This paper presents the development of mathematical, predictive and optimization models of average surface roughness parameter ( R a ) in turning hardened AISI 1060 steel using coated carbide tool in dry condition. Herein, the mathematical model is formulated by response surface methodology (RSM), predictive model by fuzzy inference system (FIS), and optimization model by simulated annealing (SA) technique. For all these models, the cutting speed, feed rate and material hardness were considered as input factors for full factorial experimental design plan. After the experimental runs, the collected data are used for model development and its subsequent validation. It was found, by statistical analysis, that the quadratic model is suggested for R a in RSM. The adequacy of the models was checked by error analysis and validation test. Furthermore, the constructed model was compared with an analytical model. The analysis of variance revealed that the material hardness exerts the most dominant effect, followed by the feed rate and then cutting speed. Eventually, the RSM model was found with a coefficient of determination value of 99.64%; FIS model revealed 79.82% prediction accuracy; and SA model resulted in more than 70% improved surface roughness. Therefore, these models can be used in industries to effectively control the hard turning process to achieve a good surface quality.