Alessio Ishizaka

Review of the main developments in the analytic hierarchy process

In this paper the authors review the developments of the analytic hierarchy process (AHP) since its inception. The focus of this paper is a neutral review on the methodological developments rather than reporting its applications that have appeared since its introduction. In particular, we discuss problem modelling, pair-wise comparisons, judgement scales, derivation methods, consistency indices, incomplete matrix, synthesis of the weights, sensitivity analysis and group decisions. All have been important areas of research in AHP.

Analytic Hierarchy Process and Expert Choice: Benefits and limitations

This article describes the original Analytic Hierarchy Process (AHP) as it is implemented in the software package Expert Choice. We demonstrate its application through a practical example. In particular, we discuss problem modelling, pairwise comparisons, judgement scales, derivation methods, consistency indices, synthesis of the weights and sensitivity analysis. Finally, the limitations of the original AHP along with the new proposed development are explained.

How to derive priorities in AHP: a comparative study

A heated discussion has arisen over the “best” priorities derivation method. Using a Monte Carlo simulation this article compares and evaluates the solutions of four AHP ratio scaling methods: the right eigenvalue method, the left eigenvalue method, the geometric mean and the mean of normalized values. Matrices with different dimensions and degree of impurities are randomly constructed. We observe a high level of agreement between the different scaling techniques. The number of ranking contradictions increases with the dimension of the matrix and the inconsistencies. However, these contradictions affect only close priorities.

A Web-based decision support system with ELECTRE III for a personalised ranking of British universities

Reliance upon multi-criteria decision methods, like ELECTRE III, has increased many folds in the past few years. However, ELECTRE III has not yet been applied in ranking universities. League tables are important because they may have an impact on the number and quality of the students. The tables serve an indication of prestige. This paper describes a three-tier Web-system, which produces a customised ranking of British Universities with ELECTRE III reflecting personal preferences, where information is uncertain and vague. Using this case study, the benefits of ELECTRE III in the ranking process are illustrated.

AHPSort: an AHP-based method for sorting problems

Six problem formulations exist in the multi-criteria decision analysis (MCDA): choice, sorting, ranking, description, elimination and design problems. The analytic hierarchy process (AHP) is a useful and widespread method for solving choice and ranking problems. However, it is not adapted for sorting problems. Moreover, another practical limitation of AHP is that a high number of alternatives implies a large number of comparisons. This paper presents AHPSort, a new variant of AHP, used for the sorting of alternatives into predefined ordered categories. Furthermore, AHPSort requires far less comparisons than AHP, which facilitates decision making within large-scale problems. In this paper, a real case study for supplier selection is used to illustrate our approach. First, the candidates are sorted with AHPSort within two classes: accepted and rejected suppliers. Then, a single supplier is selected with AHP among the accepted suppliers.

Calibrated fuzzy AHP for current bank account selection

Fuzzy AHP is a hybrid method that combines Fuzzy Set Theory and AHP. It has been developed to take into account uncertainty and imprecision in the evaluations. Fuzzy Set Theory requires the definition of a membership function. At present, there are no indications of how these membership functions can be constructed. In this paper, a way to calibrate the membership functions with comparisons given by the decision-maker on alternatives with known measures is proposed. This new technique is illustrated in a study measuring the most important factors in selecting a student current account.

Influence of aggregation and measurement scale on ranking a compromise alternative in AHP

Analytic Hierarchy Process (AHP) is one of the most popular multi-attribute decision aid methods. However, within AHP, there are several competing preference measurement scales and aggregation techniques. In this paper, we compare these possibilities using a decision problem with an inherent trade-off between two criteria. A decision-maker has to choose among three alternatives: two extremes and one compromise. Six different measurement scales described previously in the literature and the new proposed logarithmic scale are considered for applying the additive and the multiplicative aggregation techniques. The results are compared with the standard consumer choice theory. We find that with the geometric and power scales a compromise is never selected when aggregation is additive and rarely when aggregation is multiplicative, while the logarithmic scale used with the multiplicative aggregation most often selects the compromise that is desirable by consumer choice theory.

Does AHP Help Us Make a Choice? An Experimental Evaluation

In this paper, we use experimental economics methods to test how well Analytic Hierarchy Process (AHP) fares as a choice support system in a real decision problem. AHP provides a ranking that we statistically compare with three additional rankings given by the subjects in the experiment: one at the beginning, one after providing AHP with the necessary pair-wise comparisons and one after learning the ranking provided by AHP. While the rankings vary widely across subjects, we observe that for each individual all four rankings are similar. Hence, subjects are consistent and AHP is, for the most part, able to replicate their rankings. Furthermore, while the rankings are similar, we do find that the AHP ranking helps the decision makers reformulate their choices by taking into account suggestions made by AHP.

Clusters and pivots for evaluating a large number of alternatives in AHP

AHP has been successful in many cases but it has a major limitation: a larger number of alter- natives requires a high number of judgements in the comparison matrices. In order to reduce this problem, we present a method with clusters and pivots. This method also helps with a further four problems of the Analytic Hierarchy Process. It enlarges the comparison scale, facilitates the construction of a consistent or near consistent matrix, eliminates the problem of the choice of the priorities derivation method and allows the use of incomparable alternatives.

Selecting the best statistical distribution with PROMETHEE and GAIA

Three methods have previously been presented in Computer and Industrial Engineering for the selection of a statistical distribution to describe a data-set: the weighted sum model, the weighted multiplication model and data envelopment analysis. These are based on distinctive preset of parameters and result in three different rankings. In these approaches there is no interaction with the decision-maker (DM). This leads to the question: which method should a DM choose? In this paper, we adopt another approach where the DM is the central actor. Based on the multi-criteria decision aid methods, PROMETHEE and GAIA, we will show that different preference parameters (given by the DM) lead to different rankings. Finally, a group decision can be reached using its extension: PROMETHEE GDSS.