Petra Grošelj

Acceptable consistency of aggregated comparison matrices in analytic hierarchy process

The analytic hierarchy process is a method for solving multiple criteria decision problems, as well as group decision making. The weighted geometric mean method is appropriate when aggregation of individual judgements is used. This paper presents a new proof which confirms the property that if the comparison matrices of all decision makers are of acceptable consistency, then the weighted geometric mean complex judgement matrix (WGMCJM) also is of acceptable consistency. This property was presented and first proved by Xu (2000), but Lin et al. (2008) rejected the proof. We also discuss under what conditions the WGMCJM is of acceptable consistency when not all comparison matrices of decision makers are of acceptable consistency. For this case we determine the sufficient condition for the WGMCJM to be of acceptable consistency and provide numerical examples. For a special case of two decision makers with 3×3 comparison matrices we find out some additional conditions for the WGMCJM to be of acceptable consistency.

Comparison of some aggregation techniques using group analytic hierarchy process

We presented and employed seven simple group AHP aggregation techniques.The LW-AHP model was a well evaluated group AHP method.For non-homogenous group we suggest to divide the group in smaller homogenous groups.One of our new group methods, the WGM-WAM or the WGM-LW-AHP can be employed. Group decision making is an important part of multiple criteria decision making and the analytic hierarchy process (AHP). The aim of this paper was to compare group AHP methods. Seven simple group AHP aggregation techniques that could be attractive for applications selected from the vast array of group AHP models proposed in the literature were selected for evaluation. We developed three new measures of evaluation: group Euclidean distance, group minimum violations, and distance between weights for the purpose of evaluation. The results of seven group AHP methods of the theoretical example were evaluated by three new evaluation measures, satisfactory index and fitting performance index. Furthermore, a case study of a decision making problem from the construction engineering field was performed and nine group AHP aggregation techniques, seven of them formerly presented and two new two stage group approaches were applied. Finally, the case study was evaluated using all five measures for each of the nine group decision making methods. The results showed that not all group AHP methods are equally convenient and that the selection of the method depended on the specific application.

Evaluation of several approaches for deriving weights in fuzzy group analytic hierarchy process

Abstract The paper discusses fuzzy group analytic hierarchy process. In the literature, there are found several approaches for determining weights either directly from the individual judgments or via group comparison matrix. However, the quality of the group weights was not studied yet. In the paper, we propose two new measures for the evaluation of the group weights that are adapted from classical analytic hierarchy process. We selected six approaches for deriving weights and use them in an application from the literature. We evaluated the gained weights. Our results show that the weights derived by the most popular extent analysis method are questionable in their reliability.

Comparison of Different Construction Types for Public Buildings Applying the Analytic Hierarchy Process

Considering the growing importance of energy-efficient building methods, timber construction will play an increasingly important role in the future. In order to determine advantages and disadvantages of using wood as a leading constructional material, different construction types were compared: solid wood, wood-frame, concrete, and brick construction. To quantify the comparisons the analytic hierarchy process (AHP) was applied. AHP enables the inclusion of various parameters, including descriptive ones, in a mathematical model through which the importance of each construction criterion forming part of the system can be calculated in order to provide objective decisions for construction. Analysis revealed that the top ranked criteria in decision-making include embodied energy, construction cost and design. On comparing different construction types the wood-frame construction, which can have very low or negative carbon footprint, was considered as the most suitable option for public building.