arXiv subjects

José Rui Figueira

Publications and source records attributed to José Rui Figueira.

At least 19 recordsLinked to original sources

arXiv2026

A hybrid approach for building fuzzy numbers based on data and expert knowledge

This paper presents a hybrid socio-technical methodology for constructing fuzzy numbers from numerical data while incorporating expert knowledge through an interactive Deck of Cards (DoC) process. The approach extends the existing DoC membership function construction framework by introducing a data-driven pipeline based on a convex version of fuzzy $k$-Means in which each computational step produces intermediate outputs that are translated into card-based structures for expert validation and tuning. The proposed method ensures interpretability, adaptability, and consistency between empirical evidence and expert semantics.

math.GM↗

arXiv2026

AIdentifyAGE Ontology for Decision Support in Forensic Dental Age Assessment

Age assessment is crucial in forensic and judicial decision-making, particularly in cases involving undocumented individuals and unaccompanied minors, where legal thresholds determine access to protection, healthcare, and judicial procedures. Dental age assessment is widely recognized as one of the most reliable biological approaches for adolescents and young adults, but current practices are challenged by methodological heterogeneity, fragmented data representation, and limited interoperability between clinical, forensic, and legal information systems. These limitations hinder transparency and reproducibility, amplified by the increasing adoption of AI- based methods. The AIdentifyAGE ontology is domain-specific and provides a standardized, semantically coherent framework, encompassing both manual and AI-assisted forensic dental age assessment workflows, and enabling traceable linkage between observations, methods, reference data, and reported outcomes. It models the complete medico-legal workflow, integrating judicial context, individual-level information, forensic examination data, dental developmental assessment methods, radiographic imaging, statistical reference studies, and AI-based estimation methods. It is being developed together with domain experts, and it builds on upper and established biomedical, dental, and machine learning ontologies, ensuring interoperability, extensibility, and compliance with FAIR principles. The AIdentifyAGE ontology is a fundamental step to enhance consistency, transparency, and explainability, establishing a robust foundation for ontology-driven decision support systems in medico-legal and judicial contexts.

cs.AI↗

arXiv2025

The Tournament Tree Method for preference elicitation in Multi-criteria decision-making

Pairwise comparison methods, such as Fuzzy Preference Relations and Saaty's Multiplicative Preference Relations, are widely used to model expert judgments in multi-criteria decision-making. However, their application is limited by the high cognitive load required to complete $m(m-1)/2$ comparisons, the risk of inconsistency, and the computational complexity of deriving consistent value scales. This paper proposes the Tournament Tree Method (TTM), a novel elicitation and evaluation framework that overcomes these limitations. The TTM requires only $m-1$ pairwise comparisons to obtain a complete, reciprocal, and consistent comparison matrix. The method consists of three phases: (i) elicitation of expert judgments using a reduced set of targeted comparisons, (ii) construction of the consistent pairwise comparison matrix, and (iii) derivation of a global value scale from the resulting matrix. The proposed approach ensures consistency by design, minimizes cognitive effort, and reduces the dimensionality of preference modeling from $m(m-1)/2$ to $m$ parameters. Furthermore, it is compatible with the classical Deck of Cards method, and thus it can handle interval and ratio scales. We have also developed a web-based tool that demonstrates its practical applicability in real decision-making scenarios.

cs.AI↗

arXiv2025

Interval-valued Value Functions from Uncertain Preferences

The construction of numerical value scales (or priority values) is a recurrent topic in decision-aiding research. However, in real contexts, uncertainty and limited cognitive precision often lead decision-makers to provide interval judgments rather than exact values. In this scenario, even though obtaining a numerical value scale from interval preferences could be feasible, it implies a loss of information and an oversimplification of the input information. This paper proposes a general framework for deriving interval-valued value scales from interval-valued pairwise comparisons. This implies addressing fundamental challenges regarding the elicitation, the determination of representative value functions, and the preservation of properties such as monotonicity and interpretability. We start by presenting a new definition for the consistency of an interval-valued preference relation. We show that when consistency holds, interval-valued value functions can be determined, and we establish conditions for their uniqueness. Furthermore, we show that our proposal extends and unifies classical models such as fuzzy preference relations, Saaty's preference relations, and the Deck of Cards Method. Methodologically, we develop optimization models that provide procedures to guide decision-makers towards consistency when contradictions arise. The framework provides a coherent and interpretable foundation for constructing monotonic interval value functions, bridging classical and interval-valued preference models, and enhancing robustness in decision-making.

