The weak consistency of an interval-valued intuitionistic fuzzy matrix

During the process of decision making, due to time limitation, knowledge structure and environmental factors, decision makers can not provide accurate numbers to express their preferences and have some hesitation to make decisions. In this condition, it will be better to use interval-valued intuitionistic fuzzy numbers to express decision makerspsila preferences. Therefore, the weak consistency of an interval-valued intuitionistic fuzzy matrix was defined, and some properties were proposed to judge the weak consistency of an interval-valued intuitionistic fuzzy matrix. Then the acceptability of a given interval-valued intuitionisitic fuzzy matrix can be measured and advice can be given to a decision maker to adapt his/her preference if the given matrix is not weakly consistent. Meanwhile, illustrated examples were given.