arXiv subjects

Salvatore Greco

Publications and source records attributed to Salvatore Greco.

At least 37 records · Page 2Linked to original sources

arXiv2022

Dominance-based Rough Set Approach, basic ideas and main trends

Dominance-based Rough Approach (DRSA) has been proposed as a machine learning and knowledge discovery methodology to handle Multiple Criteria Decision Aiding (MCDA). Due to its capacity of asking the decision maker (DM) for simple preference information and supplying easily understandable and explainable recommendations, DRSA gained much interest during the years and it is now one of the most appreciated MCDA approaches. In fact, it has been applied also beyond MCDA domain, as a general knowledge discovery and data mining methodology for the analysis of monotonic (and also non-monotonic) data. In this contribution, we recall the basic principles and the main concepts of DRSA, with a general overview of its developments and software. We present also a historical reconstruction of the genesis of the methodology, with a specific focus on the contribution of Roman Słowiński.

cs.AI↗

arXiv2022

A multiple criteria methodology for priority based portfolio selection

This paper presents a new methodology that combines a multiple criteria sorting or ranking method with a project portfolio selection procedure. The multicriteria method permits to compare projects in terms of their priority assessed on the basis of a set of both qualitative and quantitative criteria. Then, a feasible set of projects, i.e. a portfolio, is selected according to the priority defined by the multiple criteria method. In addition, the portfolio must satisfy a set of resources constraints, e.g. budget available, as well as some logical constraints, e.g. related to projects to be selected together or projects mutually exclusive. The proposed portfolio selection methodology can be applied in different contexts. We present an application in the urban planning domain where our approach allows to select a set of urban projects on the basis of their priority, budgetary constraints and urban policy requirements. Given the increasing interest of historical cities to reuse their cultural heritage, we applied and tested our methodology in this context. In particular, we show how the methodology can support the prioritization of the interventions on buildings with some historical value in the historic city center of Naples (Italy), taking into account several points of view.

cs.CY↗

arXiv2022

Fuzzy granular approximation classifier

In this article, a new Fuzzy Granular Approximation Classifier (FGAC) is introduced. The classifier is based on the previously introduced concept of the granular approximation and its multi-class classification case. The classifier is instance-based and its biggest advantage is its local transparency i.e., the ability to explain every individual prediction it makes. We first develop the FGAC for the binary classification case and the multi-class classification case and we discuss its variation that includes the Ordered Weighted Average (OWA) operators. Those variations of the FGAC are then empirically compared with other locally transparent ML methods. At the end, we discuss the transparency of the FGAC and its advantage over other locally transparent methods. We conclude that while the FGAC has similar predictive performance to other locally transparent ML models, its transparency can be superior in certain cases.

cs.AI↗

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.

math.OC↗

arXiv2022

Multiobjective Combinatorial Optimization with Interactive Evolutionary Algorithms: the case of facility location problems

We consider multiobjective combinatorial optimization problems handled by means of preference driven efficient heuristics. They look for the most preferred part of the Pareto front on the basis of some preferences expressed by the Decision Maker during the process. In general, what is searched for in this case is the Pareto set of efficient solutions. This is a problem much more difficult than optimizing a single objective function. Moreover, obtaining the Pareto set does not mean that the decision problem is solved since one or some of the solutions have to be chosen. Indeed, to make a decision, it is necessary to determine the most preferred solution in the Pareto set, so that it is also necessary to elicit the preferences of the user. In this perspective, what we are proposing can be seen as the first structured methodology in facility location problems to search optimal solutions taking into account preferences of the user. With this aim, we approach facility location problems using a recently proposed interactive evolutionary multiobjective optimization procedure called NEMO-II-Ch. NEMO-II-Ch is applied to a real world multiobjective location problem with many users and many facilities to be located. Several simulations considering different fictitious users have been performed. The results obtained by NEMO-II-Ch are compared with those got by three algorithms which know the user's true value function that is, instead, unknown to NEMO-II-Ch. They show that in many cases NEMO-II-Ch finds the best subset of locations more quickly than the methods knowing, exactly, the whole user's true preferences.

math.OC↗

arXiv2022

Multi-class granular approximation by means of disjoint and adjacent fuzzy granules

