Fuzzy modelling using a new compact fuzzy system: A special application to the prediction of the mechanical properties of alloy steels

Abstract

In high-dimensional modelling cases, a fuzzy modelling approach based on the grid-partitioning of fuzzy sets always meets great challenges, as it cannot avoid the problem of introducing a huge number of fuzzy rules. To tackle this issue, a new grid-partitioning based fuzzy modelling paradigm is proposed in this paper to construct a compact fuzzy system by including ‘short fuzzy rules’, in which only a few but strategic premises are used. In the proposed approach, the generation of fuzzy rules is data-orientated, a consideration which can greatly reduce the computational complexity. A new framework for fuzzy reasoning and defuzzification is also devised, which employs some archived reference data to help choose the most suitable fuzzy rules. In material engineering, describing the behaviour of mechanical properties of alloys is often a high-dimensional modelling problem, which involves the complexity of materials' chemical composites and their underlying physical processing mechanisms. In this paper, the proposed approach was successfully applied to generate models of ultimate tensile strength of alloy steel. Compared with the standard grid-partitioning based fuzzy modelling paradigms, the new method shows an improvement in both complexity and interpretability. Compared with the clustering-based fuzzy modelling approaches, the proposed method can achieve the same accuracy level and is more transparent.