Analytic hierarchy process-fuzzy sorting: an analytic hierarchy process based method for fuzzy classification in sorting problems

Analytic Hierarchy Process (AHP) is a well-founded and popular method in the Multi-Criteria Decision Analysis (MCDA) field. Recently, AHPSort, a sorting variant, uses crisp class-assignment of alternatives. This can sometimes be misleading, especially for alternatives near the border of two classes. This paper aims at making the class assignment process in AHPSort more flexible by using fuzzy sets theory, which facilitates soft transitions between classes and provides additional information about the membership of alternatives in each class that can be used to fine tune actions beyond the crisp sorting process. This essentially complements the ordinal information of its crisp variant with cardinal information as to the degree of membership of an alternative to each class. The applicability of the proposed approach is illustrated in a case study that regards the classification of London boroughs according to their safety levels.