In granular computing, fuzzy sets can be approximated by granularly representable sets that are as close as possible to the original fuzzy set w.r.t. a given closeness measure. Such sets are called granular approximations. In this article, we introduce the concepts of disjoint and adjacent granules and we examine how the new definitions affect the granular approximations. First, we show that the new concepts are important for binary classification problems since they help to keep decision regions separated (disjoint granules) and at the same time to cover as much as possible of the attribute space (adjacent granules). Later, we consider granular approximations for multi-class classification problems leading to the definition of a multi-class granular approximation. Finally, we show how to efficiently calculate multi-class granular approximations for Łukasiewicz fuzzy connectives. We also provide graphical illustrations for a better understanding of the introduced concepts.

cs.AI↗

arXiv2021

A Novel Machine Learning Approach to Data Inconsistency with respect to a Fuzzy Relation

Inconsistency in prediction problems occurs when instances that relate in a certain way on condition attributes, do not follow the same relation on the decision attribute. For example, in ordinal classification with monotonicity constraints, it occurs when an instance dominating another instance on condition attributes has been assigned to a worse decision class. It typically appears as a result of perturbation in data caused by incomplete knowledge (missing attributes) or by random effects that occur during data generation (instability in the assessment of decision attribute values). Inconsistencies with respect to a crisp preorder relation (expressing either dominance or indiscernibility between instances) can be handled using symbolic approaches like rough set theory and by using statistical/machine learning approaches that involve optimization methods. Fuzzy rough sets can also be seen as a symbolic approach to inconsistency handling with respect to a fuzzy relation. In this article, we introduce a new machine learning method for inconsistency handling with respect to a fuzzy preorder relation. The novel approach is motivated by the existing machine learning approach used for crisp relations. We provide statistical foundations for it and develop optimization procedures that can be used to eliminate inconsistencies. The article also proves important properties and contains didactic examples of those procedures.

cs.AI↗

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.

math.OC↗

arXiv2021

Explaining the Deep Natural Language Processing by Mining Textual Interpretable Features

Despite the high accuracy offered by state-of-the-art deep natural-language models (e.g. LSTM, BERT), their application in real-life settings is still widely limited, as they behave like a black-box to the end-user. Hence, explainability is rapidly becoming a fundamental requirement of future-generation data-driven systems based on deep-learning approaches. Several attempts to fulfill the existing gap between accuracy and interpretability have been done. However, robust and specialized xAI (Explainable Artificial Intelligence) solutions tailored to deep natural-language models are still missing. We propose a new framework, named T-EBAnO, which provides innovative prediction-local and class-based model-global explanation strategies tailored to black-box deep natural-language models. Given a deep NLP model and the textual input data, T-EBAnO provides an objective, human-readable, domain-specific assessment of the reasons behind the automatic decision-making process. Specifically, the framework extracts sets of interpretable features mining the inner knowledge of the model. Then, it quantifies the influence of each feature during the prediction process by exploiting the novel normalized Perturbation Influence Relation index at the local level and the novel Global Absolute Influence and Global Relative Influence indexes at the global level. The effectiveness and the quality of the local and global explanations obtained with T-EBAnO are proved on (i) a sentiment analysis task performed by a fine-tuned BERT model, and (ii) a toxic comment classification task performed by an LSTM model.

cs.CL↗

arXiv2021

Data Envelopment Analysis models with imperfect knowledge of input and output values: An application to Portuguese public hospitals

Assessing the technical efficiency of a set of observations requires that the associated data composed of inputs and outputs are perfectly known. If this is not the case, then biased estimates will likely be obtained. Data Envelopment Analysis (DEA) is one of the most extensively used mathematical models to estimate efficiency. It constructs a piecewise linear frontier against which all observations are compared. Since the frontier is empirically defined, any deviation resulting from low data quality (imperfect knowledge of data or IKD) may lead to efficiency under/overestimation. In this study, we model IKD and, then, apply the so-called Hit \& Run procedure to randomly generate admissible observations, following some prespecified probability density functions. Sets used to model IKD limit the domain of data associated with each observation. Any point belonging to that domain is a candidate to figure out as the observation for efficiency assessment. Hence, this sampling procedure must run a sizable number of times (infinite, in theory) in such a way that it populates the whole sets. The DEA technique is used during the execution of each iteration to estimate bootstrapped efficiency scores for each observation. We use some scenarios to show that the proposed routine can outperform some of the available alternatives. We also explain how efficiency estimations can be used for statistical inference. An empirical case study based on the Portuguese public hospitals database (2013-2016) was addressed using the proposed method.

