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FUSIGEMAP

FUSIGEMAP - FUzzy SImilarity measures and GEneralized Metrics with Applications to Perception (and robotics)

PID2022-139248NB-I00 (2023-2027)

MICIU

Similarity measures (fuzzy or crisp) and generalized metrics (GM) have been theoretically studied separately, and certain relationships of duality have been stated between them. This duality plays a key role because it allows introducing methods that construct new similarity measures from generalized metrics, and vice-versa, what may be better adapted to the specific problem under consideration. In the literature, there is a shortage of cases of similarity measures which turns out to be a drawback when one wants to apply them to engineering problems. Inspired by this fact, in project FUZZYMAR (PGC2018-095709-B-C21), we explored in depth the duality problem in such a way that we developed specific techniques for generating two particular classes of similarity measures, fuzzy metrics (FM) and indistinguishability operators (IO), from classical metrics and, reciprocally, classical metrics from FM and IO.

Despite the progress made in FUZZYMAR regarding FM and IO and the duality technique, and their applications in engineering, there remain many theoretical matters to be addressed about similarity measures and GM in a more general framework, and also regarding their application onto problems that can be generally framed within the Artificial Intelligence domain, and more specifically onto Perception and Robotics, the latter both by extension of the former, i.e. an autonomous robot has to be able to perceive its environment, and alone within the context of heterogeneous multi-agent systems (HMAS).

With FUSIGEMAP we intend to go further ahead into the theoretical study of general similarity measures (modular fuzzy similarities, fuzzy binary relations and metric similarities) and their relationship with generalized metrics, as well as focus on using the new theoretical background in perception and robotics: (1) to consider jointly the generic problems of deciding whether two entities are the same [matching] or how similar/dissimilar they are [grouping], (2) to advance on robust model fitting with regard to the results achieved in FUZZYMAR, (3) to revisit state estimation for dynamic systems, and (4) to address the modelling of heterogeneous multi-agent systems.

Hence, FUSIGEMAP is a project that focuses on advancing the state of knowledge both at the theoretical and applied levels. Moreover, the focus is on delving into the theoretical-practical development of similarity measures (fuzzy and crisp) and generalized metrics by stablishing a strong synergy with applications where the fuzzy approach has been relevant in the past.

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