Abstrakt
In this paper we focus on real situations where certain perfectly divisible estate has to be divided among claimants who can merely indicate the range of their claims, and the available amount is smaller than the aggregated claim. Funds' allocation of a firm among its divisions, taxation problems, priority problems, distribution of costs of a joint project among the agents involved, various disputes including those generated by inheritance, or by cooperation in joint projects based on restricted willingness to pay, fit into this framework.
The corresponding claim of each claimant can vary within a closed interval or fuzzy interval. For claims, fuzzy intervals are applied whenever the claimants can distinguish a possibility of attaining the amount of estate, and/or its membership degree of a possibility of attainment.
When claims of claimants have fuzzy interval uncertainty, we settle such type of division problems by transforming it into bankruptcy problems under interval uncertainty by interval valued mappings. A similar approach is applied to deal with uncertainty of estate to be divided.
Here, a probability interpretation can also be considered e.g. in taxation problems. We consider the division problems under uncertainty of claims and/or estate and present bankruptcy rule, which are consistent with the classical bankruptcy proportional rule.
Several examples are presented to illustrate particular problems and solution concepts.