Fuzzy Decomposition Method by Mapping Analysis
The max-min composition of fuzzy relation equation takes the extreme value as the solution; such a characteristic induces the solution of decomposition to be a possible region. The solution region has just one maximum and probably more than one minimum. The maximum solution has the 'possibility' characteristic, and the minimum has the 'necessity' trait. For the needs of greater efficiency and more effectiveness in regard to performance, this paper proposes a new analytical method for the use of decomposition. The algorithm of logical mapping analysis is used for the new method. Mapping status, such as Unique Mapping, Overlapped Mapping, Redundant mapping, and Together Mapping, is introduced to construct the algorithm of logical mapping analysis. Then, by the principle of just one single freedom for every maximum and minimum solution, the status of overlapped and redundant mappings will be eliminated and the together mapping status will be separated as an individual presentation. This proposed method not only discovers all of the real solutions, but is also easily programmed for computer analysis.
decomposition mapping analysis fuzzy relation equation freedom of solution