math.GM↗

arXiv2025

Building Interval Type-2 Fuzzy Membership Function: A Deck of Cards based Co-constructive Approach

Since its inception, Fuzzy Set has been widely used to handle uncertainty and imprecision in decision-making. However, conventional fuzzy sets, often referred to as type-1 fuzzy sets (T1FSs) have limitations in capturing higher levels of uncertainty, particularly when decision-makers (DMs) express hesitation or ambiguity in membership degree. To address this, Interval Type-2 Fuzzy Sets (IT2FSs) have been introduced by incorporating uncertainty in membership degree allocation, which enhanced flexibility in modelling subjective judgments. Despite their advantages, existing IT2FS construction methods often lack active involvement from DMs and that limits the interpretability and effectiveness of decision models. This study proposes a socio-technical co-constructive approach for developing IT2FS models of linguistic terms by facilitating the active involvement of DMs in preference elicitation and its application in multicriteria decision-making (MCDM) problems. Our methodology is structured in two phases. The first phase involves an interactive process between the DM and the decision analyst, in which a modified version of Deck-of-Cards (DoC) method is proposed to construct T1FS membership functions on a ratio scale. We then extend this method to incorporate ambiguity in subjective judgment and that resulted in an IT2FS model that better captures uncertainty in DM's linguistic assessments. The second phase formalizes the constructed IT2FS model for application in MCDM by defining an appropriate mathematical representation of such information, aggregation rules, and an admissible ordering principle. The proposed framework enhances the reliability and effectiveness of fuzzy decision-making not only by accurately representing DM's personalized semantics of linguistic information.

cs.AI↗

arXiv2025

A Multi-Objective Portfolio of Portfolios Problem with Qualitative Performance Assessments

We present a multi-objective portfolio decision model that involves selecting both a portfolio of projects and a set of elements to allocate to each project. Our model includes a defined set of objectives to optimize, with projects contributing to these objectives in various ways. The elements included in the portfolios are assessed based on both qualitative and quantitative criteria. Projects can only be selected for the portfolio if they meet specific requirements defined by threshold values on the criteria. The model is adaptable to include temporal considerations and stochastic, making it suitable for a wide range of real-life applications. To manage the decision-making process, we employ an interactive multi-objective method that integrates the selection of both portfolios and elements. After making initial selections, we ask the decision-maker to evaluate the portfolios, from which we derive a series of rules to be incorporated into the multiobjective model until the decision-maker is satisfied. We illustrate the functionality of our model through an illustrative case study.

math.CO↗

arXiv2024

On the Computational Complexity of Multi-Objective Ordinal Unconstrained Combinatorial Optimization

Multi-objective unconstrained combinatorial optimization problems (MUCO) are in general hard to solve, i.e., the corresponding decision problem is NP-hard and the outcome set is intractable. In this paper we explore special cases of MUCO problems that are actually easy, i.e., solvable in polynomial time. More precisely, we show that MUCO problems with up to two ordinal objective functions plus one real-valued objective function are tractable, and that their complete nondominated set can be computed in polynomial time. For MUCO problems with one ordinal and a second ordinal or real-valued objective function we present an even more efficient algorithm that applies a greedy strategy multiple times.

cs.DM↗

arXiv2024

New Multi-objective Partial Optimisation Decomposition Strategies for the Thesis Defence Scheduling Problem

A new multi-objective method for the thesis defence scheduling problem is introduced. The problem involves appointing committees to defences and assigning them to a time slot and room. A multi-objective approach is necessary to provide a better understanding of possible solutions and trade-offs to decision-makers. However, this type of approach is often time-consuming. The new multi-objective optimisation approach decomposes the monolithic problem into a sequence of multi-objective problems. This leads to significant efficiency gains compared to the augmented-e constraint method. The monolithic model is decomposed into two submodels solved sequentially. In the first stage, genetic algorithms find multiple committee configurations. The performance of these solutions is assessed based on committee assignment quality objectives and a proxy objective predicting performance in the next stage. In the second stage, considering multiple partial solutions found previously, an augmented e-constraint method is solved to find non-dominated solutions regarding the assignment of time slots to defences. These solutions consider schedule quality objectives. Finally, non-dominated solutions are presented based on objective function performance for both points of view. For small-size instances, the method takes 8-32% of the time of an augmented e-constraint method but finds non-dominated sets with slightly worse hyper-volume indicator values. For larger instances, times are 6-18% of monolithic resolutions, and hyper-volume indicator values are better. A real-world case study is presented. The experiment with decomposition found 39 non-dominated solutions in 1600 seconds. The augmented e-constraint method found 9 solutions in 2400 seconds. For the three objectives, the new method found a solution improving the best-performing solution with the other method in the time limit.

