Possibility Approach for Solve the Data Envelopment Analytical Hierarchy Process (deahp) with Fuzzy Judgment Scales

The data envelopment analytical hierarchy process (DEAHP) is a type of the analytical hierarchy process (AHP), which used the concept of data envelopment analysis (DEA) for generating LW from the judgment matrices and aggregating them to be final weight (FW) in AHP. In general, the judgment scales in AHP is built based on decision maker. It is unrealistic to expect that the decision maker has complete information of all aspects of the problem. Thus, the fuzzy judgment scales will be firstly modeled in this paper. Sometime, there are many decision makers. It is a caused of randomness of judgment scales. In this case, the fuzzy judgment scales are treated to be the random variable (RV), which is the fuzzy random variable (FRV). However, the traditional DEAHP model has often treated judgment scales as being crisp deterministic. Then, it cannot be solved by the standard linear programming concept. In this paper, the concept of chance-constrained programming (CC) and the possibility approach (PA) are chosen to convert the fuzzy stochastic data envelopment analytical hierarchy process (FSDEAHP) model into equivalent crisp deterministic DEAHP (E-CDDEAHP) model. It can be solved by traditional mathematical programming.