Abstract
In this paper, a methodology to derive reliable intervals for multiplicative preference relations (or pairwise comparison matrices) satisfying consistency and consensus indexes is introduced. Our approach is proposed via a combination of numerical algorithms and a nonlinear optimization algorithm. A synthesis of reliable intervals is achieved, where group decision makers show evidence of these intervals to express flexibility in the manner of their preferences, while accomplishing some a priori decision targets, rules and advice given by their current framework. The algorithms are applied to some examples in order to illustrate our results and compare them with other methodologies.
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