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The analytic hierarchy process (AHP) is one of the most popular multi-criteria decision-making (MCDM) methods, and so is its extension fuzzy analytic hierarchy process (FAHP). However, the FAHP, unlike the AHP, easily handles the trusted weights by the consistency index (CI) or consistency ratio (CR). We need to first derive the consistent fuzzy pairwise comparison matrix (FPCM) by the transitivity axiom and then drive fuzzy weights. We also need a flexible mechanism for users to control the spread of fuzzy weights under tolerable consistency. In this paper, we propose a novel model based on mathematical programming to derive rational fuzzy weights of the FAHP and provide a parameter for decision-makers to control the spread of fuzzy weights. Three examples are used to demonstrate the proposed method and compared with others to validate and justify the proposed method. [ABSTRACT FROM AUTHOR]