Partnership Selection Involving Mixed Types of Uncertain Preferences

Partnership selection is an important issue in management science. This study proposes a general model based on mixed integer programming and goal-programming analytic hierarchy process (GP-AHP) to solve partnership selection problems involving mixed types of uncertain or inconsistent preferences. The proposed approach is designed to deal with crisp, interval, step, fuzzy, or mixed comparison preferences, derive crisp priorities, and improve multiple solution problems. The degree of fulfillment of a decision maker’s preferences is also taken into account. The results show that the proposed approach keeps more solution ratios within the given preferred intervals and yields less deviation. In addition, the proposed approach can treat incomplete preference matrices with flexibility in reducing the number of pairwise comparisons required and can also be conveniently developed into a decision support system. 1. Introduction Partnership selection is an important issue in management science. The partnership selection problem can be formulated as a multiple criteria decision making problem [1]. Many researchers have adopted the Analytic Hierarchy Process (AHP; [2]) to solve related problems [3, 4], which uses exact values to express a decision maker’s pairwise comparison judgments in complete preference matrices. However, because the information about future partners is usually incomplete and vague, a decision maker’s judgments are often uncertain, inconsistent, and incomplete. Several methods have been developed to deal with partner selection problems with uncertain preferences. For instance, Mikhailov [1] proposed a new Fuzzy Preference Programming (FPP) method based on interval pairwise comparison judgments and then used the AHP method to derive global priorities for all possible alternatives. His method can be used for deriving crisp priorities from exact or interval comparison matrices regardless of their consistency. However, the FPP method may yield multiple solution problems resulting in various ranking for partner selection. In addition, this method is unable to treat judgments with step preferences in which the degree of fulfillment is constant over the same step. Herrera-Viedma et al. [5] developed the consistent fuzzy preference (CFP) method to construct the decision matrices of pairwise comparisons. Wang and Chen [6] applied the CFP method to partnership selection problems; their method can significantly reduce the number of pairwise comparisons since it can deal with incomplete preference matrices. The basic assumption of the CFP method is that a