Fuzzy decomposition method by the elimination analysis of freedom

Fuzzy maximum (∨) & minimum (∧) composition operation always has only one solution. But the inverse operation of fuzzy decomposition will be a bounded region of solution. It has only one maximum solution at the top end, but may be not single one minimum solution at the foot end of region. In fuzzy decomposition operation, it makes union and intersection operation in the final steps. Both of union and intersection operation, the solutions will be the extreme one, and both of the maximum and minimum solution has only one freedom. This paper proposed a new method of decomposition by the way of redundant mapping elimination. It also means, there is only one freedom of the extreme value provided for not only one minimum solution to share-together. For the analyzing needs, this paper proposed two procedures for solving the maximum. And for process the overlapped and share-together mapping relations, five procedures for solving the minimum solutions are proposed here. By these procedures the redundant mappings of overlapped relations will be eliminated first, then the residual mappings of share-together mappings will be separated. This paper also proposes a sagittal mapping diagram for the assistance of analyzing. Finally the new method programmed on website for evaluation analysis, and evaluator training successfully.