Summary. In: Interval-Valued Methods in Classifications and Decisions. Studies in Fuzziness and Soft Computing, vol 378. Springer, Cham. https://doi.org/10.1007/978-3-030-12927-9_7

Download citation

Publish with us

Policies and ethics