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Basic generated universal fuzzy measures. (English) Zbl 1190.28012

Summary: The concept of basic generated universal fuzzy measures is introduced. Special classes and properties of basic generated universal fuzzy measures are discussed, especially the additive, the symmetric and the maxitive case. Additive (symmetric) basic universal fuzzy measures are shown to correspond to the Yager quantifier-based approach to additive (symmetric) fuzzy measures. The corresponding fuzzy integral-based aggregation operators are introduced, including the generated OWA operators.
Reviewer: Hans Weber (Udine)

MSC:

28E10 Fuzzy measure theory
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[1] Beljakov, G.; Mesiar, R.; Valášková, L’., Fitting generated aggregation operators to empirical data, Int. J. Uncertainty Fuzziness Knowledge-Based Syst., 12, 219-236 (2004) · Zbl 1073.28012
[2] Calvo, T.; Kolesárová, A.; Komorníková, M.; Mesiar, R., Aggregation operators: properties, classes and construction methods, (Calvo, T.; Mayor, G.; Mesiar, R., Aggregation Operators (2002), Physica-Verlag: Physica-Verlag Heidelberg), 3-107 · Zbl 1039.03015
[3] Denneberg, D., Non-additive Measure and Integral (1994), Kluwer Acad. Publ.: Kluwer Acad. Publ. Dordrecht · Zbl 0826.28002
[4] Dubois, D.; Prade, H., Fuzzy Sets and Systems: Theory and Applications (1980), Academic Press: Academic Press New York · Zbl 0444.94049
[5] Grabisch, M., Fuzzy integral in multicriteria decision making, Fuzzy Sets Syst., 69, 279-298 (1995) · Zbl 0845.90001
[6] Grabisch, M.; Murofushi, T.; Sugeno, M., Fuzzy Measures and Integrals (2000), Physica-Verlag: Physica-Verlag Heidelberg · Zbl 1113.91313
[7] Klir, G. J.; Folger, T. A., Fuzzy Sets. Uncertainty, and Information (1988), Prentice-Hall: Prentice-Hall Englewoods Cliffs, NJ · Zbl 0675.94025
[8] Kolesárová, A.; Komorníková, M., Triangular norm-based iterative compensatory operators, Fuzzy Sets Syst., 104, 109-120 (1999) · Zbl 0931.68123
[9] M. Komorníková, Generated aggregation operators, in: Proc. EUSF-LAT’99, Palma de Mallorca, 1999, pp. 355-358.; M. Komorníková, Generated aggregation operators, in: Proc. EUSF-LAT’99, Palma de Mallorca, 1999, pp. 355-358.
[10] Komorníková, M., Aggregation operators and additive generators, Int. J. Uncertainty Fuzziness and Knowledge-Based Syst., 9, 205-215 (2001) · Zbl 1113.68524
[11] Mesiar, R.; Mesiarová, A., Fuzzy integrals, (Torra, V.; Narukawa, Y., Modeling Decisions for Artificial Intelligence. Modeling Decisions for Artificial Intelligence, LNAI 3131 (2004), Springer: Springer Berlin), 7-14 · Zbl 1110.28015
[12] R. Mesiar, L’. ValáŠková, Universal fuzzy measures, in: Proc. 10th IFSA World Congress, Istanbul, Turkey, 2003, pp. 139-142.; R. Mesiar, L’. ValáŠková, Universal fuzzy measures, in: Proc. 10th IFSA World Congress, Istanbul, Turkey, 2003, pp. 139-142.
[13] Mesiar, R.; Mesiarová, A.; Valášková, L’., Generated universal fuzzy measures, (Torra, V.; Narukawa, Y.; Valls, A.; Domingo-Ferrer, J., Modelling Decisions for Artificial Intelligence. Modelling Decisions for Artificial Intelligence, LNAI 3885 (2006), Springer: Springer Berlin), 191-202 · Zbl 1235.28012
[14] Mišík, L., Sets of positive integers with prescribed values of densities, Math. Slovaca, 52, 289-296 (2002) · Zbl 1005.11004
[15] Mišík, L.; Tóth, J., On asymptotic behaviour of universal fuzzy measures, Kybernetika, 42, 3, 379-388 (2006) · Zbl 1249.28026
[16] Pap, E., Null-additive Set Functions (1995), Kluwer Acad. Publ.: Kluwer Acad. Publ. Dordrecht · Zbl 0856.28001
[17] Struk, P., Extremal fuzzy integrals, Soft Comput., 10, 502-505 (2006) · Zbl 1097.28013
[18] M. Sugeno, Theory of Fuzzy Integrals and Applications, Ph.D. thesis, Tokyo Institute of Technology, 1974.; M. Sugeno, Theory of Fuzzy Integrals and Applications, Ph.D. thesis, Tokyo Institute of Technology, 1974.
[19] Štrauch, O.; Tóth, J., Asymptotic density and density of ratio set \(R(A)\), Acta Arith., LXXXVII, 67-78 (1998) · Zbl 0923.11027
[20] Yager, R. R., On ordered weighted averaging aggregation operators in multicriteria decision making, IEEE Trans. Syst. Man Cyber., 18, 183-190 (1988) · Zbl 0637.90057
[21] Yager, R. R.; Filev, D. P., Essentials of Fuzzy Modelling and Control (1994), J. Wiley & Sons: J. Wiley & Sons New York
[22] Yager, R. R.; Kacprzyk, J., The ordered weighted averaging operators, Theory and Applications (1997), Kluwer Academic Publishers: Kluwer Academic Publishers Boston · Zbl 0948.68532
[23] L’. ValáŠková, Non-additive Measures and Integrals. Ph.D. thesis, Slovak University of Technology, 2006.; L’. ValáŠková, Non-additive Measures and Integrals. Ph.D. thesis, Slovak University of Technology, 2006.
[24] Wang, Z.; Klir, G. J., Fuzzy Measure Theory (1992), Plenum Press: Plenum Press New York · Zbl 0812.28010
[25] Zadeh, L. A., Fuzzy sets as a basis for a theory of possibility, Fuzzy Sets Syst., 1, 3-28 (1978) · Zbl 0377.04002
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