The objective of the work is to perform precision turning using a conventional lathe on Ti6Al4V under dry working conditions. In this paper, a new approach for the optimisation of the precision turning process with multiple performance characteristics based on the orthogonal array with the grey relational analysis has been studied. A grey relational grade obtained from the grey relational analysis is used to solve the precision turning process with the multiple performance characteristics. Fuzzy inference system (Mamdani fuzzy logic) to predict the dimensional accuracy in part produced by precision turning. The model uses all input and output variables in linguistic terms enabling it convenient for practitioners. The inference engine in Mamdani type FIS uses rules which are obtained with the help of design of experimental technique (DOE). © 2016 Inderscience Enterprises Ltd.