Research Into Debt Relations Using Fuzzy Mathematical Methods

In this paper, the fuzzy matrix expression of debt relations is given and its power operation is used to judge the existence of the indirect debt relation . We describe and analyze debt chain,debt circle and debt quantity by using the power operations on fuzzy matrix. It is useful to analyze a debt network and provide a basis in the decision process.It is not easy to clear up debt chains efficiently through through settlement making by means of transferring accounts. It is the first time to describe the process and result of transferring accounts through a unified formula. It simplifies the debt relations and optimizes the system. Furthermore, we show the rationality of this method by proving the invariance of debt of every company is in the transfer process. Transferring a debt matrix to a simple matrix is our main goal and the equivalent statement of a simple matrix is given. The discussion of finiteness of steps of transferring a debt matrix to a simple matrix is useful to develop programs for simplifying the debt network and to find optimization schemes.In this paper,we also give a new mathematical model about allocation relations which does not appear in other papers . It is easy to understand that the concepts and methods introduced here are not only applicable in a debt network, but also can be generalized to areas such as water supply in cities, commodity circulating etc.