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On Model Evaluation, Indexes of Importance, and Interaction Values in Rough Set Analysis

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Rough-Neural Computing

Part of the book series: Cognitive Technologies ((COGTECH))

Summary

As with most data models, “computing with words” uses a mix of methods to achieve its aims, including several measurement indexes. In this chapter, we discuss some proposals for such indexes in the context of rough set analysis, and we present some new ones.

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References

  1. J.F. Banzhaf. Weighted voting doesn’t work: A mathematical analysis.Rutgers Law Review19: 317–343,1965.

    Google Scholar 

  2. J. Cohen. Statistical Power Analysis for the Behavioral Sciences. Erlbaum, Hillsdale, NJ, 1988.

    MATH  Google Scholar 

  3. J. Cohen. Things I have learned (so far).American Psychologist45: 1304–1312,1990.

    Article  Google Scholar 

  4. P. Dubey. On the uniqueness of the Shapley value.International Journal of Game Theory4: 131–139, 1975.

    Article  MathSciNet  MATH  Google Scholar 

  5. P. Dubey, L. Shapley. Mathematical properties of the Banzhaf power index.Mathematics of Operations Research4(2): 99–131, 1979.

    Article  MathSciNet  MATH  Google Scholar 

  6. D. Dubois, M. Grabisch, F. Modave, H. Prade. Relating decision under uncertainty and multicriteria decision making models. Technical Report, IRIT-CNRS Université P. Sabatier, Toulouse, 1997.

    Google Scholar 

  7. I. Düntsch, G. Gediga. Statistical evaluation of rough set dependency analysis.International Journal of Human Computer Studies46: 589–604,1997.

    Article  Google Scholar 

  8. I. Düntsch, G. Gediga. Uncertainty measures of rough set prediction.Artificial Intelligence106(1): 77–107, 1998.

    Article  MathSciNet  Google Scholar 

  9. I. Düntsch, G. Gediga.Rough Set Data Analysis: A Road to Non-Invasive Knowledge DiscoveryVol. 2 ofMethoSos Primers. MethoSos Publishers (UK), Bangor, 2000.

    Google Scholar 

  10. G. Gediga, I. Düntsch. Rough approximation quality revisited.Artificial Intelligence132: 219–234, 2001.

    Article  MATH  Google Scholar 

  11. M. Grabisch. The application of fuzzy integrals in multicriteria decision making.European Journal of Operational Research89: 445–456, 1996.

    Article  MATH  Google Scholar 

  12. M. Grabisch. k-additive and k-decomposable measures. InProceedings of the Linz Seminar1997.

    Google Scholar 

  13. S. Greco, B. Matarazzo, R. Slowinski. Fuzzy measure technique for rough set analysis. In H.-J. Zimmermann, editorProceedings of the 6th European Congress on Intelligent Techniques and Soft Computing (EUFIT’98)99–103, Verlag Mainz, Aachen, 1998.

    Google Scholar 

  14. S. Greco, B. Matarazzo, R. Slowinski. Rough sets theory for multicriteria decision analysis.European Journal of Operational Research129: 1–47, 2001.

    Article  MathSciNet  MATH  Google Scholar 

  15. D. Hildebrand, J. Laing, H. Rosenthal. Prediction logic and quasi-independence in empirical evaluation of formal theory.Journal of Mathematical Sociology3: 197–209, 1974.

    Article  MATH  Google Scholar 

  16. J. Komorowski, Z. Pawlak, L. Polkowski, A. Skowron. Rough sets: A tutorial. In S.K. Pal, A. Skowron, editorsRough Fuzzy Hybridization: A New Trend in Decision-Making3–98, Springer, Singapore, 1999.

    Google Scholar 

  17. A. Laruelle, F. Valenciano. Shapley-Shubik and Banzhaf indices revisited.Mathematics of Operations Research(in press).

    Google Scholar 

  18. J.-L. Marichal. An axiomatic approach of the discrete Choquet integral as a tool to aggregate interacting criteria.IEEE Transactions on Fuzzy Systems(submitted).

