Fuzzy AHP with incomplete information

We deal with fuzzy comparison ratios which are more comfortable than crisp ones for expressing human´s intuition. The proposed method is the fuzzy extension of interval AHP (Analytic Hierarchy Process) which estimates the interval weights. It reflects human fuzzy judgments on the interval priority weights. Based on the given fuzzy pairwise comparisons, we can obtain the intervals with h-level sets. The fuzzy intervals are analyzed from two concepts called least upper and greatest lower bounds, respectively. In this sense, two models are similar to upper and lower approximations of rough sets. Since the proposed method resorts to LP, it can be applied to a matrix with some unknown elements. It can be said that the lower h-level value is, the wider the obtained interval width is