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.
Thioacetamide (TAA) is widely used in the production of drugs, pesticides and dyeing auxiliaries. Moreover, it is a chemical that can cause liver damage and cancer. TAA has recently been identified to cause bone damage in animal models. However, the type of bone damage that TAA causes and its potential pathogenic mechanisms remain unclear. The toxic effects of TAA on the femurs of New Zealand white rabbits and the underlying toxicity mechanism were investigated in this study. Serum samples, the heart, liver, kidney and femurs were collected from rabbits after intraperitoneal injection of TAA for 5 months (100 and 200 mg/kg). The New Zealand white rabbits treated with TAA showed significant weight loss and femoral shortening. The activities of total bilirubin, total bile acid and gamma-glutamyl transpeptidase in the serum were increased following treatment with TAA. In addition, the cortical bone became thinner, and the trabecular thickness decreased significantly in TAA-treated rabbits, which was accompanied by significantly decreased mineral density of the cortical and trabecular bone. Moreover, there was a significant decrease in modulus of elasticity and maximum load on bone stress in TAA-treated rabbits. The western blotting results showed that the expression of phosphorylated (p)-p38 and p-ERK in femur tissues of rabbits were increased after TAA administration. Collectively, these results suggested that TAA may lead to femoral damage in rabbits by activating the p38/ERK signaling pathway.