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Keywords:
bi-capacity; cumulative prospect theory; decomposable capacity; uninorm
bi-capacity; cumulative prospect theory; decomposable capacity; uninorm
Summary:
We propose a concept of decomposable bi-capacities based on an analogous property of decomposable capacities, namely the valuation property. We will show that our approach extends the already existing concepts of decomposable bi-capacities. We briefly discuss additive and $k$-additive bi-capacities based on our definition of decomposability. Finally we provide examples of decomposable bi-capacities in our sense in order to show how they can be constructed.
References:
[1] Calvo T., Kolesárová A., Komorníková, M., Mesiar R.: Aggregation operators: Properties, classes and construction methods. In: Aggregation Operators (T. Calvo, G. Mayor, and R. Mesiar, eds.), Physica–Verlag, Heidelberg 2002, pp. 3–104 MR 1936384 | Zbl 1039.03015
[2] Choquet G.: Theory of capacities. Ann. Inst. Fourier (Grenoble) 5 (1953–1954), 131–292 DOI 10.5802/aif.53 | MR 0080760
[3] Fodor J. C., Yager R. R., Rybalov A.: Structure of uninorms. Internat. J. Uncertain. Fuzziness Knowledge-based Systems 5 (1997), 411–427 DOI 10.1142/S0218488597000312 | MR 1471619 | Zbl 1232.03015
[4] Grabisch M.: $k$-order additive discrete fuzzy measures and their representation. Fuzzy Sets and Systems 92 (1997), 167–189 DOI 10.1016/S0165-0114(97)00168-1 | MR 1486417 | Zbl 0927.28014
[5] Grabisch M., Baets, B. De, Fodor J.: On symmetric pseudo-additions and pseudo-multiplications: Is it possible to build a ring on [-1,1]? In: Proc. 9th Internat. Conference on Information Processing and Management of Uncertainty in Knowledge-based Systems (IPMU 2002), Volume III, Annecy (France), July 2002, pp. 1349–1363
[6] Grabisch M., Labreuche C.: Bi-capacities. In: Proc. First Internat. Conference on Soft Computing and Intelligent Systems (SCIC), Tsukuba (Japan), 2002 Zbl 1208.91029
[7] Grabisch M., Labreuche C.: Bi-capacities for decision making on bipolar scales. In: Proc. Seventh Meeting of the EURO Working Group on Fuzzy Sets (EUROFUSE), Varenna (Italy), 2002, pp. 185–190
[8] Grabisch M., Labreuche C.: Capacities on lattices and $k$-ary capacities. In: Proc. 3rd Internat. Conference in Fuzzy Logic and Technology (EUSFLAT 2003), Zittau (Germany), 2003, pp. 304–307
[9] Greco S., Matarazzo, B., Slowinski R.: Bipolar Sugeno and Choquet integrals. In: Proc. Seventh Meeting of the EURO Working Group on Fuzzy Sets (EUROFUSE), Varenna (Italy), 2002, pp. 191–196
[10] Greco S., Matarazzo, B., Slowinski R.: The axiomatic basis of multicriteria noncompensatory preferences. In: Proc. Fourth International Workshop on Preferences and Decisions, Trento (Italy), 2003, pp. 81–86
[11] Klement E. P., Mesiar, R., Pap E.: Integration with respect to decomposable measures, based on a conditionally distributive semiring on the unit interval. Internat. J. Uncertain. Fuzziness Knowledge-based Systems 8 (2000), 701–717 DOI 10.1142/S0218488500000514 | MR 1803475 | Zbl 0991.28014
[12] Klement E. P., Mesiar, R., Pap E.: Triangular Norms. Kluwer, Dordrecht 2000 MR 1790096 | Zbl 1087.20041
[13] Mesiar R.: Generalization of $k$-order additive discrete fuzzy measures. Fuzzy Sets and Systems 102 (1999), 423–428 DOI 10.1016/S0165-0114(98)00216-4 | MR 1676909
[14] Mesiar R.: $k$-order additive measures: Internat. J. Uncertain. Fuzziness Knowledge-based Systems 7 (1999), 6, 561–568 DOI 10.1142/S0218488599000489 | MR 1764304
[15] Mesiar R.: $k$-order additivity and maxitivity. Atti Sem. Mat. Fis. Univ. Modena LI (2003), 179–189 MR 1993888 | Zbl 1220.28001
[16] Mesiar R., Saminger S.: Decomposable bi-capacities: In: Proc. Summer School on Aggregation Operators 2003 (AGOP 2003), University Alcala de Henares (Spain), 2003, pp. 155–158
[17] Miranda P., Grabisch, M., Gil P.: $p$-symmetric fuzzy measures. Internat. J. Uncertain. Fuzziness Knowledge-based Systems 10 (2002), 105–123 DOI 10.1142/S0218488502001867 | MR 1962672 | Zbl 1068.28013
[18] Pap E.: Null-Additive Set Functions. Kluwer, Dordrecht 1995 MR 1368630 | Zbl 1003.28012
[19] Sander W.: Associative aggregation operators. In: Aggregation Operators (T. Calvo, G. Mayor, and R. Mesiar, eds.), Physica–Verlag, Heidelberg, 2002, pp. 124–158 MR 1936386 | Zbl 1025.03054
[20] Wang Z., Klir G. J.: Fuzzy Measure Theory. Plenum Press, New York 1992 MR 1212086 | Zbl 0812.28010
[21] Weber S.: $\perp $-decomposable measures and integrals for Archimedean t-conorms $\perp $. J. Math. Anal. Appl. 101 (1984), 114–138 DOI 10.1016/0022-247X(84)90061-1 | MR 0746230 | Zbl 0614.28019
[22] Yager R. R., Rybalov A.: Uninorm aggregation operators. Fuzzy Sets and Systems 80 (1996), 111–120 DOI 10.1016/0165-0114(95)00133-6 | MR 1389951 | Zbl 0871.04007
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