Research lines
Fuzzy Arrovian models
Fuzzy Arrovian models are a class of decision-making models that incorporate the concept of fuzzy sets to deal with imprecise or uncertain information. These models are based on the work of Nobel laureate economist Kenneth Arrow and seek to extend his insights into the realm of fuzzy logic.
My research focus on the study of the mathematical structure of these models and their classification in terms of possibility/impossibility and cardinal/ordinal properties.
Photo of Mumbai, made by Johnny Miller.
Polarization measures
Polarization measures are used to quantify the degree of polarization within a given population or society. They aim to capture the extent to which individuals are clustered or separated based on some observable characteristics such as income, education, or political beliefs.
Our studies have focused on the Esteban-Ray polarization measures. They measure the polarization in societies defined by quantitative properties (such as income). I have studied the axiomatization defining this family of measures and their properties.
Combinatorial topology and Arrovian model
The Arrow’s impossibility theorem is a well-known result in mathematical economics. However, there are still some questions which remain open. Baryshnikov, in 1993, proposed a topological approach to address the problem of domain restrictions based on simplicial complexes and homology groups.
In these works, we apply techniques from combinatorial topology to study domain restrictions and derive social welfare functions in such domains.
Publications
2023
@article{campión2023decomposition,
title={Decomposition of Fuzzy Relations: An Application to the Definition, Construction and Analysis of Fuzzy Preferences},
author={Campión, María Jesús and Induráin, Esteban and Raventós-Pujol, Armajac},
journal={Axioms},
year={2023},
volume={12},
number={12},
doi={10.3390/axioms12121077}
}2022
@article{a. raventós-pujol2022fuzzy,
title={Fuzzy Arrovian theorems when preferences are strongly-connected},
author={A. Raventós-Pujol},
journal={Iranian Journal of Fuzzy Systems},
year={2022},
volume={19},
pages={45-56},
doi={10.22111/ijfs.2022.7085}
}@inproceedings{sergio rajsbaum 2022distributed,
title={A Distributed Combinatorial Topology Approach to Arrow's Impossibility Theorem},
author={Sergio Rajsbaum and Armajac Raventós-Pujol},
booktitle={Proceedings of the 2022 ACM Symposium on Principles of Distributed Computing},
year={2022},
pages={471--481},
publisher={Association for Computing Machinery}
}@article{m.j. campión 2022multidistances,
title={Multidistances and inequality measures on abstract sets: An axiomatic approach},
author={M.J. Campión and I Díaz and E Induráin and J Martín and G Mayor and S Montes and A Raventós-Pujol},
journal={Fuzzy Sets and Systems},
year={2022},
volume={437},
pages={53-68}
}@article{humberto bustince 2022aggregation,
title={Aggregation of Individual Rankings Through Fusion Functions: Criticism and Optimality Analysis},
author={Humberto Bustince and Benjamin Bedregal and Maria Jesus Campion and Ivanosca da Silva and Javier Fernandez and Esteban Indurain and Armajac Raventos-Pujol and Regivan H N Santiago},
journal={IEEE Transactions on Fuzzy Systems},
year={2022},
volume={30},
pages={638-648},
month={3},
doi={10.1109/TFUZZ.2020.3042611}
}2021
@inproceedings{maría jesús campión 2021use,
title={Why use topological and analytical methods in aggregation of fuzzy preferences?},
author={María Jesús Campión and Esteban Enduráin Eraso and Armajac Raventós Pujol},
booktitle={TEMat monográficos, 2 (2021): Proceedings of the 3rd BYMAT Conference},
year={2021},
pages={59-62}
}@article{isabel abinzano 2021sports,
title={Sports Betting and The Black-Litterman Model: A New Portfolio-Management Perspective},
author={Isabel Abinzano and Maria Jesus Campion and Luis Muga and Armajac Raventós-Pujol},
journal={International Journal of Sport Finance},
year={2021},
volume={16}
}@inproceedings{maría jesús campión 2021fusing,
