Fuzzy Relational Dynamic System with Smooth Fuzzy Composition

Fuzzy relational models of functions have been developed in recent two decades which has led to fuzzy relational models of dynamic systems which we call fuzzy relational dynamic systems (FRDS). In this paper the effectiveness of smooth fuzzy relational compositions (FRC) in such dynamic models is studied after introducing a general framework for modeling of dynamic systems using FRDS, and so the smooth FRDS is developed. A modeling structure is presented in this regard as well as a related identification algorithm. Finally, the modeling capability of the proposed smooth FRDS is verified via some simulations on various benchmark problems and actual dynamic systems.