Some New Smooth Fuzzy Relational Compositions

Fuzzy relational compositions (FRCs) are the core of the fuzzy relational models (FRMs) which play a significant role in the fuzzy linguistic modeling. In this paper, we introduce some new fuzzy relational compositions. These FRCs are composed of some new t-norms and t-conorms and have some good properties such as differentiability. In this regard, the properties of the proposed t-norms and t-conorms are studied and compared with the other ones. Finally, as the most important applications of the FRCs suggest that the new FRCs are to be used in fuzzy relational modeling of some benchmark problems to justify their usage. We show by simulations that the proposed FRCs yield fuzzy relational dynamic systems with very good modeling capabilities.