stat.ME↗

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.

math.OC↗

arXiv2020

The {0,1}-knapsack problem with qualitative levels

A variant of the classical knapsack problem is considered in which each item is associated with an integer weight and a qualitative level. We define a dominance relation over the feasible subsets of the given item set and show that this relation defines a preorder. We propose a dynamic programming algorithm to compute the entire set of non-dominated rank cardinality vectors and we state two greedy algorithms, which efficiently compute a single efficient solution.

cs.DS↗

arXiv2020

Multiple criteria decision analysis with the SRF-II method to compare hypotheses of adaptive reuse for an iconic historical building

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.

cs.CY↗

arXiv2019

A robust hierarchical nominal classification method based on similarity and dissimilarity using loss function and an improved version of the deck of cards 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.

cs.AI↗

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.

math.OC↗

arXiv2019

Robust measurement of innovation performances in Europe with a hierarchy of interacting composite indicators

For long time the measurement of innovation has been in the forefront of policy makers' and researchers' agenda worldwide. Therefore, there is an ongoing debate about which indicators should be used to measure innovation. Recent approaches have favoured the use of composite innovation indicators. However, there is no consensus about the appropriate methodology to aggregate the varying dimensions of innovation into a single summary indicator. One of the best known examples of composite innovation indicators is the European Innovation Scoreboard (EIS). It is a relevant tool for benchmarking innovation in Europe. Still, the EIS lacks a proper scheme for weighting the included indicators according to their relative importance. In this context, we propose an appraisal methodology permitting to take into consideration the interaction of criteria and robustness concerns related to the elicitation of the weights assigned to the elementary indicators. With this aim, we apply the hierarchical-SMAA-Choquet integral approach. This integrated multicriteria decision making (MCDM) method helps the users to rank and benchmark countries' innovation performance taking into account the importance and interaction of criteria assigned by themselves, rather than equal weights or weights exogenously fixed by external experts.

q-fin.GN↗

arXiv2019

Electre-Score: A first outranking based method for scoring actions

In this paper we present (to the best of our knowledge) the first outranking method to assign a score to each alternative. It is a method of the Electre family, and we will call it Electre-Score. Contrarily to the Multi-Attribute Value Theory methods, Electre-Score does not construct a value function for each criterion, and then proceeds to the aggregation into a single value. It rather, makes use of the outranking relations to make a comparison with reference sets of actions (to which a score is assigned) and proposes a score range to each alternative, instead of a single value. This is a more robust way of proceeding given the fragility of a single score. The sets of limiting profiles are defined with the help of Electre Tri-nB and the reference scores are assigned to them through the application of the deck of cards technique. The fact of being able to use outranking relations, makes it also possible to take into account the imperfect knowledge of data and avoids systematic compensatory effects. Some fundamental theoretical results guaranteeing the consistency of the method and an illustrative example are also provided in this paper.

cs.CE↗

arXiv2019

A new scaling MCDA procedure putting together pairwise comparison tables and the deck of cards method

This paper deals with an improved version of the deck of the cards method to render the construction of the ratio and interval scales more `accurate'. The improvement comes from the fact that we can account for a richer and finer preference information provided by the decision-makers, which permits a more accurate modelling of the strength of preference between two consecutive levels of a scale. Instead of considering only the number of blank cards between consecutive positions in the ranking of objects such as criteria and scale levels, we consider also the number of blank cards between non consecutive positions in the ranking. This information is collected in a pairwise comparison table that it is not necessarily built with precise values. We can consider also missing information and imprecise information provided in the form of ranges. Since the information provided by the decision-makers is not necessarily consistent, we propose also some procedures to help the decision-maker to make consistent his evaluations in a co-constructive way interacting with an analyst and reflecting and revising her/his judgments. The method is illustrated through and example in which, generalizing the SWING method, interacting criteria are aggregated through the Choquet integral.

math.OC↗