Nowadays hard turning is noticed to be the most dominating machining activity especially for difficult to cut metallic alloys. Attributes of dry hard turning are highly influenced by the amount of heat generation during cutting. Some major challenges are rapid tool wear, lower tool-life span, and poor surface finish but simultaneously generated heat is enough to provide thermal softening of hard work material and facilitates easier shear deformation thus easy cutting. Also, plenty of works reported the utilization of various cooling methods as well as coolants which successfully retard the intensity of cutting heat but this leads to additional cost as well as environmental and health issues. However, still, there is scope to select proper cutting tool materials, its geometry, and appropriate values of cutting parameters to get favorable machining outcomes under dry hard turning and avoid the cooling cost, environmental, and health issue. Considering these challenges, current work utilizes PVD-coated (TiAlN) carbide insert in dry hard turning of AISI D2 steel. The multi-responses like tool-flank wear, chip morphology, and chip reduction coefficient are considered. The amalgamation of input processing variables must be optimum for the effectual performance of hard to process materials turning. Generally, the Fuzzy logic hypothesis represents the uncertainties co-related with fuzziness, and deficiency in the data concerned with the problem. Further, to achieve the best combination of input cutting terms, grey-fuzzy hybrid optimization (Type I and Type II) is utilized considering the Gaussian membership function. Type II grey-fuzzy system attributed to 15 % less error (between GRG and GFG) compared to Type I. Hence, Type II grey-fuzzy system is utilized to get the optimal set of input terms. The optimal combination of input terms is found as t-1 (0.15 mm), s-4 (0.25 mm/rev) and is Vc-2 (100 m/min) which is comparable to the results obtained under spray impingement cooling using CVD tool in the literature. However, hard turning can be assessed under the dry condition with a PVD tool at the obtained optimal input condition for industrial uses. Further, six different types of cascade-forward-back propagation neural network modelling is accomplished. Among all models, CFBNN-4 model exhibited the best prediction results with a mean absolute error of 2.278% for flank wear (VBc) and 0.112% for the chip reduction coefficient (CRC). However, this model can be recommended for other engineering modelling problems. The outcomes of this research may be of immense importance to the tool manufacturers and machining industry.