    Google Scholar 

  19. J.-L. Marichal, P. Mathonet. On comparison meaningfulness of aggregation function.Journal of Mathematical Psychology45: 213–223,2000.

    Article  Google Scholar 

  20. F. Miller. Computer study into the causes of 1965–1966 traffic deaths in Jacksonville, Florida (manuscript).

    Google Scholar 

  21. T. Murofushi, S. Soneda. Techniques for reading fuzzy measures iii: Interaction index. InProceedings of the 9th Fuzzy System Symposium693–696, Sapporo, Japan, 1993 (in Japanese).

    Google Scholar 

  22. Z. Pawlak. Rough sets.International Journal of Computer and Information Sciences11: 341–356,1982.

    Article  MATH  Google Scholar 

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

    MATH  Google Scholar 

  24. Z. Pawlak. Rough set approach to knowledge-based decision support.European Journal of Operational Research99(1): 48–57, 1997.

    Article  MATH  Google Scholar 

  25. Z. Pawlak, K. Slowinski, R. Slowinski. Rough classification of patients after highly selective vagotomy for duodenal ulcer.International Journal of Man-Machine Studies24: 413–433, 1986

    Article  Google Scholar 

  26. A.E. Roth, editor.The Shapley Value - Essays in Honor of Lloyd S. Shapley.Cambridge University Press, Cambridge, 1976.

    Google Scholar 

  27. M. Roubens. Interaction between criteria through the use of fuzzy measures. Technical Report number 96.007 of the Institute de Mathématique, Université de Liège, Liège, 1996.

    Google Scholar 

  28. L.S. Shapley. A value for n-person games. In H. W. Kuhn, A. W. Tucker, editorsContributions to the Theory of Games II307–317, Princeton University Press, Princeton, NJ, 1953.

    Google Scholar 

  29. M. Shubik (1997). Game theory, complexity, and simplicity (manuscript). Available athttp://citeseer.nj.nec.com/article/shubik97game.html.

    Google Scholar 

  30. K. Slowirski. Rough classification of HSV patients. In R. Slowinski, editorIntelligent Decision Support: Handbook of Applications and Advances of Rough Set Theory77–94, Kluwer, Dordrecht, 1992.

    Chapter  Google Scholar 

  31. J. Stepaniuk. Knowledge discovery by application of rough set models. In L. Polkowski, S. Tsumoto, S., T. Y. Lin, editorsRough Set Methods and Applications: New Developments in Knowledge Discovery in Information Systems137–233, Physica, Heidelberg, 2000.

    Chapter  Google Scholar 

  32. S.S. Stevens. Mathematics, measurement, and psychophysics. In S.S. Stevens, editorHandbook of Experimental PsychologyWiley, New York, 1951.

    Google Scholar 

  33. P.D. Straffin. The Shapley-Shubik and Banzhaf power indices as probabilities. In [26], 71–81, 1976.

    Google Scholar 

  34. F. Vogel. Probleme und Veifahren der numerischen Klassifikation. Vandenhoeck & Ruprecht, Göttingen, 1975.

    Google Scholar 

  35. D.H. Wolpert, W.G. Macready. No free lunch theorems for search. Technical Report number SFI-TR-95–02–010 of the Santa Fe Institute, Santa Fe, NM, 1995.

    Google Scholar 

  36. L. A. Zadeh. From computing with numbers to computing with words: From manipulation of measurements to manipulation of perceptions.IEEE Transactions in Circuits and Systems45(1): 105–119, 1999.

    Article  MathSciNet  Google Scholar 

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Gediga, G., Düntsch, l. (2004). On Model Evaluation, Indexes of Importance, and Interaction Values in Rough Set Analysis. In: Pal, S.K., Polkowski, L., Skowron, A. (eds) Rough-Neural Computing. Cognitive Technologies. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-18859-6_10

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  • DOI: https://doi.org/10.1007/978-3-642-18859-6_10

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-62328-8

  • Online ISBN: 978-3-642-18859-6

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