Non-conventional machining processes are the requirements of the fastest growing industries because of the precision, complex, intricate shape of the work material, higher tolerances and economically. Hard materials and super alloys such as titanium alloys, tungsten carbides, high carbon tool steels generally used in tool industries, automotive and electronics industries, medical and aerospace are very difficult—to-machine by conventional manufacturing processes. Therefore, the ease of material cutting and machining non-conventional machining is preferred. WEDM is generally used to produce complex shapes die cavities and forming tools, fixtures, gauges, etc. which are difficult to produce by means of any other conventional and non-conventional machining methods except micro-machining .
Titanium alloys (Ti-alloys) are mostly utilized in aerospace and automotive industries to manufacture higher precision components. Ti–6Al–4V grade 5 titanium alloy is used for the manufacturing of diesel engine components such as connecting rods, gas turbine parts, intake valves, etc. and this alloy covers the 50% of total global consumption .
WEDM is a variation and development of EDM. In 1969, the Swiss firm Agie developed and delivered the world’s initially WEDM machine. These machines had machining ability to cut the material about 21 mm2/min per hour. These machines were extremely slow in production rate. After the continuous improvements in the machining ability, the machining speed improved. WEDM removes material from the work metal with the use of electricity by means of spark erosion as shown in Fig. 1 [1, 3]. It is most important requirement that the work material should be electrically conductive. AC servo motors are exploited to provide positioning, stability and enhancement of wire tension. A DC or AC servo mechanism maintains the gap (0.051–0.076 mm) between the electrode and the work material. This maintained gap prevents the short circuiting of wire.
‘Dielectric’ is the shield between the wire electrode and material. De-ionized water is generally used as a dielectric medium because the dielectric medium acts as an insulator. In this process, the material is submerged in the dielectric medium. When the voltage is applied, the electric pulses are generated, fluid ionizes and a spark generates between the electrode wire and work material, the controlled spark precisely erodes the metal from the work material causing it to melt and vaporize. Pressurized dielectric fluid flows continuously. It cools the vaporize material and carry away the particles from the cutting section. The dielectric passes through the filter to remove suspended particles and it is used continuously. Chillers are used to maintain the temperature of dielectric fluids for higher machining efficiency and accuracy. In WEDM the wire electrode never comes in contact with the work piece, therefore this process is stress free cutting operation [1, 4,5,6].
Various researchers have been reported working on WEDM to measure the influence of input parameters on performance parameters such as, Liao and Woo  reported the influence of wire-EDM constraints such as ‘on time’ (Ton), ‘off time’ (Toff) and feed rate on the behavior of pulse train i.e. short ratio, arc ratio, normal ratio and gap width. Experiments were conducted on SKD 11 tool steel. The authors concluded that ‘on time’ was a significant factor for arc ratio . Miller et al.  demonstrated the capability of WEDM to machine advanced materials such as porous metal foams, diamond grinding wheels, sintered Nd–Fe–B magnets, etc. Author examined the influence of spark on time duration and spark on time ratio on surface roughness and MRR by using Brother HS-5100 WEDM .
Mahapatra et al.  optimized the WEDM performance parameters such as MRR, SR and kerf width by using the Taguchi method. ROBOFIL100 5-axis CNC WEDM was used for experimental work. Experiments were conducted on D2 tool steel by using zinc-coated copper wire having 0.25 mm diameter. The author concluded that discharge current, pulse duration and the dielectric flow rate had the significant effect on the performance parameters.
Kumar et al.  demonstrated the effect of Ton (pulse on time), Toff (pulse off time), Ip (peak current), spark gap voltage, wire feed (WF) and wire tension (WT) on the surface roughness of machined titanium grade-2 workpieces. The author concluded that pulse on time, pulse off time, peak current and spark voltage had higher impact on surface roughness . Manjaia et al.  statistically optimized the pulse on time, pulse off time, servo voltage and wire feed for WEDM of AISI D2 tool steel for the response of MRR and SR. The author resulted the higher significance of pulse on time and servo voltage on performance parameters .
Kumar et al.  concluded that the surface roughness increases with the increase in peak current because peak current increases the discharge energy. They conducted the experimental work on tungsten carbide with brass wire. Wire feed, flushing pressure and current were the significant parameters for surface roughness . Vijaya Babu  concluded that the peak current was the significant parameter for surface roughness after they studied the effect of pulse on time, pulse off time and peak current on Inconel 625. Maniappan et al.  reported the influence of peak current on kerf width. The experiments were conducted on Al 6061 alloy with zinc coated brass wire .
Various researchers have been reported the use of ANFIS to predict the performance of machining such as turning, ball milling, WEDM etc. Kar et al.  explained the applications of Neuro-fuzzy system in various fields such as stock market, financial trading, hazard assessment, etc. Caydas et al.  worked to measure the impact of pulse duration, open circuit voltage, wire feed and dielectric flushing pressure on white layer thickness and SR. Author developed the ANFIS model for the prediction of performance parameters .
Hossain and Ahmad  developed the ANFIS model for the prediction of performance parameters of ball end milling. The authors compared the ANFIS model results with the response surface methodology and found more accurate . Abdul Mayu et al. developed the ANFIS model for the prediction of hardness of TiAlN coatings. Author compared and validated their model with fuzzy and RMS model. They concluded that the triangular membership function obtains best results than other MF’s.
Anwar et al.  demonstrated the ANFIS model for the prediction of surface roughness and chipping size of rotary ultrasonic drilling (RUM). The authors compared the ANFIS results with the regression models. They achieved the lover mean absolute percentage error in ANFIS model .
Boral and Chakraborty  developed case-base reasoning system for machine tool selection and for non-traditional machining process selection. Sarikaya et al. developed a multi-objective optimization model for the selection of micro-electrical discharge drilling of AISI 304 stainless steel using S/N, RSM, RA and ANN method [18,19,20]. Chatterjee et al. proposed a novel hybrid model encompassing factor relationship (FARE) and MABAC (multi-attributed border approximation area comparison) method for selection and evaluation of non-conventional machining [21, 22].
From the literature survey, it is ascertained that no plausible work has been reported on the application of ANFIS system in WEDM. Therefore, the main objective of this work is, (1) to optimize the performance parameters by multi-parametric optimization using grey relation method (GRA) and (2) to develop the ANFIS model for the prediction of two major performance parameters namely surface roughness and material removal rate in WEDM by considering the five major input parameters.