Abstract
This paper studies some relationships between fuzzy relations, fuzzy graphs and fuzzy measure. It is shown that a fundamental theorem of Discrete Convex Analysis is derived from the theory of fuzzy measures and the Choquet integral.
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References
A. Alaoui, (1999), On fuzzification of some concepts of graphs, Fuzzy Sets and Systems, 101 363–389.
P. Benvenuti, R. Mesiar, D. Vivona, (2002), Monotone Set Functions-Based Integrals, in Handbook of Measure Theory, E. Pap, (Ed.), Elsevier.
M. J. Beynon, (2003), The introduction and utilization of (l, u)-graphs in the extended variable precision rough sets model, Int. J. of Intel. Systems, 18:10 1035–1055.
K. R. Bhutani, A. Battou, (2003), On M-strong fuzzy graphs, Information Sciences, 155 103–109.
K. R. Bhutani, A. Rosenfeld, (2003), Strong arcs in fuzzy graphs, Information Sciences 152 319–322.
R. Blanco, I. Inza, P. Larranaga, (2003), Learning Bayesian networks in the space of structures by estimation of distribution algorithms, Int. J. of Intel. Systems, 18:2 205–220.
M. Blue, B. Bush, J. Puckett, (2002), Unified approach to fuzzy graph problems, Fuzzy Sets and Systems 125 355–368.
C. Borgelt, R. Kruse, (2003), Learning Possibilistic Graphical Models From Data, IEEE Trans. on Fuzzy Systems 11:2 159–172.
A. Boulmakoul, (2004), Generalized path-finding algorithms on semirings and the fuzzy shortest path problem, J. of Computational and Applied Mathematics, 162:1 263–272.
T. Calvo, A. Kolesarova, M. Komornikova, R. Mesiar, (2002), Aggregation Operators: Propertes, Classes and Construction Methods, in T. Calvo, G. Mayor, R. Mesiar, Eds., Aggregation operators: New trends and applications, Physica-Verlag, Springer, 3–104.
G. Choquet, (1954), Theory of Capacities, Ann. Inst. Fourier 5, 131–296.
D. Denneberg, (1997 (2nd ed)), Non-additive measure and integral, Kluwer.
C. Fellbaum, (1998), WordNet: An Electronic Lexical Database, The MIT Press
S. Fujishige, (1991), Submodular Functions and Optimization, North-Holland.
L. Loväsz, (1983), Submodular functions and convexity, in Mathematical programming: the state of the art, Bonn 1982 / edited by A. Bachem, M. Grotschel, B. Korte, Springer-Verlag.
S. Medasani, R. Krishnapuram, Y. Choi, (2001), Graph Matching by Relaxation of Fuzzy Assignments, IEEE Trans. on Fuzzy Systems 9:1 173–182.
Y. Miao, Z.-Q. Liu, (2000), On Causal Inference in Fuzzy Cognitive Maps, IEEE Trans. on Fuzzy Systems 8:1 107–119.
K. Murota (2000), Matrices and Matroids for Systems Analysis. Algorithms and Combinatorics, Vol.20, Springer-Verlag.
K. Murota (2003), Discrete Convex Analysis. SIAM Monographs on Discrete Mathematics and Applications, Vol.10, Society for Industrial and Applied Mathematics.
Y. Narukawa and T. Murofushi, (2003) Choquet integral and Sugeno integral as aggregation functions, in: Information Fusion in Data Mining, V. Torra, ed., (Springer) pp. 27–39.
G. Pasi, (2003), Modeling users’ preferences in systems for information access, Intl. J. of Intelligent Systems, 18:7 793–808.
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Narukawa, Y., Torra, V. (2005). Fuzzy Measures and Choquet Integral on Discrete Spaces. In: Reusch, B. (eds) Computational Intelligence, Theory and Applications. Advances in Soft Computing, vol 33. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-31182-3_53
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DOI: https://doi.org/10.1007/3-540-31182-3_53
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-22807-3
Online ISBN: 978-3-540-31182-9
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