Skip to main content
SpringerLink
Log in
Book cover

Rough Sets in Knowledge Discovery 2 pp 13–36Cite as

Rough Approximation of a Preference Relation in a Pairwise Comparison Table

  • Chapter

Part of the book series: Studies in Fuzziness and Soft Computing ((STUDFUZZ,volume 19))

Abstract

A methodology for using rough sets for preference modelling in multi-criteria decision problems is presented. It operates on a pairwise comparison table (PCT), i.e. an information table whose objects are pairs of actions instead of single actions, and whose entries are binary relations (graded preference relations) instead of attribute values. PCT is a specific information table and, therefore, all the concepts of the rough set analysis can be adapted to it. However, the classical rough set approximations based on indiscernibility relation do not consider the ordinal properties of the criteria in a decision problem. To deal with these properties, a rough approximation based on graded dominance relations has been recently proposed. The decision rules obtained from these rough approximations can be used to obtain a recommendation in different multi-criteria decision problems. The methodology is illustrated by an example which compares the results obtained when using the rough approximation by indiscernibility relation and the rough approximation by graded dominance relations, respectively.

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

Chapter
USD   29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD   169.00
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD   219.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD   219.99
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

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Bouyssou, D.: Ranking methods based on valued preference relations: a characterization of the net flow method. European Journal of Operational Research 60 (1992a) 61–68

    Article  Google Scholar 

  2. Bouyssou, D.: A note on the sum of differences choice function for fuzzy preference relations. Fuzzy sets and systems 47 (1992b) 197–202

    Article  Google Scholar 

  3. Bouyssou, D.: Outranking relations: do they have special properties?. Journal of Multi-Criteria Decision Analysis 5/2 (1996) 99–111

    Google Scholar 

  4. Brans, J. P., Vincke, Ph.: A preference ranking organization method. Management Science 31 (1985) 647–656

    Article  Google Scholar 

  5. Cozzens, M., Roberts, F.: Multiple semiorders and multiple indifference graphs. SIAM Journal of Algebraic Discrete Methods 3 (1982) 566–583

    Article  Google Scholar 

  6. Doignon, J.P.: Threshold representation of multiple semiorders. SIAM Journal of Algebraic Discrete Methods 8 (1987) 77–84

    Article  Google Scholar 

  7. Doignon, J. P., Monjardet, B., Roubens, M., Vincke, Ph.: Biorder families, valued relations and preference modelling,. Journal of Mathematical Psychology 30 (1986) 435–480

    Article  Google Scholar 

  8. Fishburn, P. C. Methods for estimating additive utilities. Management Science 13 (1967) 435–453

    Article  Google Scholar 

  9. Fishburn, P. C.: The theory of social choice. Princeton University Press, Princeton NJ (1973)

    Google Scholar 

  10. Fodor, J., Roubens, M.: Fuzzy preference modelling and multicriteria decision support. Kluwer Academic Publishers, Dordrecht (1994)

    Book  Google Scholar 

  11. Goodman, L. A.: On methods of amalgamation. In: R.M. Thrall, C.H. Coombs and R.L. Davis (eds.), Decision processes, Wiley, New York (1954) 39–48.

    Google Scholar 

  12. Greco S., Matarazzo, B., Slowinski, R.: Rough set approach to multi-attribute choice and ranking problems. ICS Research Report 38/95, Warsaw University of Technology, Warsaw (1995). Also in: G. Fandel and T. Gal (eds.), Multiple criteria decision making. Proceedings of the Twelfth International Conference, Hagen ( Germany) Springer-Verlag, Berlin (1997) 318–329

    Google Scholar 

  13. Greco S., Matarazzo, B., Slowinski, R.: Rough approximation of a preference relation by dominance relations. ICS Research Report 16/96, Warsaw University of Technology, Warsaw (1996)

    Google Scholar 

  14. Greco S., Matarazzo, B., Slowinski, R., Tsoukias, A.: Exploitation of a rough approximation of the outranking relation. In: Selected papers of the Thirteenth International Conference on Multiple Criteria Decision Making, CapeTown (South Africa), Springer-Verlag, Berlin (1997)

    Google Scholar 

  15. Grzymala-Busse, J.W.: ‘LERS–a system for learning from examples based on rough sets. In: R. Slowinski (ed.), Intelligent decision support. Handbook of applications and advances of the rough sets theory, Kluwer Academic Publishers, Dordrecht (1992) 3–18

    Chapter  Google Scholar 

  16. Henriet, D.: The Copeland choice function–an axiomatic characterization. Social Choice and Welfare 2 (1985) 49–64

    Article  Google Scholar 

  17. Jacquet-Lagrèze, E.: Systèmes de décision et acteurs multiples - contribution à une théorie de l’action pour les sciences des organisations. Thèse d’Etat, Université de Paris-Dauphine, Paris (1981)

    Google Scholar 

  18. Jacquet-Lagrèze, E.: Interactive assessment of preference using holistic judgements–the PREFCALC system. In: C. A. Bana e Costa (ed.), Readings in multiple criteria decision aid, Springer-Verlag, Berlin 335–350

    Google Scholar 

  19. Jacquet-Lagrèze, E., Siskos, J.: Assessing a set of additive utility functions for multicriteria decision-making, the UTA method. European Journal of Operational Research 10 (1982) 151–164

    Article  Google Scholar 

  20. Keeney, R. L., Raiffa, H.: Decision with multiple objectives - preferences and value tradeoffs. Wiley, New York (1976)

    Google Scholar 

  21. March, J. G.: Bounded rationality, ambiguity, and the engineering of choice. In: D. E. Bell, H., Raiffa, A. Tversky (eds), Decision making, descriptive, normative and prescriptive interactions, Cambridge University Press, New York (1988) 33–58