math.OC↗

arXiv2023

A hybrid meta-heuristic for the generation of feasible large-scale course timetables using instance decomposition

This study introduces a hybrid meta-heuristic for generating feasible course timetables in large-scale scenarios. We conducted tests using our university's instances. The current commercial software often struggles to meet constraints and takes hours to find satisfactory solutions. Our methodology combines adaptive large neighbourhood search, guided local search, variable neighbourhood search, and an innovative instance decomposition technique. Constraint violations from various groups are treated as objective functions to minimize. The search focuses on time slots with the most violations, and if no improvements are observed after a certain number of iterations, the most challenging constraint groups receive new weights to guide the search towards non-dominated solutions, even if the total sum of violations increases. In cases where this approach fails, a shaking phase is employed. The decomposition mechanism works by iteratively introducing curricula to the problem and finding new feasible solutions while considering an expanding set of lectures. Assignments from each iteration can be adjusted in subsequent iterations. Our methodology is tested on real-world instances from our university and random subdivisions. For subdivisions with 400 curricula timetables, decomposition reduced solution times by up to 27%. In real-world instances with 1,288 curricula timetables, the reduction was 18%. Clustering curricula with more common lectures and professors during increments improved solution times by 18% compared to random increments. Using our methodology, viable solutions for real-world instances are found in an average of 21 minutes, whereas the commercial software takes several hours.

math.OC↗

arXiv2022

A multiple criteria approach for constructing a pandemic impact assessment composite indicator: The case of Covid-19 in Portugal

The Covid-19 pandemic has caused impressive damages and disruptions in social, economic, and health systems (among others), and posed unprecedented challenges to public health and policy/decision-makers concerning the design and implementation of measures to mitigate its strong negative impacts. The Portuguese health authorities are currently using some decision analysis-like techniques to assess the impact of this pandemic and implementing measures for each county, region, or the whole country. Such decision tools led to some criticism and many stakeholders asked for novel approaches, in particular those having in consideration dynamical changes in the pandemic behavior arising, e.g., from new virus variants or vaccines. A multidisciplinary team formed by researchers of the Covid-19 Committee of Instituto Superior Técnico at Universidade de Lisboa (CCIST analysts team) and medical doctors from the Crisis Office of the Portuguese Medical Association (GCOM experts team) gathered efforts and worked together in order to propose a new tool to help politicians and decision-makers in the combat of the pandemic. This paper presents the main steps and elements, which led to the construction of a pandemic impact assessment composite indicator, applied to the particular case of {\sc{Covid-19}} in Portugal. A multiple criteria approach based on an additive multi-attribute value theory (MAVT) aggregation model was used to construct the pandemic assessment composite indicator (PACI). The parameters of the additive model were built through a sociotechnical co-constructive interactive process between CCIST and GCOM team members. The deck of cards method was the technical tool adopted to help in building the value functions and the assessment of the criteria weights.

math.OC↗

arXiv2022

A Multi-Objective Model for Thesis Defence Scheduling

We address the thesis defence scheduling problem, a critical academic scheduling management process, which has been overshadowed in the literature by its counterparts, course timetabling and exam scheduling. Specifically, the single defence assignment type of thesis defence scheduling problems, where each committee is assigned to a single defence, scheduled for a specific day, hour and room. We formulate a multi-objective mixed-integer linear programming model, which aims to be a general representation of the problem mentioned above, and that can, therefore, be applied to a broader set of cases than other models present in the literature, which have a focus on the characteristics of their universities. We introduce a new decision variable, propose constraint formulations that are not policy specific, and offer new takes on the more common objectives seen in the literature. We also include new objective functions based on our experience with the problem at our university. We also propose a two-stage solution approach. The first stage is employed to find the number of schedulable defences, enabling the optimisation of instances with unschedulable defences. The second stage is an implementation of the augmented e-constraint method, which allows for the search of a set of different and non-dominated solutions while skipping redundant iterations. A novel instance generator for thesis scheduling problems is presented. Its main benefit is the generation of the availability of committee members and rooms in availability and unavailability blocks, resembling their real-world counterparts. A set of 96 randomly generated instances of varying sizes is solved and analysed. The proposed method can find the optimal number of schedulable defences and present non-dominated solutions within the set time limits for every tested instance.

