Quasi-consistency of interval complementary judgment matrix and its weights

Based on the idea of the relative superiority degree found in the additive consistency and the multiplicative consistency of fuzzy complementary judgment matrix (FCJM), the quasi-additive consistency and the quasi-multiplicative consistency of interval complementary judgment matrix (ICJM) were given. And they were merged into the quasi-consistency of ICJM by the complementary property of possibility degree. The problem of how to determine ICJM weights was analyzed under two conditions. In the condition of the IRJM with quasi-consistency, by the method of possibility degree an FCJM was derived from the comparison among its interval weights, and its precise value ranking vector was also achieved using the middle translation method. Then, under the condition of general ICJM, its interval weights were obtained by a deviation model which is established by the deviation between ICJM and its interval weights in the respect of possibility degree. And an FCJM was derived from the comparison among its interval weights, and its precise value ranking vector was also achieved using the middle translation method. And it was pointed out that the solution process of the former condition is in fact the specific one of the latter condition. A necessary and sufficient condition of the quasi-consistency of ICJM was achieved. Finally, the validity and the practicability of the proposed method were illustrated with an example.