Design of Takagi–Sugeno fuzzy systems by learning from examples in case a number of available data is not sufficient

Abstract

The paper describes a solution of a problem of developing of fuzzy rules compliant with the Takagi-Sugeno approach where a number of available examples (observations) is not sufficient. Modeling of fuzzy premises and generating functions describing a dependence of a result variable on antecedents are described. In our original approach a problem of identification of membership functions of variables com-posing premises and a problem of consequent parameters identification are solved. For the first one, we used a simple technique based on individual judgements of experts. The second one is solved with a linear programming method. In particular, our approach to formulate the consequent parameter identification problem allows using of an extremely effective T-S method when a data-driven approach cannot be applied. In the paper we present a description of our methods and results of simulations of accuracy of the proposed approach, based on commonly known benchmarks. The achieved accuracy of classification is sufficient for the most of decision-making systems of an expert nature.