The analytic hierarchy process (AHP) is a popular tool used in decision making for ranking alternatives based on quantitative and qualitative criteria. In this thesis, we investigate two applications involving the AHP: determining the greatest sports records and generating priority vectors for inconsistent interval judgments. We determine rankings of the greatest active single-season, career, and single-event sports records by applying the ratings mode of the AHP. In addition, we present an extension to a linear programming method used for generating priority vectors for interval pairwise comparison matrices. By introducing multiplicative stretch factors for each interval comparison, our linear programming method with stretching can be used to solve problems when inconsistent interval judgments are present. We describe the linear programming method, apply it to three problems, and compare its performance to other methods for solving inconsistent interval AHP problems.