Abstract
Fuzzy measures on multisets are studied. We show that a class of multisets can be represented as a subset of positive integers. Comonotonicity for multisets are defined. We show that a fuzzy measure on multisets with some comonotonicity condition can be represented by generalized fuzzy integral.
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References
Benvenuti, P., Mesiar, R., Vivona, D.: Monotone set functions-based integrals. In: Pap, E. (ed.) Handbook of Measure Theory, pp. 1329–1379. Elsevier, Amsterdam (2002)
Choquet, G.: Theory of capacities. Ann. Inst. Fourier 5, 131–295 (1953-1954)
Dellacherie, C.: Quelques commentaires sur les prolongements de capacités, Séminaire de Probabilités 1969/1970. Lecture Notes in Mathematics, Strasbourg, vol. 191, pp. 77–81 (1971)
Grabisch, M.: k-order additive discrete fuzzy measures and their representation. Fuzzy Sets and Systems 92(2), 167–189 (1997)
Guo, C., Zhang, D.: On set-valued fuzzy measures. Information Sciences 160, 13–25 (2004)
Hickman, J.L.: A note on the concept of multiset. Bulletin of the Australian Mathematical Society 22, 211–217 (1980)
Klement, E.P., Mesiar, R., Pap, E.: Triangular Norms. Kluwer Academic Publishers, Dordrecht (2000)
Klement, E.P., Mesiar, R., Pap, E.: Integration with respect to decomposable measures, based on a conditionally distributive semiring on the unit interval. Int. J. of Unc., Fuzziness and Knowledge Based Systems 8(6), 701–717 (2000)
Ling, C.H.: Representation of associative functions. Publ. Math. Debrecen 12, 189–212 (1965)
Marichal, J.-L., Roubens, M.: Entropy of discrete fuzzy measures. Int. J. of Unc., Fuzz. and Knowledge Based Systems 8(6), 625–640 (2000)
Miyamoto, S.: Generalizations of multisets and rough approximations. Int. J. of Intel. Syst. 19, 639–652 (2004)
Murofushi, T., Sugeno, M.: An interpretation of fuzzy measures and the Choquet integral as an integral with respect to a fuzzy measure. Fuzzy Sets and Systems 29, 201–227 (1989)
Narukawa, Y., Torra, V.: Multidimensional generalized fuzzy integral. Fuzzy Sets and Systems 160, 802–815 (2009)
Ralescu, D., Adams, G.: The fuzzy integral. J. Math. Anal. Appl. 75, 562–570 (1980)
Sugeno, M.: Theory of fuzzy integrals and its applications, Ph. D. Dissertation, Tokyo Institute of Technology (1974)
Sugeno, M., Murofushi, T.: Pseudo-additive measures and integrals. J. Math. Anal. Appl. 122, 197–222 (1987)
Torra, V., Narukawa, Y.: Modeling decisions: information fusion and aggregation operators. Springer, Heidelberg (2007)
Torra, V., Stokes, K., Narukawa, Y.: Fuzzy Measures on Multisets (submitted)
Yager, R.R.: On the theory of bags. Int. J. of General Systems 13, 23–37 (1986)
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Narukawa, Y., Stokes, K., Torra, V. (2011). Fuzzy Measures and Comonotonicity on Multisets. In: Torra, V., Narakawa, Y., Yin, J., Long, J. (eds) Modeling Decision for Artificial Intelligence. MDAI 2011. Lecture Notes in Computer Science(), vol 6820. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-22589-5_4
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DOI: https://doi.org/10.1007/978-3-642-22589-5_4
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