메뉴 건너뛰기




Volumn 5, Issue 2, 2007, Pages 117-142

Quadratic distances for capacity and bi-capacity approximation and identification

Author keywords

Bi capacity; Capacity; Choquet integral; Multi attribute utility theory; Quadratic programming

Indexed keywords


EID: 34547295747     PISSN: 16194500     EISSN: 16142411     Source Type: Journal    
DOI: 10.1007/s10288-006-0014-4     Document Type: Article
Times cited : (11)

References (37)
  • 1
    • 84878994392 scopus 로고    scopus 로고
    • Bana e Costa CA, De Corte JM, Vansnick JC (2005) On the mathematical foundations of MACBETH. In Figueira J, Greco S, Ehrgott M (eds) multiple criteria decision analysis: state of the art surveys, Springer, Berlin Heidelberg New York pp 409-442
    • Bana e Costa CA, De Corte JM, Vansnick JC (2005) On the mathematical foundations of MACBETH. In Figueira J, Greco S, Ehrgott M (eds) multiple criteria decision analysis: state of the art surveys, Springer, Berlin Heidelberg New York pp 409-442
  • 2
    • 85028993410 scopus 로고    scopus 로고
    • Probabilistic values for bicooperative games
    • Technical report, University of Seville, Sevilla, Spain
    • Bilbao JM, Fernández JR, Jimńez N, López JJ (2004) Probabilistic values for bicooperative games. Technical report, University of Seville, Sevilla, Spain
    • (2004)
    • Bilbao, J.M.1    Fernández, J.R.2    Jimńez, N.3    López, J.J.4
  • 3
    • 38249022049 scopus 로고
    • Some characterizations of lower probabilities and other monotone capacities through the use of Möbius inversion
    • Chateauneuf A, Jaffray J-Y (1989) Some characterizations of lower probabilities and other monotone capacities through the use of Möbius inversion. Math Soc Sci 17 (3): 263-283
    • (1989) Math Soc Sci , vol.17 , Issue.3 , pp. 263-283
    • Chateauneuf, A.1    Jaffray, J.-Y.2
  • 5
    • 33747203974 scopus 로고    scopus 로고
    • Some characterizations of k-monotonicity through the bipolar Möbius transform in bi-capacities
    • Fujimoto K, Murofushi T (2005) Some characterizations of k-monotonicity through the bipolar Möbius transform in bi-capacities. J Adv Comput Intell Inform 9 (5): 484-495
    • (2005) J Adv Comput Intell Inform , vol.9 , Issue.5 , pp. 484-495
    • Fujimoto, K.1    Murofushi, T.2
  • 6
    • 0020826623 scopus 로고
    • A numerically stable dual method for solving strictly convex quadratic programs
    • Goldfarb D, Idnani A ( 1983) A numerically stable dual method for solving strictly convex quadratic programs. Math Program 27:1-33
    • (1983) Math Program , vol.27 , pp. 1-33
    • Goldfarb, D.1    Idnani, A.2
  • 7
    • 0030105047 scopus 로고
    • The application of fuzzy integrals in multicriteria decision making
    • Grabisch M (1992) The application of fuzzy integrals in multicriteria decision making. Eur J Oper Res 89: 445-456
    • (1992) Eur J Oper Res , vol.89 , pp. 445-456
    • Grabisch, M.1
  • 8
    • 0000870802 scopus 로고    scopus 로고
    • k-order additive discrete fuzzy measures and their representation
    • ISSN 0165-0114
    • Grabisch M (1997) k-order additive discrete fuzzy measures and their representation. Fuzzy Sets Syst 92(2):167-189 ISSN 0165-0114
    • (1997) Fuzzy Sets Syst , vol.92 , Issue.2 , pp. 167-189
    • Grabisch, M.1
  • 10
    • 23044528766 scopus 로고    scopus 로고
    • The symmetric and asymmetric Choquet integrals on finite spaces for decision making
    • Grabisch M, Labreuche C (2002) The symmetric and asymmetric Choquet integrals on finite spaces for decision making. Stat Papers 43: 37-52
    • (2002) Stat Papers , vol.43 , pp. 37-52
    • Grabisch, M.1    Labreuche, C.2
  • 11
    • 13644281303 scopus 로고    scopus 로고
    • Bi-capacities I : Definition, Möbius transform and interaction
