A Similarity Reasoning Scheme for Modelling of Monotonic Multi-Input Fuzzy Inference Systems

In this paper, a Similarity Reasoning (SR) scheme for monotonic multi-input Fuzzy Inference System (FISs) is proposed. The sufficient conditions for an FIS to be of monotonicity are exploited as part of the SR and FIS modeling procedure. We first assume that the fuzzy membership functions of an FIS are designed according to the sufficient conditions. We then argue that a conventional SR scheme that adopts a simple weighted addition has difficulty in deducing a set of monotonic-ordered conclusions, thus, it is not suitable for tackling the monotonic multi-input FIS modelling problem. As such, a new SR scheme is formulated as a constrained optimization problem in this paper. It consists of an objective function to be optimized under a set of inequality constraints. We further solve the proposed SR scheme with the non-linear programming and genetic algorithm techniques. A simulated example is presented, and the results indicate the usefulness of the new SR scheme in constructing a monotonic multi-input FIS model.