    Google Scholar 

  22. Mienko, R., Stefanowski, J., Toumi, K., Vanderpooten, D.: Discovery-oriented induction of decision rules. Cahier du LAMSADE 141 Université de Paris - Dauphine, Paris (1996)

    Google Scholar 

  23. Moreno, J.A., Tsoukias, A.: On nested interval orders and semiorders. Annals of Operations Research (1996) (to appear)

    Google Scholar 

  24. Mousseau, V.: Problèmes liés à l’évaluation de l’importance en aide multicritère à la décision: réflexions théoriques et expérimentations. Thèse, Université de Paris-Dauphine, Paris (1993)

    Google Scholar 

  25. Pawlak, Z.: Rough sets. International Journal of Information & Computer Sciences 11 (1982) 341–356

    Article  Google Scholar 

  26. Pawlak, Z.: Rough sets: theoretical aspects of reasoning about data. Kluwer Academic Publishers, Dordrecht (1991)

    Google Scholar 

  27. Pawlak, Z., Slowinski, R.: Rough set approach to multi-attribute decision analysis. European Journal of Operational Research 72 (1994) 443–459

    Article  Google Scholar 

  28. Roberts, F. S.: Homogeneous families of semiorders and the theory of probabilistic consistency. J. Math. Psycho. 8 (1971) 248–263

    Article  Google Scholar 

  29. Roubens, M., Vincke, Ph.: Preference modelling. Springer-Verlag, Berlin (1985)

    Book  Google Scholar 

  30. Roy, B.: Méthodologie multicritère d’aide à la décision. Economica, Paris (1985)

    Google Scholar 

  31. Roy, B.: The outranking approach and the foundation of ELECTRE methods. Theory and Decision 31 (1991) 49–73

    Article  Google Scholar 

  32. Roy, B.: Decision science or decision aid science. European Journal of Operational Research. Special Issue on Model Validation in Operations Research 66 (1993) 184–203

    Google Scholar 

  33. Roy, B., Slowinski, R., Treichel, W.: Multicriteria programming of water supply systems for rural areas. Water Resources Bulletin 28/1 (1992) 13–31

    Google Scholar 

  34. Rubinstein, A: Ranking the participants in a tournament. SIAM Journal of Applied Mathematics 38 (1980) 108–111

    Article  Google Scholar 

  35. Skowron, A.: Boolean reasoning for decision rules generation. In: J. Komorowski, Z.W. Ras, (eds.), Methodologies for Intelligent Systems, Lecture Notes in Artificial Intelligence 689 Springer -Verlag, Berlin (1993) 295–305

    Chapter  Google Scholar 

  36. Slovic, P.: Choice between equally-valued alternatives. Journal of Experimental Psychology: Human Perception Performance 1 (1975) 280–287

    Article  Google Scholar 

  37. Slowinski, R.: Rough set learning of preferential attitude in multi-criteria decision making. In: J. Komorowski, Z.W. Ras (eds.), Methodologies for Intelligent Systems, Lecture Notes in Artificial Intelligence 689 Springer-Verlag, Berlin (1993) 642–651

    Chapter  Google Scholar 

  38. Slowinski, R., Stefanowski, J.: RoughDAS and RoughClass software implementations of the rough sets approach. In: R. Slowinski (ed.), Intelligent decision support. Handbook of applications and advances of the rough sets theory, Kluwer Academic Publishers, Dordrecht (1992) 445–456

    Chapter  Google Scholar 

  39. Tsoukias, A., Vincke, Ph.: A survey on non-conventional preference modelling. Ricerca Operativa 61 (1992) 5–49

    Google Scholar 

  40. Tsoukias, A., Vincke, Ph.: A new axiomatic foundation of the partial comparability theory. Theory and Decision 39 (1995) 79–114

    Article  Google Scholar 

  41. Ziarko, W., Golan, D., Edwards, D.: An application of DATALOGIC/R knowledge discovery tool to identify strong predictive rules in stock market data. In: Proc. AAAI Workshop on Knowledge Discovery in Databases, Washington D.C. (1993) 89–101.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Faculty of Economics, University of Catania, Corso Italia, 55, 95129, Catania, Italy

    Salvatore Greco & Benedetto Matarazzo

  2. Institute of Computing Science, Poznan University of Technology, 60-965, Poznan, Poland

    Roman Słowiński

Authors
  1. Salvatore Greco
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Benedetto Matarazzo
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Roman Słowiński
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. Institute of Mathematics, Warsaw University of Technology, Pl. Politechniki 1, 00-665, Warsaw, Poland

    Lech Polkowski

  2. Polish-Japanese Institute of Computer Techniques, Koszykowa 86, 02-008, Warsaw, Poland

    Lech Polkowski

  3. Institute of Mathematics, Warsaw University, ul. Banacha 2, 02-097, Warsaw, Poland

    Andrzej Skowron

Rights and permissions

Reprints and permissions

Copyright information

© 1998 Springer-Verlag Berlin Heidelberg

About this chapter

Cite this chapter

Greco, S., Matarazzo, B., Słowiński, R. (1998). Rough Approximation of a Preference Relation in a Pairwise Comparison Table. In: Polkowski, L., Skowron, A. (eds) Rough Sets in Knowledge Discovery 2. Studies in Fuzziness and Soft Computing, vol 19. Physica, Heidelberg. https://doi.org/10.1007/978-3-7908-1883-3_2

Download citation

  • DOI: https://doi.org/10.1007/978-3-7908-1883-3_2

  • Publisher Name: Physica, Heidelberg

  • Print ISBN: 978-3-7908-2459-9

  • Online ISBN: 978-3-7908-1883-3

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics

Search

Navigation