Related publications

The following publications present most of the concepts and methods implemented in Kappalab. They are organized according to their main topic.

Set functions, capacities, Choquet integral, Sugeno integral

• Denneberg (2000), Non-additive measure and integral, basic concepts and their role for applications, in: M. Grabisch, T. Murofushi, and M. Sugeno Eds, Fuzzy Measures and Integrals: Theory and Applications, Physica-Verlag, pages 42-69.


• M. Grabisch (2000), A graphical interpretation of the Choquet integral, IEEE Transactions on Fuzzy Systems 8, pages 627-631 [Preliminary pdf version].


• M. Grabisch and Ch. Labreuche (2002), The symmetric and asymmetric Choquet integrals on finite spaces for decision making, Statistical Papers 43, pages 37-52 [Preliminary pdf version].


• J.-L. Marichal (2000), An axiomatic approach of the discrete Choquet integral as a tool to aggregate interacting criteria, IEEE Transactions on Fuzzy Systems 8:6, pages 800-807 [Preliminary pdf version].


• J-L. Marichal (2000), On Sugeno integral as an aggregation function, Fuzzy Sets and Systems 114, pages 347-365 [Preliminary pdf version].


• J-L. Marichal (2001), An axiomatic approach of the discrete Sugeno integral as a tool to aggregate interacting criteria in a qualitative framework, IEEE Transactions on Fuzzy Systems 9:1, pages 164-172 [Preliminary pdf version].


• T. Murofushi and M. Sugeno (1993), Some quantities represented by the Choquet integral, Fuzzy Sets and Systems 56, pages 229-235.


• T. Murofushi and M. Sugeno (2000), Fuzzy measures and fuzzy integrals, in: M. Grabisch, T. Murofushi, and M. Sugeno Eds, Fuzzy Measures and Integrals: Theory and Applications, Physica-Verlag, pages 3-41 [Preliminary pdf version].

k-additive set functions, Möbius and interaction transform

• A. Chateauneuf and J-Y. Jaffray (1989), Some characterizations of lower probabilities and other monotone capacities through the use of Möbius inversion, Mathematical Social Sciences 17, pages 263-283.


• M. Grabisch (2000), The interaction and Möbius representations of fuzzy measures on finites spaces, k-additive measures: a survey, in: Fuzzy Measures and Integrals: Theory and Applications, M. Grabisch, T. Murofushi, and M. Sugeno Eds, Physica Verlag, pages 70-93 [Preliminary pdf version].


• M. Grabisch, J.-L. Marichal, and M. Roubens (2000), Equivalent representations of set functions, Mathematics of Operations Research 25:2, 157-178 [Preliminary pdf version].

Capacities in decision making

• M. Grabisch (1996), The application of fuzzy integrals in multicriteria decision making, European Journal of Operational Research 89, pages 445-456 [Preliminary pdf version].


• M. Grabisch (2000), Fuzzy integral for classification and feature extraction, in: Fuzzy Measures and Integrals: Theory and Applications, M. Grabisch, T. Murofushi, and M. Sugeno Eds, Physica Verlag, pages 415-434 [Preliminary pdf version].


• M. Grabisch, J. Duchêne, F. Lino and P. Perny (2002), Subjective evaluation of discomfort in sitting position, Fuzzy Optimization and Decision Making 1:3, pages 287-312 [Preliminary pdf version].


• J.-L. Marichal (2000), Behavioral analysis of aggregation in multicriteria decision aid, in: J. Fodor, B. De Baets, and P. Perny Eds, Preferences and Decisions under Incomplete Knowledge. Series: Studies in Fuzziness and Soft Computing 51, Physica Verlag, Heidelberg, pages 153-178 [Preliminary pdf version].


• J.-L. Marichal (2004), Tolerant or intolerant character of interacting criteria in aggregation by the Choquet integral, European Journal of Operational Research 155:3, pages 771-791 [Preliminary pdf version].

Entropy

• J.-L. Marichal (2002), Entropy of discrete Choquet capacities, European Journal of Operational Research 137:3, pages 612-624 [Preliminary pdf version].


• I. Kojadinovic, J-L. Marichal and M. Roubens (2005), An axiomatic approach to the definition of the entropy of a discrete Choquet capacity, Information Sciences 172, pages 131-153 [Preliminary pdf version].

Identification of capacities

• M. Grabisch (1995), A new algorithm for identifying fuzzy measures and its application to pattern recognition, Int. Joint Conf. of the 4th IEEE Int. Conf. on Fuzzy Systems and the 2nd Int. Fuzzy Engineering Symposium, Yokohama, Japan, pages 145-150 [Preliminary pdf version].


• M. Grabisch and M. Roubens (2000), Application of the Choquet Integral in Multicriteria Decision Making, in: Fuzzy Measures and Integrals: Theory and Applications, M. Grabisch, T. Murofushi, and M. Sugeno Eds, Physica Verlag, pages 415-434 [Preliminary pdf version].


• M. Grabisch (2003), Modelling data by the Choquet integral, in: Information fusion in data mining, V. Torra Ed, Physica Verlag, pages 135-148 [Preliminary pdf version].


• M. Grabisch, I. Kojadinovic and P. Meyer (2007), A review of methods for capacity identification in Choquet integral based multi-attribute utility theory: Applications of the Kappalab R package, European Journal of Operational Research, in press [Preliminary pdf version].


• I. Kojadinovic (2004), Estimation of the weights of interacting criteria from the set of profiles by means of information-theoretic functionals, European Journal of Operational Research 155:3, pages 741-751 [Preliminary pdf version].


• I. Kojadinovic (2005), Unsupervised aggregation of commensurate correlated attributes by means of the Choquet integral and entropy functionals, International Journal of Intelligent Systems, in press [Preliminary pdf version].


• I. Kojadinovic (2007), Minimum variance capacity identification, European Journal of Operational Research 177:1, pages 498-514 [Preliminary pdf version].


• I. Kojadinovic (2007), Quadratic distances for capacity and bi-capacity approximation and identification, 4OR: A Quarterly Journal of Operations Research 5:2, pages 117-142 [Preliminary pdf version].


• P. Meyer, M. Roubens (2005), Choice, Ranking and Sorting in Fuzzy Multiple Criteria Decision Aid, in: J. Figueira, S. Greco, and M. Ehrgott Eds, Multiple Criteria Decision Analysis: State of the Art Surveys, volume 78 of International Series in Operations Research and Management Science, chapter 12, pages 471-506. Springer Science + Business Media, Inc., New York [Preliminary pdf version].


• P. Miranda and M. Grabisch (1999), Optimization issues for fuzzy measures, International Journal of Fuzziness and Knowledge-based Systems 7:6, pages 545-560 [Preliminary pdf version].