New data fusion methods for application in general machine learning problems
General description of the project
This line of research focuses on the study and generalisation of the mathematical functions used in these models, with the aim of broadening their applicability and making them more flexible in order to represent different types of information. In particular, aggregation functions are analysed, understood as operators that condense a set of data into a single representative value, allowing the relevant information in the set to be captured efficiently.
The project investigates how the design of new mathematical tools can lead to artificial intelligence models capable of representing data more accurately, using the least amount of information necessary. The choice of an appropriate aggregation function is neither unique nor universal, but depends on the nature of the data and the phenomenon to be analysed. While in some contexts it is appropriate to use measures based on averages, in others the most relevant information may be associated with extreme values, such as maximums or minimums.
The systematic development of new aggregation functions and their integration into artificial intelligence models allows the analysis process to be adapted to each specific problem, improving the representational capacity of the data and contributing to theoretical and methodological advances in the field of artificial intelligence.
Objectives
The aim of this project is to carry out a theoretical study of aggregation functions and their relationship with artificial intelligence, focusing on the analysis of their mathematical foundations within complex algebraic structures. The purpose of this analysis is to establish a solid theoretical basis that will enable the development of more robust and generalisable mathematical concepts capable of supporting more efficient and consistent artificial intelligence models from a formal point of view.
In this framework, consolidating a coherent and well-structured theoretical framework that facilitates the generalisation of mathematical tools and their subsequent application in the design and development of artificial intelligence models, as well as in other related areas.
The generalisations addressed in this project can be developed using different complementary approaches.
On the one hand, we propose the construction of aggregation functions defined on abstract algebraic bodies. Although previous methods exist in the literature, their complete characterisation has not been established, and the construction proposed in this project introduces an innovative approach that offers greater flexibility and generalisation capacity than existing formulations.
On the other hand, the project involves the study of complex algebraic structures, in particular the hypercube, as a mathematical framework for the simultaneous processing of multiple data vectors. This structure allows for the modelling of situations in which information is available from numerous individuals, each described by a broad set of variables, as occurs, for example, in the analysis of patients with multiple symptoms or clinical conditions. However, the use of the hypercube poses significant theoretical challenges, as fundamental properties such as symmetry, associativity, and monotony do not admit a single natural generalisation, which opens up ample space for the development of new concepts and results.
The project also addresses the analysis of independence and dependence between data as a central aspect of the aggregation process. Determining whether variables are independent or dependent is essential for the accurate representation of information. While well-established mathematical frameworks exist for independent data, the modelling of dependencies remains an open problem that requires new theoretical tools. In this context, the objective is to describe and develop aggregation functions that explicitly respect these relationships, or their absence, and that can be adapted to the specific needs of each analysis.
Scientific production
A. Goñi, M. Gómez and R. Pérez,‘Construction of uninorms on bounded lattices: augmenting the flexibility of choice’ presented at the 14th Conference of the European Society for Fuzzy Logic and Technology Riga, Latvia, Jul 21-25, 2025.
A. Goñi, M. Gómez and R. Pérez,‘Introduction to uninorms on bounded lattices. Working with the flexibility of choice’, seminary presented at the VI European Summer School on Fuzzy Logic and Applications, Riga, Latvia, Jul 28–Aug 1, 2025
A. Goñi, M. Gómez and R. Pérez,‘Families of uninorms’ poster presented at the RSME's 7th Congress of Young Researchers, Bilbao, Spain, Jan 13–17, 2025
Funding
Collaboration agreement signed with Fundación Caja Navarra as part of its programme of pre-doctoral research grants in computational neuroscience.
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