title={Fusing Fuzzy Preferences in Contexts of Social Choice: Towards a Topological Structure},
author={María Jesús Campión and Esteban Induráin and Armajac Raventós-Pujol},
booktitle={Intelligent and Fuzzy Techniques: Smart and Innovative Solutions. INFUS 2020. Advances in Intelligent Systems and Computing},
year={2021},
pages={1301-1308},
publisher={Springer International Publishing}
}2020
@article{armajac raventós-pujol 2020decomposition,
title={Decomposition and Arrow-Like Aggregation of Fuzzy Preferences},
author={Armajac Raventós-Pujol and María Jesús Campión and Esteban Induráin},
journal={Mathematics},
year={2020},
volume={8},
pages={436},
publisher={Multidisciplinary Digital Publishing Institute},
doi={10.3390/math8030436}
}@article{a. raventos-pujol 2020arrow,
title={Arrow theorems in the fuzzy setting},
author={A. Raventos-Pujol and María Jesús Campión and E. Indurain},
journal={Iranian Journal of Fuzzy Systems},
year={2020},
volume={17},
pages={29-41},
doi={10.22111/ijfs.2020.5512}
}@article{gianni bosi 2020topologies,
title={Topologies for semicontinuous Richter--Peleg multi-utilities},
author={Gianni Bosi and Asier Estevan and Armajac Raventós-Pujol},
journal={Theory and Decision},
year={2020},
volume={88},
pages={457-470},
month={11},
doi={10.1007/s11238-019-09730-7}
}2018
@article{maría jesús campión 2018geometrical,
title={Geometrical aggregation of finite fuzzy sets},
author={María Jesús Campión and Raquel G Catalán and Esteban Induráin and Inmaculada Lizasoain and Armajac Raventós-Pujol and Óscar Valero},
journal={International Journal of Approximate Reasoning},
year={2018},
volume={103},
pages={248-266},
doi={https://doi.org/10.1016/j.ijar.2018.10.005}
}@article{maría jesús campión 2018survey,
title={A survey on the mathematical foundations of axiomatic entropy: Representability and orderings},
author={María Jesús Campión and C Gómez-Polo and E Induráin and A Raventós-Pujol},
journal={Axioms},
year={2018},
volume={7},
publisher={MDPI AG},
doi={10.3390/axioms7020029}
}Preprints
My working papers uploaded on repositiories.
@article{sergio rajsbaum 2022combinatorial,
title={A Combinatorial Topology Approach to Arrow's Impossibility Theorem},
author={Sergio Rajsbaum and Armajac Raventós-Pujol},
journal={Munich Personal RePEc Archive},
year={2022}
}@article{isaac lara 2024generalization,
title={A Generalization of Arrow's Impossibility Theorem Through Combinatorial Topology},
author={Isaac Lara and Sergio Rajsbaum and Armajac Raventós-Pujol},
journal={arXiv},
year={2024}
}Conferences
Polarization indices: Calibrating the sensitivity in the distance
talk in the 48th Simposio de la Asociación Española de Economía-Spanish Economic Association (SAEe) (December 2023).
The role of the distance in polarization indices. Were we wrong?
talk in the 13th Conference on Economic Design (June 2023).
A case in Social Choice: From Combinatorics to Algebraic and Combinatorial Topology
talk in the Fourth BYMAT Conference: Bringing Young Mathematicians Together (December 2022).
A combinatorial topology approach to Arrow's impossibility theorem.
talk in the 16th meeting of the Society for Social Choice and Welfare (June 2022).
Revisiting topology in social choice.
talk in XVIII Meeting of the Red Española de Elección Social (November 2021).
Why using topological and analytical methods in aggregation of fuzzy preferences?
poster in the Third BYMAT Conference: Bringing Young Mathematicians Together (December 2020).
Fusing fuzzy preferences in contexts of Social Choice: Towards a topological structure
talk in the International Conference on Intelligent and Fuzzy Systems (INFUS) (July 2020).
Unexpected thresholds from Independence of Irrelevant Alternatives in Fuzzy Arrow Theorems
talk in the XVI Encuentro de la Red Social Española de Elección Social (November 2019).
Aggregation vs Disaggregation: A geometrical approach
talk in International Symposium on Aggregation and Structures (June 2018).
You can see my participation in seminars and other events here.