# A Prognostic Based Fuzzy Logic Method to Speculate Yarn Quality Ratio in Jute Spinning Industry

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## Abstract

**:**

## 1. Introduction

## 2. Materials and Methods

#### 2.1. Materials

#### 2.2. Yarn Preparation

#### 2.3. Measurement of Quality Ratio (QR)

#### 2.4. Development of Fuzzy Modelling for Jute Yarn Quality Ratio

## 3. Results and Discussion

#### 3.1. Operation of Fuzzy Prediction Model

- (i)
- Fuzzification process or determine membership degrees

_{L}(LB) = 0, μ

_{M}(LB) = 1, μ

_{H}(LB) = 0; μ

_{L}(SB) = 0, μ

_{M}(SB) = 0.98, μ

_{H}(SB) = 0; μ

_{L}(TB) = 0.33, μ

_{M}(TB) = 0.233, μ

_{H}(TB) = 0, μ

_{L}(TM) = 0, μ

_{M}(TM) = 0.28, μ

_{H}(TM) = 0.21.

- (ii)
- Fuzzy if-then rules

_{M}(LB) and μ

_{M}(SB) and μ

_{L}(TB) and μ

_{M}(TM)$\Rightarrow $µ

_{LM}(QR)

_{M}(LB) and μ

_{M}(SB) and μ

_{L}(TB) and μ

_{H}(TM)$\Rightarrow $µ

_{M}(QR)

- (iii)
- Determine fuzzy output by implication method (min)

_{M}(LB) and μ

_{M}(SB) and μ

_{L}(TB) and μ

_{M}(TM))$\Rightarrow $µ

_{LM}(QR)

_{M}(5.5), μ

_{M}(2.27), μ

_{L}(0.107), μ

_{M}(5.77))$\Rightarrow $µ

_{LM}(QR)

_{LM}(QR)

_{LM}(QR)

_{M}(LB) and μ

_{M}(SB) and μ

_{L}(TB) and μ

_{H}(TM))$\Rightarrow $µ

_{M}(QR)

_{M}(5.5), μ

_{M}(2.27), μ

_{L}(0.107), μ

_{H}(5.77))$\Rightarrow $µ

_{M}(QR)

_{M}(QR)

_{M}(QR)

- (iv)
- Aggregation(max) of 14 and 15 rules only

_{M}(5.5), μ

_{M}(2.27), μ

_{L}(0.107), μ

_{M}(5.77)), min(μ

_{M}(5.5), μ

_{M}(2.27), μ

_{L}(0.107), μ

_{H}(5.77))

- (v)
- Defuzzification (centroid)

_{i}belongs to the i

^{th}universe and μ

_{i}is the firing strength of truth values of rule i (i = 1, 2 … n and n = number of observations) [40].

#### 3.2. Influence of Input Parameters on Jute Yarn Quality Ratio

#### 3.3. Model Validation

^{2}) correlation and the mean absolute error% of the real and forecast consistency ratio of the yarn. The results are provided in Table 3 and are also shown in Figure 11. It is noted that correlation coefficients (R

^{2}) are found to be 0.93 for both triangular membership and gaussian membership. That means that the proposed fuzzy model can be explained up to 93% by the triangular membership and gaussian membership function for both yarn counts. In the case of 173 tex and 241 tex, Table 3 shows that the mean absolute error for triangular and gaussian membership functions is 1.46 and 1.48, respectively. This error% is less than acceptable limits (5%). Therefore, the validation of our developed fuzzy model will be applicable in the industrial scale for predicting the quality of the jute yarn.

## 4. Conclusions

- The proposed model shows that the load at break greatly affects the jute yarn quality such as strain at break, tenacity at break, and tensile modulus. Although the proposed fuzzy model showed that (S.B and T.M), and (S.B and T.B) together account for the highest value of yarn quality. Therefore, the presented fuzzy model gives clear explanations of the interaction between the input variables and their effect on the jute yarn quality.
- For both the triangular and the gaussian membership function, the correlation coefficient was 0.93. This means that the developed fuzzy model can predict up to 93% of total jute yarn quality.
- In the case of varying spindle speed, for both yarn counts, the mean relative error was found to be 1.46% (triangular membership) and 1.48% (gaussian membership), respectively, which validates the model’s relative effectiveness for an industrial application, although triangular membership functions show a slight good result in terms of prediction error% than gaussian membership function.
- It can therefore be entirely assumed that the established intelligent fuzzy model can be applied as an effective tool for satisfactorily predicting the quality ratio of jute yarns before bulk production which can minimize the time, costs, and wastage of jute yarn production. The proposed fuzzy model will be very useful for spinners and textile researchers in the field of yarn engineering, particularly for jute yarn manufacturing.

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## Nomenclature

## References

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**Figure 1.**Experimental image; (

**a**) raw jute fiber, (

**b**) jute yarn sliver before spinning, (

**c**) Testing of jute yarn using UTM machine and tearing of jute yarn after applying force (

**d**).

**Figure 2.**Triangular membership function for the input parameters; (

**a**) load at break, (

**b**) strain at break, (

**c**) tenacity at break, and (

**d**) tensile modulus.

**Figure 3.**Gaussian membership function for the input parameters; (

**a**) load at break, (

**b**) strain at break, (

**c**) tenacity at break, and (

**d**) tensile modulus.

**Figure 7.**Surface view of load at break (X-axis) and strain at break (Y-axis) effect on jute yarn quality (Z-axis); (

**a**) for triangular membership function and (

**b**) gaussian membership function.

**Figure 8.**Surface view of load at break (X-axis) and tenacity at break (Y-axis) effect of jute yarn quality (Z-axis); (

**a**) for triangular membership function and (

**b**) gaussian membership function.

**Figure 9.**Surface view of tensile modulus (X-axis) and strain at break (Y-axis) effect on jute yarn quality (Z-axis); (

**a**) for triangular membership function and (

**b**) gaussian membership function.

**Figure 10.**Surface view of tenacity at break (X-axis) and strain at break (Y-axis) effect on jute yarn quality (Z-axis); (

**a**) for triangular membership function and (

**b**) gaussian membership function.

**Figure 11.**Correlation between actual and predicted yarn quality ratio using triangular membership function (

**a**) and gaussian membership function (

**b**).

Input | Output | ||||
---|---|---|---|---|---|

Linguistic variable | Load at break (LB) | Strain at break (SB) | Tenacity at break (TB) | Tensile modulus (TM) | Yarn Quality Ratio (QR)% |

Linguistic value | L_{1}, M_{2}, H_{3} | L_{1}, M_{2}, H_{3} | L_{1}, M_{2}, H_{3} | L_{1}, M_{2}, H_{3} | L_{1}, L_{1}M_{2}, M_{2}, H_{3}M_{2}, H_{3} |

Range | 4–7.5 | 1.7–3 | 0.08–18 | 3.5–6.8 | 81–104 |

_{1}: low, M

_{2}: medium, H

_{3}: high.

Rules No. | Input Variables | Output Variables QR (%) | |||
---|---|---|---|---|---|

LB | SB | TB | TM | ||

1 | L_{1} | L_{1} | M_{2} | L_{1} | L_{1} |

2 | H_{3} | L_{1} | L_{1} | M_{2} | M_{2} |

3 | M_{2} | H_{3} | L_{1} | L_{1} | L_{1}M_{2} |

4 | L_{1} | M_{2} | L_{1} | H_{3} | L_{1}M_{2} |

5 | M_{2} | L_{1} | L_{1} | H_{3} | L_{1}M_{2} |

6 | L_{1} | H_{3} | L_{1} | M_{2} | L_{1}M_{2} |

7 | M_{2} | M_{2} | L_{1} | M_{2} | L_{1}M_{2} |

8 | L_{1} | L_{1} | L_{1} | H_{3} | L_{1} |

9 | H_{3} | M_{2} | L_{1} | L_{1} | M_{2} |

10 | H_{3} | H_{3} | L_{1} | L_{1} | H_{3}M_{2} |

11 | L_{1} | M_{2} | M_{2} | H_{3} | L_{1}M_{2} |

12 | M_{2} | M_{2} | H_{3} | M_{2} | H_{3}M_{2} |

13 | L_{1} | M_{2} | H_{3} | L_{1} | L_{1} |

14 | L_{1} | H_{3} | M_{2} | M_{2} | L_{1}M_{2} |

15 | M_{2} | L_{1} | M_{2} | L_{1} | L_{1} |

16 | M_{2} | H_{3} | M_{2} | M_{2} | H_{3}M_{2} |

17 | H_{3} | L_{1} | M_{2} | H_{3} | H_{3} |

18 | M_{2} | M_{2} | M_{2} | M_{2} | H_{3}M_{2} |

19 | M_{2} | H_{3} | H_{3} | L_{1} | H_{3}M_{2} |

20 | L_{1} | L_{1} | H_{3} | H_{3} | L_{1}M_{2} |

21 | H_{3} | L_{1} | H_{3} | L_{1} | M_{2} |

22 | H_{3} | M_{2} | M_{2} | L_{1} | H_{3}M_{2} |

23 | H_{3} | H_{3} | H_{3} | H_{3} | H_{3} |

24 | H_{3} | H_{3} | M_{2} | H_{3} | H_{3} |

25 | L_{1} | H_{3} | H_{3} | L_{1} | L_{1}M_{2} |

26 | M_{2} | L_{1} | H_{3} | M_{2} | M_{2} |

27 | H_{3} | M_{2} | H_{3} | L_{1} | H_{3}M_{2} |

Yarn Count | L.B | S.B | T.B | T.M | Actual Yarn Q.R | Fuzzy Value | Absolute Error % | ||
---|---|---|---|---|---|---|---|---|---|

Tri mf | Gaus mf | Tri mf | Gaus mf | ||||||

173 tex (5 lb/spyndle) | 5.18 | 2.26 | 0.117 | 5.22 | 101.50 | 96.50 | 96.70 | 4.92 | 4.70 |

4.49 | 2.59 | 0.132 | 5.15 | 87.70 | 86.70 | 86.80 | 1.14 | 1.02 | |

4.21 | 1.78 | 0.105 | 4.63 | 84.22 | 83.40 | 84.40 | 0.97 | 0.21 | |

4.49 | 1.59 | 0.132 | 5.15 | 87.10 | 83.20 | 85.80 | 4.47 | 1.49 | |

4.05 | 1.50 | 0.134 | 5.77 | 85.10 | 83.40 | 85.70 | 1.90 | 0.70 | |

4.64 | 1.99 | 0.112 | 5.47 | 91.20 | 90.10 | 90.10 | 1.20 | 1.20 | |

4.18 | 2.26 | 0.117 | 5.22 | 83.94 | 83.10 | 84.10 | 1.00 | 0.19 | |

4.49 | 2.59 | 0.132 | 5.15 | 87.84 | 86.70 | 86.80 | 1.29 | 1.18 | |

5.21 | 2.99 | 0.133 | 6.32 | 102.50 | 102.00 | 98.50 | 0.48 | 3.90 | |

4.48 | 1.98 | 0.18 | 4.64 | 87.66 | 87.20 | 90.50 | 0.52 | 3.23 | |

4.81 | 1.98 | 0.123 | 6.62 | 94.28 | 91.60 | 91.70 | 2.84 | 2.73 | |

4.49 | 2.59 | 0.132 | 5.15 | 87.84 | 86.70 | 86.80 | 1.29 | 1.18 | |

241 tex (7 lb/spyndle) | 6.53 | 1.80 | 0.116 | 5.85 | 95.20 | 97.60 | 96.70 | 2.52 | 1.57 |

6.76 | 2.04 | 0.106 | 5.12 | 96.20 | 95.90 | 95.90 | 0.31 | 0.31 | |

7.24 | 3.00 | 0.164 | 5.83 | 103.30 | 101.00 | 102.00 | 2.22 | 1.26 | |

7.27 | 2.27 | 0.104 | 5.13 | 98.50 | 98.40 | 97.50 | 0.10 | 1.01 | |

6.76 | 2.28 | 0.112 | 4.84 | 98.50 | 99.50 | 97.70 | 1.01 | 0.81 | |

6.65 | 2.00 | 0.132 | 4.76 | 100.50 | 101.00 | 99.00 | 0.49 | 1.49 | |

7.06 | 2.35 | 0.133 | 5.55 | 101.80 | 102.00 | 102.00 | 0.19 | 0.19 | |

7.17 | 2.24 | 0.128 | 5.56 | 102.5 | 102.00 | 102,00 | 0.48 | 0.48 | |

6.92 | 1.99 | 0.132 | 6.02 | 101.80 | 102.00 | 101.00 | 0.19 | 0.78 | |

6.70 | 2.21 | 0.099 | 5.59 | 95.90 | 98.30 | 97.40 | 2.50 | 1.56 | |

6.16 | 2.97 | 0.08 | 5.07 | 89.50 | 93.90 | 92.40 | 4.90 | 3.24 | |

7.27 | 2.19 | 0.111 | 5.95 | 100.50 | 101.00 | 97.80 | 0.49 | 2.68 | |

R^{2} | 0.93 | 0.93 | |||||||

Mean absolute error % | 1.46 | 1.48 |

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## Share and Cite

**MDPI and ACS Style**

Paul, T.K.; Jalil, T.I.; Parvez, M.S.; Repon, M.R.; Hossain, I.; Alim, M.A.; Islam, T.; Jalil, M.A.
A Prognostic Based Fuzzy Logic Method to Speculate Yarn Quality Ratio in Jute Spinning Industry. *Textiles* **2022**, *2*, 422-435.
https://doi.org/10.3390/textiles2030023

**AMA Style**

Paul TK, Jalil TI, Parvez MS, Repon MR, Hossain I, Alim MA, Islam T, Jalil MA.
A Prognostic Based Fuzzy Logic Method to Speculate Yarn Quality Ratio in Jute Spinning Industry. *Textiles*. 2022; 2(3):422-435.
https://doi.org/10.3390/textiles2030023

**Chicago/Turabian Style**

Paul, Tamal Krishna, Tazin Ibna Jalil, Md. Shohan Parvez, Md. Reazuddin Repon, Ismail Hossain, Md. Abdul Alim, Tarikul Islam, and Mohammad Abdul Jalil.
2022. "A Prognostic Based Fuzzy Logic Method to Speculate Yarn Quality Ratio in Jute Spinning Industry" *Textiles* 2, no. 3: 422-435.
https://doi.org/10.3390/textiles2030023