模糊判断矩阵的一致性判定及改进方法研究

研究模糊判断矩阵的次序一致性和满意一致性问题.在模糊判断矩阵的非对角线位置不存在0.5时,提出将模糊判断矩阵转化成0-1偏好矩阵,按照布尔运算法则计算偏好矩阵的三次乘幂,得到若其对角线存在数值为1的元素,则模糊判断矩阵不具有次序一致性的结论;若模糊判断矩阵非对角线位置存在0.5,则提出查找循环链的方法进行次序一致性判定.对不具有次序一致性的模糊判断矩阵,提出启发式修改规则.提出度量模糊判断矩阵满意一致性的指标,并得到在其它元素不变的情况下使满意一致性达到最佳时的元素取值,由此提出一致性改进方法.

Research on consistency test and modification approach of fuzzy comparison matrix

The ordinal consistency and satisfactory consistency problems of the fuzzy comparison matrix are studied.First,the fuzzy comparison matrix is transformed into the preference matrix that is comprised of zero or one on condition that 0.5-inexistence in the non-diagonal position of the fuzzy comparison.Then,one can conclude that,if there exists one in the diagonal of the matrix that is powered by 3 from the preference matrix based on the boolean calculation rule,the fuzzy matrix hasn't the ordinal consistency.Or else,a loop search approach is developed for 0.5-existences in the non-diagonal position.Some heuristic modification rules are put forward to modify the ordinal inconsistent matrix.Moreover,the consistency index is developed to measure the satisfactory consistency of the fuzzy matrix.To obtain the least satisfactory consistency,the entry value is solved as the other entries are unchanged.Following that,the modification approach to improve the satisfactory consistency is put forward.