| Title:
|
Division schemes under uncertainty of claims (English) |
| Author:
|
Li, Xianghui |
| Author:
|
Li, Yang |
| Author:
|
Zheng, Wei |
| Language:
|
English |
| Journal:
|
Kybernetika |
| ISSN:
|
0023-5954 (print) |
| ISSN:
|
1805-949X (online) |
| Volume:
|
57 |
| Issue:
|
5 |
| Year:
|
2021 |
| Pages:
|
840-855 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
In some economic or social division problems, we may encounter uncertainty of claims, that is, a certain amount of estate has to be divided among some claimants who have individual claims on the estate, and the corresponding claim of each claimant can vary within a closed interval or fuzzy interval. In this paper, we classify the division problems under uncertainty of claims into three subclasses and present several division schemes from the perspective of axiomatizations, which are consistent with the classical bankruptcy rules in particular cases. When claims of claimants have fuzzy interval uncertainty, we settle such type of division problems by turning them into division problems under interval uncertainty. (English) |
| Keyword:
|
division scheme |
| Keyword:
|
bankruptcy |
| Keyword:
|
interval |
| Keyword:
|
fuzzy |
| MSC:
|
03B52 |
| MSC:
|
91A12 |
| idZBL:
|
Zbl 07478643 |
| idMR:
|
MR4363240 |
| DOI:
|
10.14736/kyb-2021-5-0840 |
| . |
| Date available:
|
2022-01-05T07:59:24Z |
| Last updated:
|
2022-02-24 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/149307 |
| . |
| Reference:
|
[1] Aumann, R. J., Maschler, M.: Game theoretic analysis of a bankruptcy problem from the Talmud..J. Econom. Theory 36 (1982), 195-213. |
| Reference:
|
[2] games, Cooperative interval: A survey..Cent. Europ. J. Oper. Res. 18 (2010), 397-411. |
| Reference:
|
[3] Branzei, R., Dimitrov, D., Pickl, S., Tijs, S.: How to cope with division problems under interval uncertainty of claims?.Int. J. Uncertain. Fuzz. 12 (2004), 191-200. |
| Reference:
|
[4] Curiel, I. J., Maschler, M., Tijs, S. H.: Bankruptcy games..Z. Oper. Res. 31 (1987), A143-A159. |
| Reference:
|
[5] Driessen, T.: Cooperative Games, Solutions and Applications..Kluwer Academic Publishers, 1988. |
| Reference:
|
[6] Elishakoff, I.: Resolution of two millennia-old Talmudic mathematical conundrums..BeOr HaTorah 21 (2012), 61-76. |
| Reference:
|
[7] Elishakoff, I., Bégin-Drolet, A.: Talmudic bankruptcy problem: special and general solutions..Scientiae Mathematicae Japonicae 69 (2009), 387-403. |
| Reference:
|
[8] Habis, H., Herings, P. J. J.: Stochastic bankruptcy games..Int. J. Game Theory 42 (2013), 973-988. |
| Reference:
|
[9] Mallozzi, L., Scalzo, V., Tijs, S.: Fuzzy interval cooperative games..Fuzzy Set Syst. 165 (2011), 1, 98-105. |
| Reference:
|
[10] Moreno-Ternero, J. D., Villar, A.: The Talmud rule and the securement of agents' awards..Math. Soc. Sci. 47 (2004), 245-257. |
| Reference:
|
[11] O'Neill, B.: A problem of rights arbitration from the Talmud..Math. Soc. Sci. 2 (1982), 345-371. 10.1016/0165-4896(82)90029-4 |
| Reference:
|
[12] Pulido, M., Sánchez-Soriano, J., Llorca, N.: Game theory techniques for university management: an extended bankruptcy model..Ann. Oper. Res. 109 (2002), 129-142. |
| Reference:
|
[13] Schmeidler, D.: The nucleolus of a characeristic function..SIAM J. Appl. Math. 17 (1969), 1163-1170. |
| Reference:
|
[14] Zhao, W. J., Liu, J. C.: Interval-valued fuzzy cooperative games based on the least square excess and its application to the profit allocation of the road freight coalition..Symmetry 10 (2018), 709. |
| Reference:
|
[15] Tijs, S.: Bounds for the core of a game and the t-value..In O. Moeschlin, & D. Pallaschke (Eds.), Game Theory Math. Econom. (1981), pp. 123-132. North-Holland Publishing Company. |
| Reference:
|
[16] Yager, R. R., Kreinovich, V.: Fair division under interval uncertainty..Int. J. Uncert. Fuzz. 8 (2000), 611-618. 10.1142/S0218488500000423 |
| Reference:
|
[17] Yu, X., Zhang, Q.: Core for game with fuzzy generalized triangular payoff value..Int. J. Uncert. Fuzz. 27 (2019), 789-813. |
| . |
