Multi-expert decisions and interactive preference aggregation

The traditional thematic profile of our research group is that of the foundations and mathematical models for the representation of preferences and their aggregation. In the context of the theory of aggregation functions, in particular, our research concerns the generalizations of the weighted mean concept, from mixture functions to Choquet integrals, with special attention to the interactive structure of the aggregation scheme.

Within the general thematic profile, some of the research areas are: (1) multicriteria decision models based on vector or matrix preference representations, in particular the representation of preferences by means of pairwise comparison matrices; (2) welfare measures and generalized Gini inequality indices, poverty measures; (3) multiagent decision models, consensus/dissensus measures, and linear and non-linear models of consensus dynamics.

The MEDIA research group, currently coordinated by R.A. Marques Pereira, consolidated in the early 1990s with the coordination of Mario Fedrizzi and has maintained a continuous international research profile in the field of mathematics applied to the study of preference structures and multicriteria decision models, with particular focus on the following recent research topics:

* Aggregation functions, classical (WA) and ordered (OWA) weighted means, capacities and Choquet integrals, interaction and k-additivity in Choquet aggregation, applications and models in decision making.

* Dual decomposition of aggregation functions, welfare functions and inequality indices, poverty measures and their decomposition.

* Welfare functions and generalized Gini inequality indices (Gini, Bonferroni, De Vergottini), ordered weighted means (OWA) and their binomial decomposition in terms of k-additivity.

* Aggregation by means of mixture functions, generating functions of the weighting structure, parametric characterization of monotonicity.

* Consistency and measures of inconsistency in preference structures expressed by means of pairwise comparison matrices, as in Saaty's Analytic Hierarchy Process (AHP).

* Aggregation models by means of the Choquet integral in the presence of interaction between criteria or agents.

* Linear consensus dynamics models with asymptotic convergence to consensus, intended as dynamic representations of aggregation models in the presence of interaction.

* Models of non-linear consensus dynamics, optimization of non-linear measures of dissensus, study of consensus dynamics under uncertainty / imprecision.

* Multidistances between n points intended as generalizations of the classical distance between two points, multidistances based on the sum and on particular types of aggregation functions: classical, ordered, and semi-arithmetic weighted averaging. Measures of dissensus based on multidistances.

* Entropy optimization within the framework of ordered weighted averaging with an orness constraint, Shannon entropy and Tsallis entropy.

The research group interacts with colleagues within the field of mathematics applied to economics and management in various national and international contexts, within a network of collaborations consolidated over the years which includes, for instance (in alphabetical order): Bilbao, Bratislava, Catania, Ghent, Lisbon, Naples, Paris, Valladolid.

The collaboration with R. A. Ribeiro (Lisbon), in particular, in both the methodological and technological contexts, has played a key role in the international research project “New Operators for Monitoring and Diagnostic Intelligent Systems” NOMDIS 2005/06, funded by the “European Space Agency” ESA, Darmstadt.

As an expression of its network of national and international collaborations, the MEDIA research group organized the following conferences in Trento:

  • XXXII Conference of the Association for Mathematics Applied to Social and Economic Sciences AMASES 2008, held at the Department of Computer Science and Business Studies and the Faculty of Economics of the University of Trento, September 1-4, 2008, visit the website https://www.unitn.it/archivio/events/amases08.html
  • Series of international conferences on "Preferences and Decisions" TRENTO 1997, 1998, 2000, 2003 and 2009, held at the Department of Computer Science and Business Studies and the Faculty of Economics of the University of Trento, visit the website http://events.unitn.it/en/trento2009

“The international workshop TRENTO 2009 focuses on Preference Modelling and Decision Theory and aims at providing an opportunity for sharing and discussing the recent research developments in this field. The scope of the international workshop TRENTO 2009 covers a wide range of topics in decision theory and preference modelling, such as preference representation and rationality, probabilistic and possibilistic decision models, cooperative game theory, multicriteria and multiagent decision models, fuzzy set theory and fuzzy logic for decision making, aggregation functions, complex network models and negotiation, interactive dynamics and consensus reaching, optimization and operational research for decision making, social choice and voting systems, soft computing and applications.”

