The use of fuzzy linear regression for the selection of the most appropriate fuzzy implication in a fly ash-based concrete model

Abstract

In this research, fuzzy linear regression (FLR) method combined with three well-known fuzzy implications was implemented for evaluating the relation among the amount of fly ash in concrete mixture and the compressive strength of concrete. More specifically, 267 experimental data 40 of which were used for testing the validation of the process were subjected to FLR method for calculating the truth values, which indicated the degree of how the experimental outputs belong to the predicted ones. Also, the degree of fuzziness was calculated for performing the sensitivity analysis of the model. The truth values that emerged were used for applying three basic fuzzy implications such as Lukasiewicz, Reinchenbach, and Kleene-Dienes implication. By evaluating and comparing the results of every fuzzy implication, it was concluded that Lukasiewicz was the most appropriate implication method as it yielded the smallest deviation of truth values (σ = 4.00) in contrast to the theoretical ones (σ = 4.83 in Reinchenbach and σ = 12.31 in Kleene-Dienes fuzzy implication). The accuracy of the FLR method was also validated for calculating the coefficient of the mean absolute percentage error level (MAPE = 5.56%) of the blind prediction process, and the results revealed that the application of fuzzy linear regression method is suitable for evaluating the truth values of experimental data in order to be used in fuzzy implications. Thus, it is a satisfactory procedure for making inferences between concrete parameters.