Personalized individual semantics (PIS) is not unusual in our daily life, and it has an important influence on the final decision results in linguistic decision making. The analytic hierarchy process (AHP) has now become a popular decision tool because of its sound mathematical design and ease of applicability to real-world decision making problems. In the AHP, two formats of preference information are included: linguistic and numerical preference information. In order to implement the computation operation, the linguistic preference information is often transformed into the numerical preference information using a fixed numerical scale function (e.g., the Saaty scale). However, the PIS is not taken into account by the AHP with a fixed numerical scale function. Therefore, this study proposes a novel AHP framework with the PIS, and develops a consistency-driven methodology to minimize the inconsistency level of numerical preference information that transformed from linguistic preference information. In the proposed AHP framework, a two-stage based optimization model is designed to deal with the PIS, and the proposed optimization models are converted into some linear programming models that can be easily solved. Finally, a practical example and a comparison experiment are proposed to verify the validity of our proposal.