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Mathematical structure of fuzzy connectives with applications in Artificial Intelligence (Doctoral thesis)

Καραμπίνης, Ιωάννης/ Karampinis, Ioannis

One of the most complex and impactful problems faced by modern societies is estimating the risk of structures from natural or man-made hazards. While this problem can be well described using natural language and engineering experience, its rigorous mathematical formulation is quite challenging due to its inherent vagueness and uncertainty involved in the magnitude of the hazard itself and the risk it might pose. Thus, to address similar problems, we must depart from classical methodologies and employ different tools. One such tool is offered by Fuzzy Logic. This methodology inherently incorporates vagueness and uncertainty into the underlying equations, thus naturally modeling the vagueness of the problem. One different approach is offered by Artificial Intelligence and Machine Learning. Fundamentally, this paradigm employs rigorous mathematical algorithms to learn patterns in the data without making any assumptions about a specific model form. In this Thesis, we explored the theory of these two distinct paradigms to examine how each of them handles uncertainty from a different perspective. We also provided novel tools for the problem of seismic risk assessment of structures, both as deformable bodies and as rigid rocking blocks. Furthermore, we examined in more detail the topic of fuzzy connectives, which play a central role in any intelligent decision-making system that combines fuzzy logic and machine learning. We provided novel theoretical results in this area and explored a procedure on how to select the best fuzzy implication from a given collection, which can then be incorporated into an intelligent decision-making system.