Skip to main content

Valued Hesitation in Intervals Comparison

  • Conference paper
Scalable Uncertainty Management (SUM 2007)

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 4772))

Included in the following conference series:

Abstract

The paper presents a valued extension of the recently introduced concept of PQI interval order. The main idea is that, while comparing objects represented by interval of values there is a zone of hesitation between strict difference and strict similarity which could be modelled through valued relations. The paper presents suitable definitions of such valued relations fulfilling a number of interesting properties. The use of such a tool in data analysis and rough sets theory is discussed in the paper.

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

Access this chapter

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 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

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.

References

  1. Luce, R.D.: Semiorders and a theory of utility discrimination. Econometrica 24, 178–191 (1956)

    Article  MATH  MathSciNet  Google Scholar 

  2. Fishburn, P.C.: Interval Orders and Interval Graphs. J. Wiley, Chichester (1985)

    Google Scholar 

  3. Pirlot, M., Vincke, Ph.: Semi Orders. Kluwer Academic, Dordrecht (1997)

    Google Scholar 

  4. Tsoukiàs, A., Vincke, Ph.: A characterization of pqi interval orders. Discrete Applied Mathematics 127(2), 387–397 (2003)

    Article  MATH  MathSciNet  Google Scholar 

  5. Ngo The, A., Tsoukiàs, A., Vincke, Ph.: A polynomial time algorithm to detect PQI interval orders. International Transactions in Operational Research 7, 609–623 (2000)

    Article  MathSciNet  Google Scholar 

  6. Ngo The, A., Tsoukiàs, A.: Numerical representation of pqi interval orders. Discrete Applied Mathematics 147, 125–146 (2005)

    Article  MATH  MathSciNet  Google Scholar 

  7. Oztürk, M., Tsoukiàs, A.: Positive and negative reasons in interval comparisons: Valued pqi interval orders. In: Proceedings of IPMU 2004, pp. 983–989 (2004)

    Google Scholar 

  8. Roy, B., Vincke, P.: Relational systems of preference with one or more pseudo-criteria: Some new concepts and results. Management Science 30, 1323–1335 (1984)

    Article  MATH  MathSciNet  Google Scholar 

  9. Roy, B., Vincke, Ph.: Pseudo-orders: definition, properties and numerical representation. Mathematical Social Sciences 14, 263–274 (1987)

    Article  MATH  MathSciNet  Google Scholar 

  10. Perny, P., Roy, B.: The use of fuzzy outranking relations in preference modelling. Fuzzy Sets and Systems 49, 33–53 (1992)

    Article  MATH  MathSciNet  Google Scholar 

  11. Dubois, D., Prade, H.: Decision making under fuzziness. In: Advances in fuzzy set theory and applications, pp. 279–302. North Holland, Amsterdam (1979)

    Google Scholar 

  12. Dubois, D., Prade, H.: Fuzzy sets and systems - Theory and applications. Academic press, New York (1980)

    MATH  Google Scholar 

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

    MATH  Google Scholar 

  14. Perny, P., Roubens, M.: Fuzzy preference modelling. In: Słowiński, R. (ed.) Fuzzy sets in decision analysis, operations research and statistics, pp. 3–30. Kluwer Academic, Dordrecht (1998)

    Google Scholar 

  15. Ovchinnikov, S.N.: Modelling valued preference relation. In: Kacprzyk, J., Fedrizzi, M. (eds.) Multiperson decion making usingfuzzy sets and possibility theory, pp. 64–70. Kluwer, Dordrecht (1990)

    Google Scholar 

  16. Van De Walle, B., De Baets, B., Kerre, E.: Charaterizable fuzzy preference structures. Annals of Operations Research 80, 105–136 (1998)

    Article  MATH  MathSciNet  Google Scholar 

  17. Ozturk, M.: Structures mathématiques et logiques pour la comparaison des intervalles. Thése de doctorat, Université Paris-Dauphine (2005)

    Google Scholar 

  18. Pawlak, Z.: Rough Sets. Theoretical Aspects of Reasoning about Data. Kluwer, Dordrecht (1991)

    MATH  Google Scholar 

  19. Slowinski, R., Vanderpooten, D.: Similarity relation as a basis for rough approximations. In: P., W., (eds) Advances in Machine Intelligence & Soft-computing, Bookwrights, Raleigh, pp. 17–33 (1997)

    Google Scholar 

  20. Slowinski, R., Vanderpooten, D.: A generalized definition of rough approximations based on similarity. IEEE Transactions on Data and Knowledge Engineering 12, 331–336 (2000)

    Article  Google Scholar 

  21. Greco, S., Matarazzo, B., Slowinski, R.: Handling missing values in rough set analysis of multi-attribute and multi-criteria decision problems. In: Zhong, N., Skowron, A., Ohsuga, S. (eds.) New Directions in Rough Sets, Data Mining, and Granular-Soft Computing. LNCS (LNAI), vol. 1711, pp. 146–157. Springer, Heidelberg (1999)

    Google Scholar 

  22. Stefanowski, J., Tsoukiàs, A.: On the extension of rough sets under incomplete information. In: Zhong, N., Skowron, A., Ohsuga, S. (eds.) RSFDGrC 1999. LNCS (LNAI), vol. 1711, pp. 73–81. Springer, Heidelberg (1999)

    Google Scholar 

  23. Stefanowski, J., Tsoukiàs, A.: Valued tolerance and decision rules. In: Ziarko, W., Yao, Y. (eds.) RSCTC 2000. LNCS (LNAI), vol. 2005, pp. 212–219. Springer, Heidelberg (2001)

    Chapter  Google Scholar 

  24. Stefanowski, J., Tsoukiàs, A.: Incomplete information tables and rough classification. Computational Intelligence 17, 454–466 (2001)

    Article  Google Scholar 

  25. Perny, P., Tsoukiàs, A.: On the continuous extension of a four valued logic for preference modelling. In: Proceedings of the IPMU 1998 conference, Paris, pp. 302–309 (1998)

    Google Scholar 

  26. Tsoukiàs, A., Perny, P., Vincke, Ph.: From concordance/discordance to the modelling of positive and negative reasons in decision aiding. In: Bouyssou, D., Jacquet-Lagrèze, E., Perny, P., Słowiński, R., Vanderpooten, D., Vincke, P. (eds.) Aiding Decisions with Multiple Criteria: Essays in Honour of Bernard Roy, pp. 147–174. Kluwer Academic, Dordrecht (2002)

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Henri Prade V. S. Subrahmanian

Rights and permissions

Reprints and permissions

Copyright information

© 2007 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Öztürk, M., Tsoukiàs, A. (2007). Valued Hesitation in Intervals Comparison. In: Prade, H., Subrahmanian, V.S. (eds) Scalable Uncertainty Management. SUM 2007. Lecture Notes in Computer Science(), vol 4772. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-75410-7_12

Download citation

  • DOI: https://doi.org/10.1007/978-3-540-75410-7_12

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-75407-7

  • Online ISBN: 978-3-540-75410-7

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics