Prognosis of Dimensional Stability and Mass per Unit Area of Single Jersey Cotton Knitted Fabric with Fuzzy Inference System Napoved dimenzijske stabilnosti in ploščinske mase bombažnega levo-desnega pletiva s sistemom mehkega sklepanja

Endeavour has been made in this research work using experimental data for constructing a fuzzy inference model based on the Mamdani approach to prognosticate the shrinkage and mass per unit area of a single jersey cotton knitted fabric. To control the dimensional stability of the cotton knitted fabric in advance, an artifi cial intelligent system is required in the knitting industry which simulates all product and process variables and is able to give human-like decisions in advance. The most important controlling parameters of knitted fabric properties such as stitch length, yarn count and overfeed percentage in stenter were considered as input variables, and mass per unit area, lengthwise shrinkage and widthwise shrinkage as output variables. Overall, 35 experiments were conducted to construct the model, varying diff erent parameters. The applicability of the model was validated by comparing the results from 15 newly conducted experiments. The coeffi cient of determination of predicted and actual data for mass per unit area, lengthwise shrinkage and widthwise shrinkage were 0.97, 0.99 and 0.99, respectively which validates the model relatively eff ectively for an industrial application. The proposed model can assist a fabric manufacturer by taking a decision in selecting knitting and fi nishing parameters prior to producing the fabric. Moreover, it can reduce the time and energy required, and waste produced in the process by skipping the sample development step before


Introduction
Knitted fabrics are generally a combination of a series of knitted loops which are readily perverted during its manufacturing process. Cotton knitted fabrics are very popular among customers, due to the excellence attributes of comfort; however, nowadays, the demand of customers has changed as they pay more attention to quality along with reasonable cost. A common complain from the customer's and manufacturer's side is the dimensional instability of cotton knitted fabrics [1]. During the knitting action, the casting off a new loop through the old loop by a needle develops some tension in yarn that initiates distortion in the loop shape. It has been reported that the stitch density of a single jersey fabric is controlled by loop length rather than yarn and knitting variables [2]. According to Munden, yarn properties would not dominante the knitted loop and after the removal of mechanical strains, the knitted loop would take a natural shape [3]. Again, the takedown mechanism and fabric spreader in the knitting machine produce both length-and widthwise tension in the fabric that also perverts the knitted loop shape. Th e latter will remain distorted aft er the removal from the machine. Th is type of loop distortion has a slight infl uence on the shrinkage properties of the fi nished fabric. Th is means that the loop distortion could be lessened by applying an appropriate fi nishing process in the knitted fabric [4]. Th e research of dimensional behaviour of weft knit ramie, cotton and viscose fabrics conducted by Li et al. [5] reveals that the loosely knitted fabrics of hydrophilic fi bres, including cotton and viscose, undergo progressive shrinkage in the vertical (wale) dimension and progressive stretch in the horizontal (course) dimension. Moreover, it has been reported in a few studies that though the types of yarn like ring or compact yarn do not have a signifi cant eff ect on shrinkage, the presence of elastomeric yarn and/ or tightness factor, yarn count and stitch length can have a great infl uence on dimensional properties [6][7][8]. Moreover, a few other factors such as the fi nishing process, washing, drying and relaxation state are also found crucial for the dimensional stability of knitted fabrics [9][10][11]. However, every change in the manufacturing process has more than one consequence; therefore, it is relatively diffi cult to improve the shrinkage property by changing a single parameter. For example, the changes in yarn count, stitch length and machine diameter during the fabric production to control shrinkage also aff ect the tightness factor, mass per unit area and width along with the shrinkage property, and also develop spirality as these all are correlated with each other. Most common methods that are used by factories for developing a new sample or upgrade existing quality are previous experience, guess work, or trial and error method that are not only expensive but also time-consuming and a waste of production resources. It is also very risky as there may not be enough time or resources to be successful. Th e necessity of establishing a prognostic model for forecasting the performance of a proposed fabric quality before its production has become obligate. Th ere are three diff erent models for predicting knitted fabric characteristics, i.e. mathematical model, statistical regression model and intelligent model. Th e mathematical models implemented by many researchers for predicting diff erent properties of a textile material are very appealing since they are established on the fundamental theories of basic science, which provide a clear conception about the work process [2,3,[12][13][14][15][16][17][18]. Th e well-developed prediction model for forecasting knitted fabric shrinkage called STARFISH has some limitations as it uses an enormous amount of data accumulated from all over the world, consequently adversely aff ecting the prediction performance. Moreover, while the program predicts the properties, the reference production condition and latest fi nishing procedure explained in STARFISH is strictly maintained for good prediction variiranjem parametrov. Uporabnost modela je bila potrjena s primerjavo z rezultati iz 15- performance that is relatively diffi cult for most factories to maintain. Th e computational database model which has been developed in an Excel spread sheet for predicting knitted fabric shrinkage used a huge amount of data for establishing a model which is very challenging to collect as well as time-consuming. Several researchers developed models using statistical regression that are used in the relevant fi eld [14][15][16][17][18][19][20][21]. Hence, large amounts of sample data, as well as a prior assessment of the relationship between inputs and outputs, are required for constructing a statistical model. Moreover, the non-linear relationship between inputs and outputs cannot be caught by both mathematical and statistical models [22][23]. Essentially, the advent of artifi cial intelligent techniques such as artifi cial neural network (ANN) and adaptive neuro-fuzzy inference system (ANFIS) has given a new incentive in the research world for developing a prediction model. Now, based on diff erent parameters, a lot of work has been done by many researchers to forecast knitted fabric attributes, e.g. bursting strength, pilling tendency, air permeability, thermal resistance, spirality, hand evaluation, defect classifi cation etc, and also in the woven and apparel industry [24][25][26][27][28][29][30]. An enormous amount of noise free data is required in establishing the ANN and ANFIS model, which becomes very diffi cult and time consuming to accumulate from the textile industry [22,23,31]. Moreover, the ANN model works like a black box as it is not able to give precise intensifi cation of non-linearity between input-outputs and core logic on which a decision could be made [22,23,32]. Conversely, the fuzzy inference system is a very profi cient modelling tool which overcomes the lacunas of ANN, ANFIS and statistical regression, as it is based on fuzzy logic that can easily interpret the knowledge of experts into a set of rules in an inference system and is focused on modes of reasoning that are fairly accurate rather than exact. Th e fuzzy expert system implementation is easier than other models, since it can execute the modelling operation with a small amount of experimental data in the non-linear, imprecise, vague, trial-error and complex textile domain [22][23][24][25][31][32][33]. Th erefore, in this current research, the predictions of mass per unit area and shrinkage properties of a plain cotton knitted fabric were performed by constructing a fuzzy knowledge-based model as it is more userfriendly, of low design cost and simply applicable.

Knitting process
100% cotton plain single jersey fabrics were knitted in 30 inches (76.2 cm) diameter, 20 gauge single jersey circular knitting machine. For constructing the fuzzy model, yarn count was considered in the English count (Ne) system as this unit is commonly used in knitting industries. In total, seven diff erent types of samples were made. Th e amount of each sample was 5 kg. Th e knitting parameters that were used during the making of samples are shown in Table 1.

Pre-treatment and fi nishing procedure
Scouring and bleaching of cotton knitted fabrics were done in a common bath. Th e process was carried on a sample dyeing machine (Sclavos, Greece) using detergent 0.5 g/l (Ecowett JTLF, Vijol, India), anti-creasing agent 0.5g/l (Lenetol PAC, Croda, India), sequestering agent 0.3 g/l (Eco SQ-114FE, Jintex, Taiwan), stabilizing agent 0.2g/l (Eco ST-201, Jintex, Taiwan), sodium carbonate (Na 2 CO 3 ) 5 g/l, sodium hydroxide (NaOH) 0.5 g/l, hydrogen peroxide 50% 4 g/l. Aft erwards, the fabric samples were washed. Finally, 1 g/l acetic acid (CH 3 COOH) and 0.2 g/l peroxide killing agent (peroxidase enzyme) were applied onto fabrics for neutralization. Aft er the scouring and bleaching, the samples were slit in a Bianco sliting machine. Th en, they were passed in a Brukner stenter machine at 13 m/min speed at 150 °C with the constant width of 1.6 m (63 inches). To observe the eff ect of overfeed percentage on mass per unit area and dimensional stability of a knitted fabric, each sample was processed with fi ve diff erent overfeed percentages, e.g. 10%, 20%, 30%, 40%, 50% of the stenter machine. Th erefore, 7 × 5 = 35 samples were obtained. Before the testing, all samples were kept on a fl at surface for conditioning for at least 24 hours. Standard atmospheric conditions, i.e. relative humidity (65 ± 2)% and temperature (20 ± 2) °C, were properly maintained during

Establishment of fuzzy prediction model
Th e fuzzy prediction model was constructed by using three diff erent variables, namely stitch length (SL), yarn count (YC) and overfeed (OF) percentage in a stenter machine as input variables, and mass per unit area (GSM), length-and widthwise shrinkage (LS, WS) of knitted fabrics as output variables. Th e selected variables have a great infl uence on the shrinkage of knitted fabrics. Th e proposed fuzzy prediction model of fabric shrinkage and GSM was developed by using a fuzzy logic toolbox from MATLAB (version 8.2.0.701). Th e construction of the fuzzy prediction model for LS, WS and GSM of knitted fabrics is illustrated in Figure 1. For fuzzifi cation, input and output variables were classed into some probable linguistic subsets for the fuzzy expert system being able to trace small changes in output variables with any variation of input variables. Th e linguistic fuzzy sets for input-output parameters are given in Table 3. Among all the membership functions, the triangular-shaped membership functions are very popular due to their simplicity and precision. In this research, triangular functions were applied for both input and output variables as variables can easily be described by them [36].
Mamdani max-min fuzzy inference mechanism assures a linear interpolation of outputs between the rules [24,25]. Therefore, the model is constructed by using this mechanism. Theoretically, there could be 4 × 3 × 5 = 60 fuzzy rules as the input variable SL has 3 linguistic levels, Count has 4 linguistic levels and Overfeed percentage in the stenter machine has 5 linguistic levels [23]. However, on the basis of expert knowledge and prior experience, only 50 rules have been used which make the fuzzy expert system simple and more easy to use [22,23]. Some examples of established fuzzy rules are revealed in Table 4.   To elucidate the fuzzifi cation process, linguistic terms for triangular membership functions can be interpreted through equation 7 [37]: .   In the same way, the linguistic expression and membership function of other variables was determined. Among diff erent defuzzifi cation methods, the centre of gravity (COG) defuzzifi cation method was used for converting the fuzzy output into non-fuzzy crisp numeric value [22,37]. Th e truth degrees (μ) of each rule are enumerated with the help of the min and by taking the max between active rules [32,38]. It can be explained by considering the following example, for crisp input SL = 2.8, count = 26 and OF = 30%, the rules 13 and 18 will be fi red. Th e truth values (α) of the two rules are given as: Th e membership function was calculated according to the Mamdani max-min inference system such as max (α 13 , α 18 ) = 0.5. Th en, the crisp output was enumerated. Hossain et al. [32] alluded that the crisp decision obtained from a system, the output of which is fuzzy by showing the output in a single scalar quantity. In this case, LS crisp (Output) was enumerated by multiplying the output membership values with their corresponding singleton values followed by dividing the obtained value by the sum of membership values which is shown in equation 16 [32,37,38]: where a i is the spot of the singleton in the i th universe and μ (i) is the fi ring strength of the truth values of rule i [22,32,37,38].

Validation of prediction ability
Th e proposed model was investigated according to the global prediction error such as mean absolute error percentage (MAEP) and coeffi cient of determination ( 2 ) for determining the prediction ability of the model. Th e formulas of accuracy measurements are given in equations 17-19 [31, 32, 37−39]: where E a is actual result, E p is predicted result, E m is mean value and N represents the number of the pattern.

Infl uence of input variables on GSM
Th e impact of count, stitch length and overfeed percentage on fabric GSM was shown in Figures   9-11. It can be seen in Figure 9 that fi ner yarn count coupled with lower stitch length exhibited higher fabric GSM. An approximately 25-30% increment in fabric GSM was found for 7% drop off in stitch length. Th is might have occurred as lower stitch length increases stitch density in the unit area, which then resulted in heavier weight of a fabric [40]. Moreover, Figure 9 also showed that yarn getting fi ner by up to 30 Ne, stitch length from 2.7 to 2.9 mm caused lighter GSM in the knitted fabric. It can be seen in Figures 10 and 11 that lower OF did not substantially aff ect fabric weight whereas at OF above 20%, the GSM of the knitted fabric increased dramatically with the rise of OF. When the OF was increased from 20% to 35% in stenter, about 15% fabric GSM was increased, which was probably due to the accumulation of the fabric in the feeding area of the stenter machine, which raised the density of the fabric [41]. However, fabric GSM came to an optimal level in between 35 to 50% OF. Figure 11 shows that GSM increased to around 73% and around 37% with thicker yarn and higher overfeed percentage, respectively.

Infl uence of input variables on lengthwise shrinkage
Eff ect of overfeed percentage, count and stitch length on lengthwise shrinkage is shown in Figures  12-14. Figure 12 depicts that LS was improved with the increase of OF and vice versa. Initially, no signifi cant eff ect was observed in LS when increasing SL. However, LS was highly aff ected by OF valued near 20% and upwards. Only SL (2.8 mm to 2.9 mm) had an individual eff ect on LS which improved steadily with the increase of OF. LS was improved at around 75% for elevating the overfeed from 20% to 50% within the range 2.65 mm to 2.75 mm SL, while no signifi cant eff ect was observed for 10% OF. Nevertheless, in the mid-range SL (2.7-2.8 mm), LS was improved by about 40% for increasing overfeed from 10% to 50%. It can also be seen in Figure 13 that the eff ect of yarn count on the length-wise shrinkage property was not linear but OF showed a linear relationship with the LS property of the fabric. LS showed relatively better performance for coarser yarn than fi ner as it was enhanced by around 67% when increasing overfeed from 10% to 50% in coarser count (22)(23)(24). Very high OF (40% to 50%) upgraded shrinkage property for both coarser and fi ner yarn count [42]. No notable improvement in lengthwise shrinkage was observed in Figure 14 for increasing stitch length in the range 2.7-2.9 mm for thicker yarn count. Conversely, thinner yarn count (28)(29)(30) showed better performance in LS from 2.65 to 2.75 mm SL, whereas with the elevation of stitch length in fi ner yarn, the LS property declined. Specifi cally, in the case of 28-30 Ne of yarn count, the increase of LS due to the increase of SL from 2.65 mm to 2.9 mm was around 60%. From the overall context, this may be justifi ed as the compact knitted structure formed by either lower SL or higher OF or coarser count or combination of them made the fabric more stable aft er the washing. Due to higher OF, the forces in the processing of a cotton fabric with lower SL and coarser count contributed to the contraction of the fabric as the forces push mechanically the knitted loops towards each other to make them closer. Hence, aft er the washing, the non-linear hysteresis eff ect caused the cotton fabric to become denser (as loops do not get enough space to shrink) and the fabric consequently became more dimensionally stable [41].

Infl uence of input variables on widthwise shrinkage
Th e impact of count, stitch length, overfeed percentage on widthwise shrinkage (WS) is shown in Figures  15-17. Th e WS of the knitted fabric improved linearly with OF and SL, which is shown in Figure 15. WS was improved by approximately 46% when overfeed was increased from 10% to 50% at 2.65 mm SL, whereas in mid-range SL (2.7-2.8mm), it progressed by about 30%. As lengthwise shrinkage improved at high overfeed percentage, the width of the fabric changed as well. Figure 16 revealed that though in the fi ner count and lower SL there was no impact on WS, the latter decreased slowly with greater SL in almost 22 to 26 Ne count. An approximately reduction in the widthwise direction increased by 25% when SL increased from 2.7 to 2.8 mm for fi ner counts, i.e. 28 and 30 Ne. As aft er washing, fi ner yarn with high stitch length gets more space for swelling and comes close together, this lessen the width of the fabric aft er relaxation. Conversely, coarser yarn with high stitch length fabric showed a lower value of shrinkage in the widthwise direction, as it contained high course length and less space between loops that caused the fabric to extend in the width direction rather than shrink [42]. Lastly, Figure 17 shows that WS enhanced significantly with higher OF percentage and vice versa. Th e eff ect of 28-30 Ne count with 10-20% OF on WS was not perceptible enough. At over 20% of OF, WS improved sharply in ascending order. In low-range count (22 to 24 Ne) with 50% OF, low WS in the fabric was found. In the light of the above context, it can be summarized that the eff ectiveness of stitch length, count and overfeed % on WS was less significant for all the fabrics as they were made in the same diameter of the knitting machine and passed in a stenter, keeping constant width.

Conclusion
Single jersey cotton knitted fabrics have the tendency to change their dimension permanently according to the variables in knitted fabric manufacturing and processing. From the prepared model, it will be possible to predict the dimension of the fabric before its production in industrial scale if the variables and their eff ects are known and controlled. From the empirical study, it has been elucidated that in addition to yarn count and stitch length, the overfeed percentage of a stenter machine also has a great impact on the fabric mass per unit area and shrinkage property of a single jersey knitted fabric. By increasing overfeed percentage in a stenter machine, the lengthwise shrinkage property of a single jersey fabric can also be improved for all yarn's count and stitch length considered in this work; however, this also increases the mass per unit area of the fabric. On the other hand, knitted fabric made from yarns with higher count with a lower range of stitch length exhibited better performance in both length-and widthwise shrinkage property. Again, the developed fuzzy intelligent model confers an outstanding clarifi cation about the interaction between the variables and their eff ect on the mass per unit area and shrinkage property of a plain single jersey knitted fabric. Th is model may act as a decision-making tool and support the textile engineer to prognosticate knitted fabric mass per unit area, and lengthand widthwise shrinkage in advance, which can minimize production time, costs and wastages generated in developing and improving the quality of the knitted fabric. In the future of this ongoing research, we will consider input variables from a compactor machine for the prediction of fi nished fabric properties, which will further extend the applicability of this model.