Identification of Choquet capacity in multicriteria sorting problems through stochastic inverse analysis

In multicriteria decision aiding (MCDA), the Choquet integral has been used as an aggregation operator to deal with the case of interacting decision criteria. While the application of the Choquet integral for ranking problems have been receiving most of the attention, this paper rather focuses on multicriteria sorting problems (MCSP). In the Choquet integral context, a practical problem that arises is related to the elicitation of parameters known as the Choquet capacities. We address the problem of Choquet capacity identification for MCSP by applying the Stochastic Acceptability Multicriteri Analysis (SMAA), proposing the SMAA-S-Choquet method. The proposed method is also able to model uncertain data that may be present in both decision matrix and limiting profiles, the latter a parameter associated with the sorting problematic. We also introduce two new descriptive measures in order to conduct reverse analysis regarding the capacities: the Scenario Acceptability Index and the Scenario Central Capacity vector.

Multiple criteria hierarchy process for sorting problems under uncertainty applied to the evaluation of the operational maturity of research institutions

Despite the availability of qualified research personnel, up-to-date research facilities and experience in developing applied research and innovation, many worldwide research institutions face difficulties when managing contracted Research and Development (R&D) projects due to expectations from Industry (private sector). Such difficulties have motivated funding agents to create evaluation processes to check whether the operational procedures of funded research institutions are sufficient to provide timely answers to demand for innovation from industry and also to identify aspects that require quality improvement in research development. For this purpose, several multiple criteria decision-making approaches can be applied. Among the available multiple criteria approaches, sorting methods are one prominent tool to evaluate the operational capacity. However, the first difficulty in applying multiple criteria sorting methods is the need to hierarchically structure multiple criteria in order to represent the intended decision process. Additional challenges include the elicitation of the preference information and the definition of criteria evaluation, since these are frequently affected by some imprecision. In this paper, a new sorting method is proposed to deal with all of those critical points simultaneously. To consider multiple levels for the decision criteria, the FlowSort method is extended to account for hierarchical criteria. To deal with imprecise data, the FlowSort is integrated with fuzzy approaches. To yield solutions that consider fluctuations from imprecise weights, the Stochastic Multicriteria Acceptability Analysis is used. Finally, the proposed method is applied to the evaluation of research institutions, classifying them according to their operational maturity for development of applied research.