A decision-making model based on interval additive reciprocal matrices with additive approximation-consistency

In order to capture the rationality experienced by decision makers in choosing the best alternative(s), of much interest is to study the consistency of preference relations in the analytic hierarchy process (AHP). When the typical AHP is extended by using fuzzy numbers to evaluate the opinions of decision makers, the consistency of fuzzy judgments is worth to be considered. In this paper, we analyze some definitions of interval additive reciprocal matrices with additive consistency. It is concluded that interval additive reciprocal matrices are inconsistent in essence. The concept of additive approximation-consistency of interval additive reciprocal matrices is proposed. Moreover, a novel exchange method is designed to enumerate all permutations of alternatives for checking the approximation-consistency. By considering the randomness exhibited in pairwisely comparing alternatives, a method of obtaining the interval weight vector is given. A new algorithm of solving the decision making problem with interval additive reciprocal matrices is proposed. Finally, two numerical examples are carried out to illustrate the new definition and some comparisons are offered.