Using Sagittal Mapping analysis for fuzzy decomposition

Solutions of fuzzy composition and decomposition are determined by extreme elements. So the solution of fuzzy decomposition operation will be a bounded region. It has only one maximum solution, but the minimum solutions may not be unique. Usually it is hard to make a decomposition operation because the minimum solution does not exist or is not unique. By using sagittal mapping analysis and combining the concept of only one freedom of minimum solution, this paper proposes a more simple, clear, and exact method for solving the minimum solution of fuzzy decomposition. The sagittal mapping diagram shows the whole relationship between every element from composition to decomposition. By using the mapping diagram, the status of Unique, Analogue, and Share Mappings are easier to figure out. So, this paper recommends three steps for the analyzing method - regulate unique mapping, regulate analogue mapping, and regulate share mapping. Finally the new method is programmed on the website for evaluation analysis and successful evaluator training.