Members of the MEDIA research group

Silvia Bortot (internal member)
Matteo Brunelli (external member)
Debora Di Caprio (internal member)
Mario Fedrizzi (external member, Professor Emeritus)
Michele Fedrizzi (external member)
R. A. Marques Pereira (coordinatore, internal member)
Franco Molinari (external member)

Selected publications of the MEDIA research group member

  • Bortot, Silvia; Marques Pereira, Ricardo Alberto; Stamatopoulou, Anastasia, "Consensus dynamics, network interaction, and Shapley indices in the Choquet framework" in SOFT COMPUTING, v. 24, n. 18, (2020), p. 13757-13768.
  • Bortot, Silvia; Marques Pereira, Ricardo Alberto; Stamatopoulou, Anastasia, "Shapley and superShapley aggregation emerging from consensus dynamics in the multicriteria Choquet framework" in DECISIONS IN ECONOMICS AND FINANCE, v. 43, n. 2, (2020), p. 583-611.
  • Brunelli, Matteo; Cavallo, Bice, "Distance-based measures of incoherence for pairwise comparisons" in KNOWLEDGE-BASED SYSTEMS, v. 187, (2020), p. 104808.
  • Fedrizzi, Michele; Brunelli, Matteo; Caprila, Alexandra, "The linear algebra of pairwise comparisons" in INTERNATIONAL JOURNAL OF APPROXIMATE REASONING, v. 118, (2020), p. 190-207.
  • Santos Arteaga, Francisco Javier; Tavana, Madjid; Di Caprio, Debora, "A new model for evaluating subjective online ratings with uncertain intervals" in EXPERT SYSTEMS WITH APPLICATIONS, v. 139, (2020), p. 112850. 
  • Santos Arteaga, Francisco Javier; Di Caprio, Debora; Cucchiari, David; Campistol, Josep M; Oppenheimer, Federico; Diekmann, Fritz; Revuelta, Ignacio, "Modeling patients as decision making units: evaluating the efficiency of kidney transplantation through data envelopment analysis" in HEALTH CARE MANAGEMENT SCIENCE, (2020), in press. https://doi.org/10.1007/s10729-020-09516-2.34, (2019), p. 966-1000.
  • Brunelli, Matteo, "A study on the anonymity of pairwise comparisons in group decision making" in EUROPEAN JOURNAL OF OPERATIONAL RESEARCH, v. 279, n. 2, (2019), p. 502-510.
  • Di Caprio, Debora; Santos Arteaga, Francisco Javier, "A novel perception-based DEA method to evaluate alternatives in uncertain online environments" in COMPUTERS & INDUSTRIAL ENGINEERING, v. 131, (2019), p. 327-343.
  • Hajipour, Vahid; Tavana, Madjid; Di Caprio, Debora; Akhgar, Majid; Jabbari, Yasaman, "An optimization model for traceable closed-loop supply chain networks" in APPLIED MATHEMATICAL MODELLING, v. 71, (2019), p. 673-699.
  • Siebert, Jana; Petri, Dario; Fedrizzi, Michele, "From Measurement to Decision: Sensitivity of Decision Outcome to Input and Model Uncertainties" in IEEE TRANSACTIONS ON INSTRUMENTATION AND MEASUREMENT, v. 68, n. 9, (2019), p. 3100-3108.
  • Bortot, Silvia; Marques Pereira, Ricardo Alberto; Nguyen, Hong Thuy, "The binomial decomposition of OWA functions, the 2-additive and 3-additive cases in n dimensions" in INTERNATIONAL JOURNAL OF INTELLIGENT SYSTEMS, v. 33, n. 1, (2018), p. 187-212.
  • Bortot, Silvia; Fedrizzi, Mario; Marques Pereira, Ricardo Alberto; Nguyen, Hong Thuy, "The binomial decomposition of generalized Gini welfare functions, the S-Gini and Lorenzen cases" in INFORMATION SCIENCES, v. 460-461, (2018), p. 555-577.
  • Fedrizzi, Michele; Ferrari, Fabio, "A Chi-square-based inconsistency index for pairwise comparison matrices" in JOURNAL OF THE OPERATIONAL RESEARCH SOCIETY, v. 69, n. 7, (2018), p. 1125-1134.
  • Sodenkamp, Mariya; Tavana, Madjid; Di Caprio, Debora,"An aggregation method for solving group multi-criteria decision-making problems with single-valued neutrosophic sets" in APPLIED SOFT COMPUTING, v. 71, (2018), p. 715-727.
  • Tavana, Madjid; Abtahi, Amir-Reza; Di Caprio, Debora; Hashemi, Reza; Yousefi-Zenouz, Reza, "An integrated location-inventory-routing humanitarian supply chain network with pre- and post-disaster management considerations" in SOCIO-ECONOMIC PLANNING SCIENCES, v. 64, (2018), p. 21-37.
