Nothing Special   »   [go: up one dir, main page]

Skip to main content

Additive Preference Model with Piecewise Linear Components Resulting from Dominance-Based Rough Set Approximations

  • Conference paper
Artificial Intelligence and Soft Computing – ICAISC 2006 (ICAISC 2006)

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 4029))

Included in the following conference series:

Abstract

Dominance-based Rough Set Approach (DRSA) has been proposed for multi-criteria classification problems in order to handle inconsistencies in the input information with respect to the dominance principle. The end result of DRSA is a decision rule model of Decision Maker preferences. In this paper, we consider an additive function model resulting from dominance-based rough approximations. The presented approach is similar to UTA and UTADIS methods. However, we define a goal function of the optimization problem in a similar way as it is done in Support Vector Machines (SVM). The problem may also be defined as the one of searching for linear value functions in a transformed feature space obtained by exhaustive binarization of criteria.

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

Access this chapter

Subscribe and save

Springer+ Basic
$34.99 /Month
  • Get 10 units per month
  • Download Article/Chapter or eBook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 139.00
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever

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.

Similar content being viewed by others

References

  1. Boros, E., Hammer, P.L., Ibaraki, T., Kogan, A., Mayoraz, E., Muchnik, I.: An Implementation of Logical Analysis of Data. IEEE Trans. on Knowledge and Data Engineering 12, 292–306 (2000)

    Article  Google Scholar 

  2. Dembczyński, K., Pindur, R., Susmaga, R.: Generation of Exhaustive Set of Rules within Dominance-based Rough Set Approach. Electr. Notes Theor. Comput. Sci. 82(4) (2003)

    Google Scholar 

  3. Dembczyński, K., Greco, S., Słowiński, R.: Second-order Rough Approximations in Multi-criteria Classification with Imprecise Evaluations and Assignments. In: Ślęzak, D., Wang, G., Szczuka, M., Düntsch, I., Yao, Y. (eds.) RSFDGrC 2005. LNCS (LNAI), vol. 3641, pp. 54–63. Springer, Heidelberg (2005)

    Chapter  Google Scholar 

  4. Frank, E., Witten, I.H.: Data Mining: Practical machine learning tools and techniques, 2nd edn. Morgan Kaufmann, San Francisco (2005)

    MATH  Google Scholar 

  5. Greco, S., Matarazzo, B., Słowiński, R.: Rough approximation of a preference relation by dominance relations. European Journal of Operational Research 117, 63–83 (1999)

    Article  MATH  Google Scholar 

  6. Greco, S., Matarazzo, B., Słowiński, R.: Rough sets theory for multicriteria decision analysis. European Journal of Operational Research 129, 1–47 (2001)

    Article  MATH  MathSciNet  Google Scholar 

  7. Greco, S., Matarazzo, B., Słowiński, R.: Axiomatic characterization of a general utility function and its particular cases in terms of conjoint measurement and rough-set decision rules. European Journal of Operational Research 158, 271–292 (2004)

    Article  MATH  MathSciNet  Google Scholar 

  8. Jacquet-Lagréze, E., Siskos, Y.: Assessing a set of additive utility functions for multicriteria decision making: The UTA method. European Journal of Operational Research 10, 151–164 (1982)

    Article  MATH  Google Scholar 

  9. Jacquet-Lagréze, E.: An application of the UTA discriminant model for the evaluation of R&D projects. In: Pardalos, P.M., Siskos, Y., Zopounidis, C. (eds.) Advances in multicriteria analysis, pp. 203–211. Kluwer Academic Publishers, Dordrecht (1995)

    Google Scholar 

  10. Newman, D.J., Hettich, S., Blake, C.L., Merz, C.J. (eds.): UCI Repository of machine learning databases. Department of Information and Computer Science. University of California, Irvine (1998), http://www.ics.uci.edu/~mlearn/MLRepository.html

  11. Skowron, A., Rauszer, C.: The discernibility matrices and functions in information systems. In: Slowinski, R. (ed.) Intelligent Decision Support. Handbook of Applications and Advances of the Rough Set Theory, pp. 331–362. Kluwer Academic Publishers, Dordrecht (1992)

    Google Scholar 

  12. Słowiński, R., Greco, S., Matarazzo, B.: Axiomatization of utility, outranking and decision-rule preference models for multiple-criteria classification problems under partial inconsistency with the dominance principle. Control & Cybernetics 31, 1005–1035 (2002)

    MATH  Google Scholar 

  13. Słowiński, R., Greco, S., Matarazzo, B.: Rough Set Based Decision Support. In: Burke, E., Kendall, G. (eds.) Introductory Tutorials on Optimization, Search and Decision Support Methodologies, ch. 16, Springer, Heidelberg (2005)

    Google Scholar 

  14. Vapnik, V.: The Nature of Statistical Learning Theory. Springer, New York (1995)

    MATH  Google Scholar 

  15. Zopounidis, C., Doumpos, M.: PREFDIS: a multicriteria decision support system for sorting decision problems. Computers & Operations Research 27, 779–797 (2000)

    Article  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2006 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Dembczyński, K., Kotłowski, W., Słowiński, R. (2006). Additive Preference Model with Piecewise Linear Components Resulting from Dominance-Based Rough Set Approximations. In: Rutkowski, L., Tadeusiewicz, R., Zadeh, L.A., Żurada, J.M. (eds) Artificial Intelligence and Soft Computing – ICAISC 2006. ICAISC 2006. Lecture Notes in Computer Science(), vol 4029. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11785231_53

Download citation

  • DOI: https://doi.org/10.1007/11785231_53

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-35748-3

  • Online ISBN: 978-3-540-35750-6

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics