Fuzzy regression analysis: An application on tensile strength of materials and hardness scales

In the present paper we use fuzzy linear regression analysis and fuzzy similarity to investigate the relation of various hardness scales to tensile strength of materials. We examine the relation of the Vickers, Brinell, Rockwell C and Shore Scleroscope hardness scales with tensile strength in a common measurement range. The fuzzy regression models that result show the existence of a linear relation. Further analysis of the resulting models with fuzzy similarity results indicates strong similarities between models of different hardness scales. The results indicate that this similarity of the fuzzy regression reflects the underling similarity of the physical quantities of materials that are measured on the different hardness scales. A comparison with conventional linear regression analysis shows that the ambiguities of the model are better reflected in the case of fuzzy regression models.