Statistical analysis of fuzzy rules for hardness prediction in steels using fuzzy least squares

Abstract

This study proposes a methodology based on a Fuzzy Inference System (FIS) to model the tempering process of D2 and H13 tool steels, transforming the FIS into a Fuzzy Least Squares (FLS) model using its rules and membership functions. An ANOVA performed on the FLS model reveals a p-value of 0.000014, indicating high statistical significance. The significance analysis identifies rules 2, 3, and 11 as consistent and relevant (p<0.05 . T_0>T_(a\/2)), with rule 2 showing notable sensitivity within its membership function intervals, essential for accurate predictions. The FLS model (R^2=0.83) significantly outperforms the FIS model (R^2=0.72), demonstrating greater precision in the results. Furthermore, the FLS model simultaneously predicts the hardness of both steels, optimizing costs and time in process control. The new FLS structure enables detailed analysis to identify the most significant rules, marking a key contribution of this work.