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.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
J.F. Banzhaf. Weighted voting doesn’t work: A mathematical analysis.Rutgers Law Review19: 317–343,1965.
J. Cohen. Statistical Power Analysis for the Behavioral Sciences. Erlbaum, Hillsdale, NJ, 1988.
J. Cohen. Things I have learned (so far).American Psychologist45: 1304–1312,1990.
P. Dubey. On the uniqueness of the Shapley value.International Journal of Game Theory4: 131–139, 1975.
P. Dubey, L. Shapley. Mathematical properties of the Banzhaf power index.Mathematics of Operations Research4(2): 99–131, 1979.
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.
I. Düntsch, G. Gediga. Statistical evaluation of rough set dependency analysis.International Journal of Human Computer Studies46: 589–604,1997.
I. Düntsch, G. Gediga. Uncertainty measures of rough set prediction.Artificial Intelligence106(1): 77–107, 1998.
I. Düntsch, G. Gediga.Rough Set Data Analysis: A Road to Non-Invasive Knowledge DiscoveryVol. 2 ofMethoSos Primers. MethoSos Publishers (UK), Bangor, 2000.
G. Gediga, I. Düntsch. Rough approximation quality revisited.Artificial Intelligence132: 219–234, 2001.
M. Grabisch. The application of fuzzy integrals in multicriteria decision making.European Journal of Operational Research89: 445–456, 1996.
M. Grabisch. k-additive and k-decomposable measures. InProceedings of the Linz Seminar1997.
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.
S. Greco, B. Matarazzo, R. Slowinski. Rough sets theory for multicriteria decision analysis.European Journal of Operational Research129: 1–47, 2001.
D. Hildebrand, J. Laing, H. Rosenthal. Prediction logic and quasi-independence in empirical evaluation of formal theory.Journal of Mathematical Sociology3: 197–209, 1974.
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.
A. Laruelle, F. Valenciano. Shapley-Shubik and Banzhaf indices revisited.Mathematics of Operations Research(in press).
J.-L. Marichal. An axiomatic approach of the discrete Choquet integral as a tool to aggregate interacting criteria.IEEE Transactions on Fuzzy Systems(submitted).
J.-L. Marichal, P. Mathonet. On comparison meaningfulness of aggregation function.Journal of Mathematical Psychology45: 213–223,2000.
F. Miller. Computer study into the causes of 1965–1966 traffic deaths in Jacksonville, Florida (manuscript).
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).
Z. Pawlak. Rough sets.International Journal of Computer and Information Sciences11: 341–356,1982.
Z. Pawlak.Rough Sets: Theoretical Aspects of Reasoning about Data.Kluwer, Dordrecht, 1991.
Z. Pawlak. Rough set approach to knowledge-based decision support.European Journal of Operational Research99(1): 48–57, 1997.
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
A.E. Roth, editor.The Shapley Value - Essays in Honor of Lloyd S. Shapley.Cambridge University Press, Cambridge, 1976.
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.
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.
M. Shubik (1997). Game theory, complexity, and simplicity (manuscript). Available athttp://citeseer.nj.nec.com/article/shubik97game.html.
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.
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.
S.S. Stevens. Mathematics, measurement, and psychophysics. In S.S. Stevens, editorHandbook of Experimental PsychologyWiley, New York, 1951.
P.D. Straffin. The Shapley-Shubik and Banzhaf power indices as probabilities. In [26], 71–81, 1976.
F. Vogel. Probleme und Veifahren der numerischen Klassifikation. Vandenhoeck & Ruprecht, Göttingen, 1975.
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.
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.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2004 Springer-Verlag Berlin Heidelberg
About this chapter
Cite this chapter
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
Download citation
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
eBook Packages: Springer Book Archive