The analytic hierarchy process (AHP) elicits a corresponding priority vector interpreting the preferred information from the decision-maker(s), based on the pairwise comparison values of a set of objects. Since pairwise comparison values are the judgments obtained from an appropriate semantic scale, in practice the decision-maker(s) usually give some or all pair-to-pair comparison values with an uncertainty degree rather than precise ratings. By employing the property of goal programming (GP) to treat a fuzzy AHP problem, this paper incorporates an absolute term linearization technique and a fuzzy rating expression into a GP-AHP model for solving group decision-making fuzzy AHP problems. In contrast to current fuzzy AHP methods, the GP-AHP method developed herein can concurrently tackle the pairwise comparison involving triangular, general concave and concave-convex mixed fuzzy estimates under a group decision-making environment. Many real world decision problems involve multiple criteria in qualitative domains. As expected, such problems will be increasingly modeled as multiple criteria decision-making problems, which involve scoring on subjective/qualitative domains. This results in a class of significant problems for which an evaluation framework, which handles occurrences of seeming intransitivity and inconsistency will be required. Another interesting issue of group decision-making analysis is how to deal with disagreements between two or more different rankings within an alternative set. These phenomena are likely to appear in qualitative/ subjective domains where the decision-making environment is ambiguous and vague. Therefore, this study proposes a GP-AHP model that is sufficiently robust to permit conflict and imprecision. Numerical examples demonstrate the effectiveness and applicability of the proposed models in deriving the most promising priority vector from a fuzzy AHP problem within a group decision-making environment. © 2002 Elsevier Science Ltd. All rights reserved.
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