Decision making is a complex process, particularly when it is carried out by multidisciplinary team. Methods based on the analytical hierarchy process have been widely employed because they provide solid mathematical background. Nevertheless, solutions such as the Aggregation of Individual Judgements (AIJ) and the Aggregation of Individual Priorities (AIP) do not offer sufficient explanatory data in regards with the final decision. We developed an agent-based decision support system (DSS) that employs fuzzy clustering to group individual evaluations and the AHP to reach a final decision. Fuzzy clustering is adequate to determine important pieces of data such as the largest group of evaluations that exist around a centroid value. On the other hand, the MAS paradigm offers capabilities for achieving distributed and asynchronous processing of data. The AHP is used after the individual evaluations are clustered, as if the group were a single evaluator. Altogether, the proposed solution enhances the quality of multi-criteria group decision making.
As it is suggested in Carmen and French (2003), modern management promotes distributed decision making carried by multidisciplinary teams. Organizations decide to promote group decision making, where experts work together but not necessarily at the same place or time (Soubie & Zaraté, 2005). For example, when it comes to acquire new manufacturing equipment (Rao, 2007), or to select the best personnel, among many alternatives (Metin, 2010), not only the opinion of one single person is taken into account. Evaluations from qualified people with different background and perspectives are favored nowadays. Top management must broadcast, to those individuals that will form the decisional group, the evaluation criteria as well as specific data of the alternatives. In turn, the evaluators must judge the alternatives, and top management shall make a final decision based on such judgements.
Thus, decision making refers at selecting, among a finite set of m alternatives, the one that complies best with a finite set of p evaluation criteria. This particular problem has been tackled by Saaty, who developed the well-known Analytic Hierarchy Process (AHP) (Saaty, 1977). Let us suppose, however, that top management decides to gather opinions from p experts. Should the AHP be used as a decision process, a pairwise comparison matrix (PCM) is formed in order to compare the relative importance of the evaluation criteria. Therefore, management will be forced to process zPCM’s to determine the group assessments.
To achieve group decision making based on the AHP, three different methods have been proposed. The Aggregation of Individual Judgements (AIJ), and the Aggregation of Individual Priorities (AIP) (Forman & Penitawi, 1998). Also, an optimization method has been proposed by Sun and Greenberg (2006). However, neither of the three mentioned approaches actually provides information on how the group of experts accommodated. For instance, it is not possible to determine how many of the evaluators agree on the resultant priorities. This is so because such techniques are based on geometrical averages.
Hence, to enhance group decision making, we developed a solution based on the combination of Multi-Agent Systems, the fuzzy C-means clustering technique and the Analytic Hierarchy Process. The proposed decision support system (DSS) allows distribution, asynchrony and clusters formation based on fuzzy c-means. Multi-Agent Systems fulfill technological needs related to automating the distribution and processing of large amounts of data. Fuzzy clustering is adequate to determine how many evaluations actually form the group majority. Also, it is established the value around which every single evaluation is close enough to be considered part of the winning cluster. This data is the largest cluster’s centroid. Furthermore, it is also possible to determine how compact the clusters are by computing data dispersion. Finally, the AHP is used to reach a final ranking of the alternatives once the experts’ evaluations are grouped.
The DSS we present provides the following modules. One module, residing at the management’s site, is used to define evaluation criteria, and broadcast such criteria to the evaluators. They, in turn, possess an evaluation module that helps collecting the judgements of experts. A third module is in charge of clustering the individual evaluations and reach a final decision.
The paper is organized as follows. Section 2 contains the related work tackling multi-criteria group decision making, particularly those techniques based on either fuzzy logic or MAS’s. Section 3 presents the mathematical description of the AHP, fuzzy C-means and the algorithm we propose to group the individual evaluations. In Section 4 we describe the Multi-Agent System, which is then shown in Section 5. The calculations are depicted in Section 6. We finish the report showing conclusions and insights about promising future work.
Decision making is a complex process, particularly when it is carried out by a multidisciplinary group of experts. On the other hand, companies are exploring state of the art decision support systems in order to promote distributed and asynchronous decision making.
The agent-based DSS we present in this article proved useful to achieve the former goals. Our agent-based DSS is a platform where top management can fix problem parameters, spread them through the company, and solve any group multi-criteria decision problem. At this regard, fuzzy C-means, used as a pre-processing step, not only helps determining the aggregated PCMG’s for both criteria and alternatives, but it is also useful to establish which evaluators actually agree on the resultant figures. This is an important piece of knowledge in order to provide feedback, and to elucidate afterwards reasons for discordant evaluations. Altogether, the distributed and intelligent system that we propose is useful for organizations that desire to improve multi-criteria group decision making.
After reviewing the related literature, we have encountered opportunities for upgrading the DSS. We can improve the evaluation process by using linguistic assessments rather than asking for absolute evaluations. On the theoretical side, we envision the calculation of fuzzy distances by means of fuzzy operators.
