Multivariate integration of functions depending explicitly on the minimum and the maximum of the variables

Journal of Mathematical Analysis and Applications

Volumn 341, Issue 1, 2008, Pages 200-210

  Marichal, Jean Luc ^a  

^a UNIVERSITY OF LUXEMBOURG   (Luxembourg)

Author keywords

Aggregation function; Andness; Cauchy mean; Crofton formula; Distribution function; Expected value; Multivariate integration; Orness

Indexed keywords

EID: 38749130101     PISSN: 0022247X     EISSN: 10960813     Source Type: Journal    
DOI: 10.1016/j.jmaa.2007.10.021     Document Type: Article

References (14)

1. Alsina C., Frank M.J., and Schweizer B. Associative Functions: Triangular Norms and Copulas (2006), World Scientific Publishing Co. Pte. Ltd., Hackensack, NJ
2. Bullen P.S. Handbook of Means and Their Inequalities. Math. Appl. vol. 560 (2003), Kluwer Academic Publishers Group, Dordrecht
3. In: Calvo T., Mayor G., and Mesiar R. (Eds). Aggregation Operators: New Trends and Applications. Stud. Fuzziness Soft Comput. vol. 97 (2002), Physica-Verlag, Heidelberg. 3-7908-1468-7
4. Cauchy A.L. Cours d'analyse de l'Ecole Royale Polytechnique, vol. I. Analyse algébrique (1821), Debure, Paris
5. J.J. Dujmović, A generalization of some functions in continuous mathematical logic-Evaluation function and its applications, in: Proc. Informatica Conference, Bled, Yugoslavia, 1973, paper d27 (in Serbo-Croatian)
6. Dujmović J.J. Weighted conjunctive and disjunctive means and their application in system evaluation. J. Univ. Belgrade EE Dept. Ser. Math. Phys. 483 (1974) 147-158
7. Dujmović J.J. Seven flavors of andness/orness. In: De Baets B., Fodor J., and Radojević D. (Eds). Proc. Eurofuse 2005 (2005), Institute "MihajloPupin", Belgrade. 86-7172-022-5 81-92
8. Eisenberg B., and Sullivan R. Crofton's differential equation. Amer. Math. Monthly 107 2 (2000) 129-139
9. Fernández Salido J.M., and Murakami S. Extending Yager's orness concept for the OWA aggregators to other mean operators. Fuzzy Sets Syst. 139 3 (2003) 515-542
10. Grabisch M., Marichal J.-L., and Roubens M. Equivalent representations of set functions. Math. Oper. Res. 25 2 (2000) 157-178
11. Kolesárová A. Revision of parametric evaluation of aggregation functions. Proc. 13th Zittau Fuzzy Colloquium (September 2006), Zittau, Germany 202-211
12. Marichal J.-L. An axiomatic approach of the discrete Choquet integral as a tool to aggregate interacting criteria. IEEE Trans. Fuzzy Syst. 8 6 (2000) 800-807
13. Marichal J.-L. Cumulative distribution functions and moments of lattice polynomials. Statist. Probab. Lett. 76 12 (2006) 1273-1279
14. J.-L. Marichal, Weighted lattice polynomials of independent random variables, http://arxiv.org/abs/0707.0953, Discrete Appl. Math., in press