A non-linear programming-based similarity reasoning scheme for modelling of monotonicity-preserving multi-input fuzzy inference systems

Abstract

In this paper, the zero-order Sugeno Fuzzy Inference System FIS that preserves the monotonicity property is studied. The sufficient conditions for the zero-order Sugeno FIS model to satisfy the monotonicity property are exploited as a set of useful governing equations to facilitate the FIS modelling process. The sufficient conditions suggest a fuzzy partition at the rule antecedent part and a monotonically-ordered rule base at the rule consequent part that can preserve the monotonicity property. The investigation focuses on the use of two Similarity Reasoning SR-based methods, i.e., Analogical Reasoning AR and Fuzzy Rule Interpolation FRI, to deduce each conclusion separately. It is shown that AR and FRI may not be a direct solution to modelling of a multi-input FIS model that fulfils the monotonicity property, owing to the difficulty in getting a set of monotonically-ordered conclusions. As such, a Non-Linear Programming NLP-based SR scheme for constructing a monotonicity-preserving multi-input FIS model is proposed. In the proposed scheme, AR or FRI is first used to predict the rule conclusion of each observation. Then, a search algorithm is adopted to look for a set of consequents with minimized root means square errors as compared with the predicted conclusions. A constraint imposed by the sufficient conditions is also included in the search process. Applicability of the proposed scheme to undertaking fuzzy Failure Mode and Effect Analysis FMEA tasks is demonstrated. The results indicate that the proposed NLP-based SR scheme is useful for preserving the monotonicity property for building a multi-input FIS model with an incomplete rule base.