  • Tavana, Madjid; Di Caprio, Debora; Santos Arteaga, Francisco Javier,  "An extended stochastic VIKOR model with decision maker's attitude towards risk" in INFORMATION SCIENCES, v. 432, (2018), p. 301-318.
  • Bortot, Silvia; Marques Pereira, Ricardo Alberto, "Algebraic representations of the weighted mean" in FUZZY SETS AND SYSTEMS, v. 308, (2017), p. 85-105.
  • Collan, Mikael; Fedrizzi, Mario; Luukka, Pasi, "Possibilistic risk aversion in group decisions: theory with applications in the insurance of giga-Investments valued through the fuzzy pay-off method" in SOFT COMPUTING, v. 21, n.15, (2017), p. 4375-4386.
  • Esmaelian, Majid; Tavana, Madjid; Di Caprio, Debora; Ansari, Reza, "A multiple correspondence analysis model for evaluating technology foresight methods" in TECHNOLOGICAL FORECASTING AND SOCIAL CHANGE, v. 125, (2017), p. 188-205.
  • Jandova, Vera; Krejčí, Jana; Stoklasa, Jan; Fedrizzi, Michele,"Computing interval weights for incomplete pairwise-comparison matrices of large dimension - a weak consistency-based approach" in IEEE TRANSACTIONS ON FUZZY SYSTEMS, v. 25, n. 6, (2017), p. 1714-1728.
  • Tavana, Madjid; Di Caprio, Debora; Santos Arteaga, Francisco Javier, "A multi-criteria perception-based strict-ordering algorithm for identifying the most-preferred choice among equally-evaluated alternatives" in INFORMATION SCIENCES, v. 381, (2017), p. 322-340.
  • Molinari, Franco, "A new criterion of choice between generalized triangular fuzzy numbers" in FUZZY SETS AND SYSTEMS, v. 296, (2016), p. 51-69.
  • Sodenkamp, Mariya; Tavana, Madjid; Di Caprio, Debora, "Modeling synergies in multi-criteria supplier selection and order allocation: An application to commodity trading" in EUROPEAN JOURNAL OF OPERATIONAL RESEARCH, v. 254, n. 3, (2016), p. 859-874.
  • Tavana, Madjid, Zareinejad, Mohsen; Di Caprio, Debora; Kaviani, Mohamad Amin, "An integrated intuitionistic fuzzy AHP and SWOT method for outsourcing reverse logistics" in APPLIED SOFT COMPUTING, v. 40, (2016), p. 544-557.
  • Brunelli, Matteo; Fedrizzi, Michele, "Axiomatic properties of inconsistency indices for pairwise comparisons" in JOURNAL OF THE OPERATIONAL RESEARCH SOCIETY, vol. 66, n. 1, (2015), p. 1-15.
  • Brunelli, Matteo; Fedrizzi, Michele, "Boundary properties of the inconsistency of pairwise comparisons in group decisions" in EUROPEAN JOURNAL OF OPERATIONAL RESEARCH, v. 240, n. 3, (2015), p. 765-773.
  • García Lapresta, José Luis; Marques Pereira, Ricardo Alberto, "The dual decomposition of aggregation functions and its application in welfare economics" in FUZZY SETS AND SYSTEMS, v. 281, (2015), p. 188-197.
  • Tavana, Madjid; Di Caprio, Debora; Santos Arteaga, Francisco Javier; O’Connor, Aidan, "A novel entropy-based decision support framework for uncertainty resolution in the initial subjective evaluations of experts: The NATO enlargement problem" in DECISION SUPPORT SYSTEMS, v. 74, (2015), p. 135-149. 
  • Bortot, Silvia; Marques Pereira, Ricardo Alberto, "The binomial Gini inequality indices and the binomial decomposition of welfare functions" in FUZZY SETS AND SYSTEMS, v. 255, (2014), p. 92-114.
  • Brunelli, Matteo; Fedrizzi, Mario; Fedrizzi, Michele, "Fuzzy m-ary adjacency relations in social network analysis: Optimization and consensus evaluation" in INFORMATION FUSION, v. 17, n. 1, (2014), p. 36-45.
  • Bortot, Silvia; Marques Pereira, Ricardo Alberto, "Inconsistency and non-additive capacities: The Analytic Hierarchy Process in the framework of Choquet integration" in FUZZY SETS AND SYSTEMS, v. 213, (2013), p. 6-26.
  • Aristondo, Oihana; García Lapresta, José Luis; Lasso de la Vega, Casilda; Marques Pereira, Ricardo Alberto, "Classical inequality indices, welfare and illfare functions, and the dual decomposition" in FUZZY SETS AND SYSTEMS, v. 228, (2013), p. 114-136.
  • Collan, Mikael; Fedrizzi, Mario; Luukka, Pasi, "A multi-expert system for ranking patents: An approach based on fuzzy pay-off distributions and a TOPSIS–AHP framework" in EXPERT SYSTEMS WITH APPLICATIONS, v. 40, n. 12, (2013), p. 4749-4759.
