Interval Type-3 Shadowed Sets as an Efficient Way to Approximate Interval Type-3 Fuzzy Systems

Nowadays, one of the most recent realms in Fuzzy Logic is the emergence of Type-3 Fuzzy Logic, with novel applications and potential to be explored. However, one of the biggest obstacles to realize the implementation of this kind of theory in real-world applications and systems is the computational complexity. The aim of this paper is to address this obstacle by proposing a new approach for modelling the Interval Type-3 Fuzzy Systems, in this case, based on Shadowed Sets, which have demonstrated to be a suitable approach for modelling Fuzzy Sets. In this case, Shadowed Sets theory is implemented in Interval Type-3 Fuzzy Sets to approximate the secondary membership functions, in this way reducing the number of \(\alpha \) $\alpha$ -planes to only two and contributing to the development of more efficient models based on Type-3 Fuzzy Logic. The obtained results with the proposed approximation are promising in terms of reducing the computational effort and offering at the same time good approximation of the original systems.