Representation of the Choquet integral with the σ-additive Möbius transform

Fuzzy Sets and Systems

Volumn 92, Issue 2, 1997, Pages 139-156

  Denneberg, Dieter ^a  

^a UNIVERSITY OF BREMEN   (Germany)

Author keywords

Choquet integral; Conditional expectation; Cooperative game; Fuzzy measure; M bius transform; Stone representation

Indexed keywords

EID: 0013335080     PISSN: 01650114     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0165-0114(97)00166-8     Document Type: Article

References (9)

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3. B.A. Davey, H.A. Priestley, Introduction to Lattices and Order, Cambridge Univ. Press, Cambridge, 1990.
4. A.P. Dempster, Upper and lower probabilities induced by a multivalued mapping, Ann. Math. Statist. 38 (1967) 325-339.
5. D. Denneberg, Non-additive Measure and Integral. Theory and Decision Library Series B, vol. 27, Kluwer Academic, Dordrecht, Boston, 1994.
6. D. Denneberg, Conditioning (updating) non-additive measures, Ann. Oper. Res. 52 (1994) 21-42.
7. I. Gilboa, D. Schmeider, Additive representations of non-additive measures and the Choquet integral, Ann. Oper. Res. 52 (1994) 43-65.
8. I. Gilboa, D. Schmeidler, Canonical representations of set functions, Math. Oper. Res. 20 (1995) 197-212.
9. M. Grabisch, k-order additive discrete fuzzy measures, Proc. 6th Internat. Conf. on Information Processing and Management of Uncertainty in Knowledge-Based Systems (IPMU), Granada, Spain, July 1996, pp. 1345-1350.