On consistency and ranking of alternatives in fuzzy analytic hierarchy process

In fuzzy AHP where pairwise comparisons are described by membership values, the treatment of consistency has largely been sketchy. This paper proposes a fuzzy consistency definition with consideration of a tolerance deviation. Essentially, the fuzzy ratios of relative importance, allowing certain tolerance deviation, are formulated as constraints on the membership values of the local priorities. The fuzzy local and global weights are determined via the extension principle. The alternatives are ranked on the basis of the global weights by application of a maximum–minimum set ranking method. Our analysis uses only the data which are considered as consistent. The proposed approach is computationally efficient as it consists of solving only linear programs. An example is included for illustrative purpose.