arXiv subjects

Sally Giuseppe Arcidiacono

Publications and source records attributed to Sally Giuseppe Arcidiacono.

5 recordsLinked to original sources

arXiv2023

Inducing a probability distribution in Stochastic Multicriteria Acceptability Analysis

In multiple criteria decision aiding, very often the alternatives are compared by means of a value function compatible with the preferences expressed by the Decision Maker. The problem is that, in general, there is a plurality of compatible value functions, and providing a final recommendation on the problem at hand considering only one of them could be considered arbitrary to some extent. For such a reason, Stochastic Multicriteria Acceptability Analysis gives information in statistical terms by taking into account a sample of models compatible with the provided preferences. These statistics are given assuming the existence of a probability distribution in the space of value functions being defined a priori. In this paper, we propose some methods aiming to build a probability distribution on the space of value functions considering the preference information given by the Decision Maker. To prove the goodness of our proposal we performed an extensive set of simulations. Moreover, a sensitivity analysis on the variables of our procedure has been done as well.

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arXiv2022

Scoring from Pairwise Winning Indices

The pairwise winning indices, computed in the Stochastic Multicriteria Acceptability Analysis, give the probability with which an alternative is preferred to another taking into account all the instances of the assumed preference model compatible with the information provided by the Decision Maker in terms of pairwise preference comparisons of reference alternatives. In this paper we present a new scoring method assigning a value to each alternative summarizing the results of the pairwise winning indices. Several procedures assigning a score to each alternative on the basis of the pairwise winning indices have been provided in literature. However, while all of them compute this score just to rank the alternatives under consideration, our method, expressing the score in terms of an additive value function, permits to disaggregate the overall evaluation of each alternative in the sum of contributions of considered criteria. This will permit not only to rank the alternatives but also to explain the reasons for which an alternative obtains its evaluation and, consequently, fills a certain ranking position. To prove the efficiency of the method in representing the preferences of the Decision Maker, we performed an extensive set of simulations varying the number of alternatives and criteria. The results of the simulations, analyzed from a statistical point of view, show the goodness of our procedure. The applicability of the method to decision making problems is explained by means of a case study related to the evaluation of financial funds.

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arXiv2021

Supporting the robust ordinal regression approach to multiple criteria decision aiding with a set of representative value functions

In this paper we propose a new methodology to represent the results of the robust ordinal regression approach by means of a family of representative value functions for which, taken two alternatives $a$ and $b$, the following two conditions are satisfied: 1) if for all compatible value functions $a$ is evaluated not worse than $b$ and for at least one value function $a$ has a better evaluation, then the evaluation of $a$ is greater than the evaluation of $b$ for all representative value functions; 2) if there exists one compatible value function giving $a$ an evaluation greater than $b$ and another compatible value function giving $a$ an evaluation smaller than $b$, then there are also at least one representative function giving a better evaluation to $a$ and another representative value function giving $a$ an evaluation smaller than $b$. This family of representative value functions intends to provide the Decision Maker (DM) a more clear idea of the preferences obtained by the compatible value functions, with the aim to support the discussion in constructive approach of Multiple Criteria Decision Aiding.

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arXiv2020

Robust stochastic sorting with interacting criteria hierarchically structured

In this paper we propose a new multiple criteria decision aiding method to deal with sorting problems in which alternatives are evaluated on criteria structured in a hierarchical way and presenting interactions. The underlying preference model of the proposed method is the Choquet integral, while the hierarchical structure of the criteria is taken into account by applying the Multiple Criteria Hierarchy Process. Considering the Choquet integral based on a 2-additive capacity, the paper presents a procedure to find all the minimal sets of pairs of interacting criteria representing the preference information provided by the Decision Maker (DM). Robustness concerns are also taken into account by applying the Robust Ordinal Regression and the Stochastic Multicriteria Acceptability Analysis. Even if in different ways, both of them provide recommendations on the hierarchical sorting problem at hand by exploring the whole set of capacities compatible with the preferences provided by the DM avoiding to take into account only one of them. The applicability of the considered method to real world problems is demonstrated by means of an example regarding rating of European Countries by considering economic and financial data provided by Standard \& Poor's Global Inc.

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arXiv2019

As simple as possible but not simpler in Multiple Criteria Decision Aiding: the ROR-SMAA level dependent Choquet integral approach

The level dependent Choquet integral has been proposed to handle decision making problems in which the importance and the interaction of criteria may depend on the level of the alternatives' evaluations. This integral is based on a level dependent capacity, which is a family of single capacities associated to each level of evaluation for the considered criteria. We present two possible formulations of the level dependent capacity where importance and interaction of criteria are constant inside each one of the subintervals in which the interval of evaluations for considered criteria is split or vary with continuity inside the whole interval of evaluations. Since, in general, there is not only one but many level dependent capacities compatible with the preference information provided by the Decision Maker, we propose to take into account all of them by using the Robust Ordinal Regression (ROR) and the Stochastic Multicriteria Acceptability Analysis (SMAA). On one hand, ROR defines a necessary preference relation (if an alternative a is at least as good as an alternative b for all compatible level dependent capacities), and a possible preference relation (if a is at least as good as b for at least one compatible level dependent capacity). On the other hand, considering a random sampling of compatible level dependent capacities, SMAA gives the probability that each alternative reaches a certain ranking position as well as the probability that an alternative is preferred to another. A real-world decision problem on rankings of universities is provided to illustrate the proposed methodology.

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