    • Grabisch M, Labreuche C (2005a) Bi-capacities I : definition, Möbius transform and interaction. Fuzzy Sets Syst 151: 211-236
    • (2005) Fuzzy Sets Syst , vol.151 , pp. 211-236
    • Grabisch, M.1    Labreuche, C.2
  • 12
    • 13644254932 scopus 로고    scopus 로고
    • Bi-capacities II: The Choquet integral
    • Grabisch M, Labreuche C (2005b) Bi-capacities II: the Choquet integral. Fuzzy Sets Syst 151: 237-259
    • (2005) Fuzzy Sets Syst , vol.151 , pp. 237-259
    • Grabisch, M.1    Labreuche, C.2
  • 13
    • 33747197395 scopus 로고    scopus 로고
    • A general construction for unipolar and bipolar interpolative aggregation
    • Barcelona, Spain, September, 2005c
    • Grabisch M, Labreuche C (2005c) A general construction for unipolar and bipolar interpolative aggregation. In: Joint 4th EUSFLAT and 11th LFA conference (EUSFLAT 2005), Barcelona, Spain, September 2005, pp 916-921
    • (2005) Joint 4th EUSFLAT and 11th LFA conference (EUSFLAT , pp. 916-921
    • Grabisch, M.1    Labreuche, C.2
  • 14
    • 85029007289 scopus 로고    scopus 로고
    • Grabisch M, Labreuche C (2005d) Bi-capacities: towards a generalization of cumulative prospect theory. Working paper
    • Grabisch M, Labreuche C (2005d) Bi-capacities: towards a generalization of cumulative prospect theory. Working paper
  • 15
    • 0037411056 scopus 로고    scopus 로고
    • On the extension of pseudo-Boolean functions for the aggregation of interacting criteria
    • Grabisch M, Labreuche Ch, Vansnick JC (2003) On the extension of pseudo-Boolean functions for the aggregation of interacting criteria. Eur J Oper Res 148: 28-47
    • (2003) Eur J Oper Res , vol.148 , pp. 28-47
    • Grabisch, M.1    Labreuche, C.2    Vansnick, J.C.3
  • 16
    • 85028959293 scopus 로고    scopus 로고
    • Grabisch M, Kojadinovic I, Meyer P (2005) kappalab: Nonadditive measure and integral manipulation functions package version 0.2
    • Grabisch M, Kojadinovic I, Meyer P (2005) kappalab: Nonadditive measure and integral manipulation functions http://www.polytech.univ-nantes.fr/kappalab. R package version 0.2
  • 17
    • 0002453010 scopus 로고
    • Quantification method in classification processes: Concept of structural α-entropy
    • Havrda J, Charvat F (1967) Quantification method in classification processes: concept of structural α-entropy. Kybernetika 3: 30-35
    • (1967) Kybernetika , vol.3 , pp. 30-35
    • Havrda, J.1    Charvat, F.2
  • 20
    • 33750457318 scopus 로고    scopus 로고
    • Minimum variance capacity identification
    • in press, DOI 10.1016/j.ejor.2005.10.059
    • Kojadinovic I (2006) Minimum variance capacity identification. Eur J Oper Res (in press). DOI 10.1016/j.ejor.2005.10.059
    • (2006) Eur J Oper Res
    • Kojadinovic, I.1
  • 21
    • 33751239780 scopus 로고    scopus 로고
    • Entropy of bi-capacities
    • in press, DOI 10.1016/j.ejor.2005.10.058
    • Kojadinovic I, Marichal J-L (2006) Entropy of bi-capacities. Eur J Oper Res (in press). DOI 10.1016/j.ejor.2005.10.058
    • (2006) Eur J Oper Res
    • Kojadinovic, I.1    Marichal, J.-L.2
  • 22
    • 18144414282 scopus 로고    scopus 로고
    • An axiomatic approach to the definition of the entropy of a discrete Choquet capacity
    • Kojadinovic I, Marichal J-L, Roubens M (2005) An axiomatic approach to the definition of the entropy of a discrete Choquet capacity. Inf Sci 172:131-153
    • (2005) Inf Sci , vol.172 , pp. 131-153
    • Kojadinovic, I.1    Marichal, J.-L.2    Roubens, M.3
  • 23
    • 0038548150 scopus 로고    scopus 로고
    • The Choquet integral for the aggregation of interval scales in multicriteria decision making
    • Labreuche C, Grabisch M (2003) The Choquet integral for the aggregation of interval scales in multicriteria decision making. Fuzzy Sets Syst 137:11-16
