Reducing data without losing information: a University thesis that analyzes the mathematics behind artificial intelligence

In a context where artificial intelligence is processing ever-increasing volumes of data, it is essential to develop methods that reduce the amount of “ data ” without losing the relevant information contained within them.

Francisco Javier Talavera Andújar (Albacete, 28 years old) holds graduate in Mathematics from the University of Alicante and Master's Degree in Computational Methods in Science from the University of Navarra. Under the supervision of Dr. Jorge Elorza, he has focused his research on information aggregation in the field of Fuzzy Logic, a branch of artificial intelligence that allows for working with imprecise concepts such as “small,” “near,” or “late.”

Thus, one of the problems addressed by his research arises when it is necessary to combine a large Issue of data that must be processed in real time. For example, “several sensors measure the temperature throughout the day, and we want to combine their readings to obtain a single value. These data can be fused in infinite ways using operations known as aggregation operators,” he explains. “The goal is to find the conditions that an aggregation operator (that is, a way to fuse the data) must satisfy so that a structure shared by the original data is preserved after the process,” he concludes.

research core topic for the future
In addition to its applications in fields such as robotics, image processing, and medical diagnostics, Talavera also highlights the importance of basic mathematical as a research source of for future scientific developments. “History has shown that discoveries that appear to be purely theoretical can, over time, become the for advancing applied fields of science,” he notes. knowledge core topic

Among his future plans, researcher aims to develop and consolidate the theory of fuzzy sets of subject ²—which are useful for addressing situations involving a high Degree of uncertainty. It is important to clearly determine which tools and methods are best suited for working with them and how they relate to one another. “We intend to dedicate another of our future lines of work to this task,” he says.

Bibliographical references

• Talavera, F. J., Ardanza-Trevijano, S., Bragard, J., & Elorza, J. (2025). New types of domination to characterize the preservation of T-subgroups under aggregation. Fuzzy Sets and Systems, 498, 109139.

• Talavera, F. J., Bejines, C., Ardanza-Trevijano, S., & Elorza, J. (2024). Aggregation of fuzzy graphs. International Journal of Approximate Reasoning, 172, 109243.