  • Molinari, Franco, "A note on regular multi-distances between fuzzy numbers" in ADVANCES IN FUZZY SETS AND SYSTEMS, v. 15, n. 2, (2013), p. 85-94.
  • Bonetti, Alessio; Bortot, Silvia; Fedrizzi, Mario; Marques Pereira, Ricardo Alberto; Molinari, Andrea, "Modelling group processes and effort estimation in project management using the Choquet integral: An MCDM approach" in EXPERT SYSTEMS WITH APPLICATIONS, v. 39, n. 18, (2012), p. 13366-13375.
  • Aristondo, Oihana; García Lapresta, José Luis; Lasso de la Vega, Casilda; Marques Pereira, Ricardo Alberto, "The Gini index, the dual decomposition of aggregation functions, and the consistent measurement of inequality" in INTERNATIONAL JOURNAL OF INTELLIGENT SYSTEMS, v. 27, n. 2, (2012), p. 132-152.
  • Molinari, Franco, "About a New Family of Multidistances" in FUZZY SETS AND SYSTEMS, v. 195, (2012), p. 118-122.
  • Bortot, Silvia; Fedrizzi, Mario; Giove, Silvio, "Modelling fraud detection by attack trees and Choquet integral" in ADVANCES IN FUZZY SETS AND SYSTEMS, v. 9, n. 2, (2011), p. 137-165.
  • Buoni, Alessandro; Fedrizzi, Mario; Mezei, Jozef, "Combining attack trees and fuzzy numbers in a multi-agent approach to fraud detection" in INTERNATIONAL JOURNAL OF ELECTRONIC BUSINESS, v. 9, n. 3, (2011), p. 186-202.
  • García Lapresta, José Luis; Lasso de la Vega, Casilda; Marques Pereira, Ricardo Alberto; Urrutia, Ana Marta, "A class of poverty measures induced by the dual decomposition of aggregation functions" in INTERNATIONAL JOURNAL OF UNCERTAINTY, FUZZINESS AND KNOWLEDGE BASED SYSTEMS, v. 18, n. 4, (2010), p. 493-511.
  • Coelho, Cláudio; Serra, Paulo; Ribeiro, Rita A.; Marques Pereira, Ricardo Alberto; Dietz, Angela; Donati, Alessandro "Fuzzy alarm system for laser gyroscopes degradation" in INTELLIGENT AUTOMATION AND SOFT COMPUTING, v. 14, n. 3, (2008), p. 351-366.
  • Marques Pereira, Ricardo Alberto; Ribeiro, Rita A.; Serra, P., "Rule correlation and Choquet integration in fuzzy inference systems" in INTERNATIONAL JOURNAL OF UNCERTAINTY, FUZZINESS AND KNOWLEDGE BASED SYSTEMS, v. 16, n. 5, (2008), p. 601-626.
  • Fedrizzi, Mario; Ventre, Viviana, "Fraud measurement using ordered weighted aggregation" in JOURNAL OF INTERDISCIPLINARY MATHEMATICS, v. 11, n. 1, (2008), p. 99-113.
  • García Lapresta, José Luis; Marques Pereira, Ricardo Alberto, "The self-dual core and the anti-self-dual remainder of an aggregation operator" in FUZZY SETS AND SYSTEMS, v. 159, n. 1, (2008), p. 47-62. 
  • Fedrizzi, Mario; Fedrizzi, Michele; Marques Pereira, Ricardo Alberto, "Consensus modelling in group decision making: a dynamical approach based on fuzzy preferences" in NEW MATHEMATICS AND NATURAL COMPUTATION (NMNC), v. 3, n. 2, (2007), p. 219-237.
  • Marques Pereira, Ricardo Alberto; Molinari, Andrea; Pasi, Gabriella, "Contextual weighted representations and indexing models for the retrieval of HTML documents" in SOFT COMPUTING, v. 9, n. 7, (2005), p. 481-492.
  • Marques Pereira, Ricardo Alberto; Ribeiro, Rita A. "Aggregation with generalized mixture operators using weighting functions" in FUZZY SETS AND SYSTEMS, v. 137, n. 1, (2003), p. 43-58.
  • Ribeiro, Rita A.; Marques Pereira, Ricardo Alberto, "Generalized mixture operators using weighting functions: a comparative study with WA and OWA" in EUROPEAN JOURNAL OF OPERATIONAL RESEARCH, v. 145, n. 2, (2003), p. 329-342.
  • Pasi, Gabriella; Marques Pereira, Ricardo Alberto, "A decision making approach to relevance feedback in information retrieval: a model based on soft consensus dynamics" in INTERNATIONAL JOURNAL OF INTELLIGENT SYSTEMS, v. 14, n. 1, (1999), p. 105-122.
  • Fedrizzi, Mario; Fedrizzi, Michele; Marques Pereira, Ricardo Alberto, "Soft consensus and network dynamics in group decision making" in INTERNATIONAL JOURNAL OF INTELLIGENT SYSTEMS, v. 14, n. 1, (1999), p. 63-77.