Fuzzy relational structures: Learning alternatives for fuzzy modeling

Fuzzy models offer a convenient way to describe complex and nonlinear systems. Fuzzy relational equations, viewed as a certain class of fuzzy models, play a pivotal role in fuzzy modeling. Their theory supports ways in which these equations could be solved and offers a characterization of the resulting families of solutions. Assuming that the corresponding relational equation or a system of relational equations is solvable, the theory provides a suite of analytical results. If this essential solvability assumption is not satisfied, we have to resort to approximate solutions and optimization techniques. In this study, we review several approaches to construct fuzzy relational models. Those methods include analytical methods, gradient-based (GB) methods, particle swarm optimization (PSO), and differential evolution (DE). We compare these methods with a hybridization of the different techniques, namely PSO-GB and DE-GB. The optimization techniques are used to design a fuzzy logic processor (FLP), which employs fuzzy logic operations in the realization of this network. Fuzzy C-Means (FCM) transforms real-world numeric data into fuzzy sets, which are used to design the fuzzy model.