为了解决模糊数间的加和减、乘和除已不再是逆运算的问题,并使得运算法则更加符合客观实际情况,而引入了经典数学中的自变量、因变量、代表系统及自由度等概念,进而对模糊数互补判断矩阵的乘性一致性进行了研究,结果发现若一个模糊数互补判断矩阵满足目前一些文献对其乘性一致性的定义则这个矩阵一定是精确数互补判断矩阵这一不合理之处。文章最后结合模糊集截集理论,利用模糊数互补判断矩阵元素间的关系,重新对乘性一致性模糊数互补判断矩阵进行了定义。
To solve the problem that the relationship between addition and subtraction and that between multipli cation and division in fuzzy numbers is no longer the inverse operation and make the operational laws more corre spond to reality, this paper studies the multiplicative consistency of fuzzy reciprocal judgment matrix by introdu cing the concepts of independent variable, dependent variable, representative system and degree of freedom in classical mathematics. Then, the result reveals that it is unreasonable that if a fuzzy reciprocal judgment matrix satisfies the conditions of multiplicative consistency defined in some existing related literatures, then this matrix must be a precise reciprocal judgment matrix. Finally, based on the fuzzy cut set theory, using the relationships among elements of fuzzy reciprocal judgment matrix, the multiplicative consistency of fuzzy reciprocal judgment matrix is redefined.