math.OC↗

arXiv2022

Exact and approximate determination of the Pareto set using minimal correction subsets

Recently, it has been shown that the enumeration of Minimal Correction Subsets (MCS) of Boolean formulas allows solving Multi-Objective Boolean Optimization (MOBO) formulations. However, a major drawback of this approach is that most MCSs do not correspond to Pareto-optimal solutions. In fact, one can only know that a given MCS corresponds to a Pareto-optimal solution when all MCSs are enumerated. Moreover, if it is not possible to enumerate all MCSs, then there is no guarantee of the quality of the approximation of the Pareto frontier. This paper extends the state of the art for solving MOBO using MCSs. First, we show that it is possible to use MCS enumeration to solve MOBO problems such that each MCS necessarily corresponds to a Pareto-optimal solution. Additionally, we also propose two new algorithms that can find a (1 + {\varepsilon})-approximation of the Pareto frontier using MCS enumeration. Experimental results in several benchmark sets show that the newly proposed algorithms allow finding better approximations of the Pareto frontier than state-of-the-art algorithms, and with guaranteed approximation ratios.

cs.AI↗

arXiv2021

New $ε$-constraint methods for multi-objective integer linear programming: a Pareto front representation approach

Dealing with multi-objective problems by using generation methods has some interesting advantages since it provides the decision-maker with the complete information about the set of non-dominated points (Pareto front) and a clear overview of the problem. However, providing many solutions to the decision-maker might also be overwhelming. As an alternative approach, presenting a representative set of solutions of the Pareto front may be advantageous. Choosing such a representative set is by itself also a multi-objective problem that must consider the number of solutions to present, the uniformity, and/or the coverage of the representation, to guarantee its quality. This paper proposes three algorithms for the representation problem for multi-objective integer linear programming problems with two or more objective functions, each one of them dealing with each dimension of the problem (cardinality, coverage, and uniformity). Such algorithms are all based on the $ε$-constraint approach. In addition, the paper also presents strategies to overcome poor estimations of the Pareto front bounds. The algorithms were tested on the ability to efficiently generate the whole Pareto front or its representation. The uniformity and cardinality algorithms proved to be very efficient both in binary and integer problems, being amongst the best in the literature. Both coverage and uniformity algorithms provide good quality representations on their targeted objective, while the cardinality algorithm appears to be the most flexible, privileging uniformity for lower cardinality representations and coverage on higher cardinality.

math.OC↗

arXiv2021

A multiple criteria approach for ship risk classification: An alternative to the Paris MoU Ship Risk Profile

The Paris Memorandum of Understanding on Port State Control (Paris MoU) is responsible for controlling substandard shipping in European waters and, consequently, increasing the standards of safety, pollution prevention, and onboard living and working conditions. Since 2011, the Memorandum adopted a system of points, named the "Ship Risk Profile" (SRP), under which each ship is assigned a risk profile according to its score on a set of criteria. Being a multiple criteria decision aiding (MCDA) tool at its core, comprising criteria, weights, and risk categories, limited research has been performed on the SRP from an MCDA perspective. The purpose of this paper is to propose an MCDA approach for ship risk classification through the Deck of Cards Method (DCM). The DCM is particularly suitable within this context as it allows, intuitively for the decision-maker, to model preference among different criteria and among different levels on criteria scales. First, a framework is built, based on the criteria established in the SRP. Second, the DCM is used to build the MCDA model, including the definition of the criteria value functions and criteria weights. Finally, the proposed MCDA model is applied to a dataset of ships and the results are discussed. Robust results have been obtained with the proposed approach, making it a potential alternative to the current SRP.

stat.AP↗

arXiv2020

Sparsifying Parity-Check Matrices

Parity check matrices (PCMs) are used to define linear error correcting codes and ensure reliable information transmission over noisy channels. The set of codewords of such a code is the null space of this binary matrix. We consider the problem of minimizing the number of one-entries in parity-check matrices. In the maximum-likelihood (ML) decoding method, the number of ones in PCMs is directly related to the time required to decode messages. We propose a simple matrix row manipulation heuristic which alters the PCM, but not the code itself. We apply simulated annealing and greedy local searches to obtain PCMs with a small number of one entries quickly, i.e. in a couple of minutes or hours when using mainstream hardware. The resulting matrices provide faster ML decoding procedures, especially for large codes.

cs.IT↗

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↗

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

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↗