Value-Driven Multiple Criteria Sorting with Probabilistic Linguistic Information Considering Uncertain Assignment Examples

Multiple criteria sorting (MCS) dedicates to assigning alternatives to one of the predefined ordered categories according to their evaluation information on multiple criteria. The utility (value) function-based sorting is a popular MCS procedure, which requires decision-makers to express their preferences through assignment examples. By taking the assignment examples as reference alternatives, the additive value function, as the preferred model of a decision maker, can be built using the preference disaggregation technique. However, the existing literature hardly considered people’s hesitancy when determining assignment examples, and ignored applying linguistic evaluation information on qualitative criteria. To fill these research gaps, this study proposes a value-driven MCS procedure with probabilistic linguistic information considering uncertain assignment examples. Specifically, the probability linguistic term set, as a flexible information representation tool, is introduced to express the hesitancy of decision-makers regarding assignment examples and the performance of alternatives on qualitative criteria. Besides, to comprehensively reflect the preference of a decision-maker, a weighted additive value function is proposed based on the preference disaggregation technique to calculate the comprehensive scores of alternatives in which the weights are determined by the best-worst method. Finally, a case study on the sorting of down coats for sale demonstrates the applicability and superiority of our proposed method.

MURAME parameter setting for creditworthiness evaluation: data-driven optimization

In this paper, we amend a multi-criteria methodology known as MURAME, to evaluate the creditworthiness of a large sample of Italian Small and Medium-sized Enterprises, using as input their balance sheet data. This methodology produces results in terms of scoring and of classification into homogeneous rating classes. A distinctive goal of this paper is to consider a preference disaggregation method to endogenously determine some parameters of MURAME, by solving a nonsmooth constrained optimization problem. Because of the complexity of the involved mathematical programming problem, for its solution we use an evolutionary metaheuristic, coupled with a specific efficient initialization. This is combined with an unconstrained reformulation of the problem, which provides a reasonable compromise between the quality of the solution and the computational burden. An extensive numerical experience is reported, comparing an exogenous choice of MURAME parameters with our approach.

A new approach for criteria weight elicitation of the ARAS-H method

Criteria weight inference is a crucial step for most of multi-criteria methods. However, criteria weights are often determined directly by the decision-maker (DM) which makes the results unreliable. Therefore, to overcome the imprecise weighting, we suggest the use of the preference programming technique. Instead of obtaining criteria weights directly from the DM, we infer them in a more objective manner to avoid the subjectivity and the unreliability of the results. Our aim is to elicit the ARAS-H criteria weights at each level of the hierarchy tree via mathematical programming, taking into account the DM’s preferences. To put it differently, starting from preference information provided by the DM, we proceed to model our constraints. The ARAS-H method is an extension of the classical ARAS method for the case of hierarchically structured criteria. We adopt a bottom-up approach in order to elicit ARAS-H criteria weights, that is, we start by determining the elementary criteria weights (i.e. the criteria at the lowest level of the hierarchy tree). The solution of the linear programs is obtained using LINGO software. The main contribution of our criteria weight elicitation procedure is in overcoming imprecise weighting without excluding the DM from the decision making process. Keywords: Multiple Criteria Decision Aiding, preference disaggregation, ARAS-H, criteria weights, mathematical programming.