In this study first, the theoretical frameworks and application of Analytic Hierarchy Process (AHP) were investigated. Then, the application and the evaluation of Some Algebraic Concepts Affecting The Vector Space Concept Over A Field Definition were studied by using AHP, one of the methods of multi criteria decision making. For this purpose Some Algebra Factors Affecting The Vector Space Concept Over A Field Definition (VSCASF) were assessed and five fundamental factors were found out. These five factors are basic concepts of algebraic structures, transformations of algebraic structures, group, ring and field. Then each of main and sub factors were ordered in order of priorities by AHP. In addition results and interpretations related to decision making problem were reviewed. Order of priorities of five main factors according to values obtained from AHP was transformations of algebraic structures (0.4090), field (0.3227), ring (0.1644), group (0.0772) and basic concepts of algebraic structures (0.0267).