    • (2003) Fuzzy Sets Syst , vol.137 , pp. 11-16
    • Labreuche, C.1    Grabisch, M.2
  • 24
    • 0037411493 scopus 로고    scopus 로고
    • Towards a theory of MCDM: Stepping away from social choice theory
    • Marchant T (2003) Towards a theory of MCDM: stepping away from social choice theory. Math Soc Sci 45:343-363
    • (2003) Math Soc Sci , vol.45 , pp. 343-363
    • Marchant, T.1
  • 26
    • 0034478787 scopus 로고    scopus 로고
    • An axiomatic approach of the discrete Choquet integral as a tool to aggregate interacting criteria
    • Marichal J-L (2000) An axiomatic approach of the discrete Choquet integral as a tool to aggregate interacting criteria. IEEE Trans Fuzzy Syst 8 (6): 800-807
    • (2000) IEEE Trans Fuzzy Syst , vol.8 , Issue.6 , pp. 800-807
    • Marichal, J.-L.1
  • 27
    • 0037117192 scopus 로고    scopus 로고
    • Entropy of discrete Choquet capacities
    • Marichal J-L (2002) Entropy of discrete Choquet capacities. Eur J Oper Res 3 (137): 612-624
    • (2002) Eur J Oper Res , vol.3 , Issue.137 , pp. 612-624
    • Marichal, J.-L.1
  • 28
    • 0742266965 scopus 로고    scopus 로고
    • Tolerant or intolerant character of interacting criteria in aggregation by the Choquet integral
    • Marichal J-L (2004) Tolerant or intolerant character of interacting criteria in aggregation by the Choquet integral. Eur J Oper Res 155 (3): 771-791
    • (2004) Eur J Oper Res , vol.155 , Issue.3 , pp. 771-791
    • Marichal, J.-L.1
  • 29
    • 28444445926 scopus 로고    scopus 로고
    • R Development Core Team, R Foundation for Statistical Computing, Vienna, Austria
    • R Development Core Team. (2005) R: A language and environment for statistical computing. R Foundation for Statistical Computing, Vienna, Austria. http://www.R-project.org. ISBN 3-900051-00-3
    • (2005) R: A language and environment for statistical computing
  • 30
    • 34347166234 scopus 로고    scopus 로고
    • Rota G-C(1964) On the foundations of combinatorial theory. I. Theory of Möbius functions. Z. Wahrscheinlichkeitstheorie und Verw. Gebiete, 2: 340-368 (1964)
    • Rota G-C(1964) On the foundations of combinatorial theory. I. Theory of Möbius functions. Z. Wahrscheinlichkeitstheorie und Verw. Gebiete, 2: 340-368 (1964)
  • 32
    • 84856043672 scopus 로고
    • A mathematical theory of communication
    • Shannon CE (1948) A mathematical theory of communication. Bell Syst Techn J 27: 379-623
    • (1948) Bell Syst Techn J , vol.27 , pp. 379-623
    • Shannon, C.E.1
  • 33
    • 85028996996 scopus 로고    scopus 로고
    • Shapley LS (1953) A value for n-person games. In: Contributions to the theory of games, 2, Annals of mathematics studies, no. 28, Princeton University Press, Princeton, pp. 307-317
    • Shapley LS (1953) A value for n-person games. In: Contributions to the theory of games, vol. 2, Annals of mathematics studies, no. 28, Princeton University Press, Princeton, pp. 307-317
  • 35
    • 85028968925 scopus 로고    scopus 로고
    • Turlach BA,Weingessel A (2004) quadprog: Functions to solve quadratic programming problems. R package version 1.4-7
    • Turlach BA,Weingessel A (2004) quadprog: Functions to solve quadratic programming problems. R package version 1.4-7
  • 36
    • 31744450082 scopus 로고    scopus 로고
    • Tversky A.Kahneman D (1992) Advances in prospect theory: cumulative representation of uncertainty. J Risk Uncertain 5: 297-323
    • Tversky A.Kahneman D (1992) Advances in prospect theory: cumulative representation of uncertainty. J Risk Uncertain 5: 297-323
  • 37
    • 85028967336 scopus 로고    scopus 로고
    • Vincke P (1992) Multicriteria decision-aid. Wiley, New York
    • Vincke P (1992) Multicriteria decision-aid. Wiley, New York


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.