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Despite its recent introduction in literature, the Best–Worst Method (BWM) is among the most well-known and applied methods in Multicriteria Decision-Making. The method can be used to elicit the relative importance (weight) of the criteria as well as to get the priorities of the alternatives on the criteria at hand. In this paper, we will present an extension of the method, namely, the parsimonious Best–Worst-Method (P-BWM) permitting to apply the BWM to get the priorities of the alternatives in case they are in a large number. At first, the Decision-Maker (DM) is asked to give a rating to the alternatives under consideration; after, the classical BWM is applied to a set of reference alternatives to get their priorities used to compute, then, the priorities of all the alternatives under consideration. We propose also a procedure to select reference alternatives, possibly in cooperation with the DM, providing a well-distributed coverage of the rating range. The new proposal requires the DM a fewer number of pairwise comparisons than the original BWM. Another contribution of the paper is related to the comparison between BWM, P-BWM, the Analytic Hierarchy Process (AHP), and the parsimonious AHP in terms of the amount of preference information provided by the DM in each method to apply it. In addition to the standard approach, we propose one alternative way of inferring the priority vectors in BWM and P-BWM based on the barycenter of the space of alternatives priorities compatible with the preferences given by the DM. Finally, an experiment with university students has been conducted to test the new proposal. Results of the experiments show that P-BWM performs better than BWM in terms of capability to represent the DM's preferences and the difference between the results of the two methods is significant from the statistical point of view. The new proposal will permit to use the potentialities of the BWM to get the alternatives’ priorities in real-world decision-maki, Transport and Logistics

The paper shows how Multiple Criteria Decision Aiding (MCDA) tools can support the analyses of six hypotheses of adaptive reuse of an iconic historical building in Turin, Italy (called Stock Exchange) to identify the preferred alternative. In the last two years, the debate around the requalification of the building has been huge for several reasons: it is perceived as a "monument" by citizens; it shows architectural and typological values nationally recognized; it involves public and private interests. In this context, interacting with experts involved in the ongoing discussion, we consider a recently proposed conjunction of four MCDA methods, namely: Multiple Criteria Hierarchy Process (MCHP), permitting to consider structural relationships between criteria; ELECTRE III, considering three types of interaction effects between criteria (strengthening, weakening and antagonistic effects); the imprecise SRF method, supplying an easily understandable approach to collect information from the DM; and Stochastic Multicriteria Acceptability Analysis (SMAA), providing robust recommendation, in terms of rankings and relations of preference, indifference and incomparability between project alternatives, at each level of the hierarchy. We propose a modification of the SRF methodology, called SFR-II, to increase the reliability of the decision aid procedure, which could constitute a significant advance for the same SRF method.

Cat-SD is a multiple criteria decision aiding method for dealing with nominal classification problems. Actions are assessed according to multiple criteria and assigned to one or more categories. A set of reference actions is used for defining each category. The assignment of an action to a given category depends on the comparison of the action to each reference set according to likeness thresholds. Distinct sets of criteria weights, interaction coefficients, and likeness thresholds can be defined per category. We propose to apply Multiple Criteria Hierarchy Process (MCHP) to Cat-SD. An adapted MCHP is proposed to take into account possible interaction effects between criteria structured in a hierarchical way. On the basis of the known deck of cards method, we also consider an imprecise elicitation of parameters permitting to take into account interactions and antagonistic effects between criteria. The elicitation procedure we are proposing can be applied to any Electre method. With the purpose of exploring the assignments obtained by Cat-SD considering possible sets of parameters, we propose to apply the Stochastic Multicriteria Acceptability Analysis (SMAA). The SMAA methodology allows to draw statistical conclusions on the classification of the actions. The proposed method, SMAA-hCat-SD, helps the decision maker to check the effects of the variation of parameters on the classification at different levels of the hierarchy. We propose also a procedure, based on the concept of loss function, to obtain a final classification fulfilling some requirements given by the decision maker and taking into account the hierarchy of criteria and the probabilistic assignments obtained applying SMAA. Also this procedure can be applied to any classification Electre method.

We propose a development of the Analytic Hierarchy Process (AHP) permitting to use the methodology also in cases of decision problems with a very large number of alternatives evaluated with respect to several criteria. While the application of the original AHP method involves many pairwise comparisons between alternatives and criteria, our proposal is composed of three steps: (i) direct evaluation of the alternatives at hand on the considered criteria, (ii) selection of some reference evaluations; (iii) application of the original AHP method to reference evaluations; (iv) revision of the direct evaluation on the basis of the prioritization supplied by AHP on reference evaluations. The new proposal has been tested and validated in an experiment conducted on a sample of university students. The new methodology has been therefore applied to a real world problem involving the evaluation of 21 Social Housing initiatives sited in the Piedmont region (Italy). To take into account interaction between criteria, the Choquet integral preference model has been considered within a Non Additive Robust Ordinal Regression approach.