Novel weight approach for interval numbers comparison matrix in the analytic hierarchy process

New consistency definitions and weight approach deriving from the interval numbers comparison matrix in the analytic hierarchy process are studied. First, define the local consistency and the local satisfactory consistency based on the idea of weight feasible region. Second, put forward a model to check whether the interval numbers comparison matrix has the local satisfactory consistency or not. Third, define the consistency degree to check the whole consistency and suggest a modification approach to adjust the interval numbers matrix with the bad consistency degree. Finally, a new approach for deriving weight from the interval numbers matrix is proposed. The objective is to seek a crisp matrix from the interval numbers matrix with the minimum consistency ratio. Then, the weight deriving from the crisp matrix can be regarded as the weight for the interval numbers matrix, which is solved by the particle swarm optimization. An example is given to illustrate the approach.