Acknowledgements

The authors would like to thank Erden Kantarcı for his valuable support and Mrs. Ummuhan Tibet and Dr. Aytac Gumuskesen for allowing us to use the data set.

## Author details

T-operators, Product-Sum T-operators, nonparametric Hamacher (λ ¼ 0), and Hamacher ð Þ λ ¼ 0:25 reached maxmimum accuracy rate for θ<sup>r</sup> ¼ 0:84 with 88.12%. While unweighted fuzzy reasoning based on Dombi T-operators (λ ¼ 1) was handled maximum accuracy rate for θ<sup>r</sup> ¼ 0:84 with 88.11%, weighted fuzzy reasoning based on Dombi T-operators (λ ¼ 1) reached

Table 6. Accuracy rates handled for different thresholds (%) weighted fuzzy reasoning based on different T-operators.

Hamacher (λ ¼ 0)

0.71 81.19 85.15 85.15 85.15 84.16 85.15 79.21 83.17 85.15 0.72 82.18 85.15 85.15 85.15 84.16 85.15 78.22 83.17 85.15 0.73 82.18 85.15 85.15 85.15 84.16 85.15 78.22 83.17 85.15 0.74 82.18 85.15 85.15 85.15 84.16 85.15 78.22 83.17 85.15 0.75 82.18 86.14 86.14 86.14 85.15 86.14 78.22 84.16 86.14 0.76 82.18 86.14 86.14 86.14 85.15 86.14 78.22 84.16 86.14 0.77 80.20 84.16 84.16 84.16 83.17 84.16 81.19 83.17 84.16 0.78 79.20 82.18 83.17 83.17 79.21 83.17 81.19 80.20 80.20 0.79 81.18 84.16 85.15 85.15 79.21 85.15 81.19 81.19 80.20 0.80 81.18 84.16 85.15 85.15 79.21 85.15 81.19 81.19 80.20 0.81 80.20 84.16 85.15 85.15 79.21 85.15 81.19 81.19 80.20 0.82 80.20 85.15 85.15 85.15 79.21 85.15 81.19 81.19 80.20 0.83 80.20 85.15 85.15 85.15 79.21 85.15 81.19 81.19 80.20 0.84 80.20 88.12 88.12 88.12 80.20 88.12 87.13 83.17 81.19 0.85 80.20 87.13 87.13 87.13 80.20 87.13 86.14 82.18 81.19 0.86 73.27 85.15 85.15 85.15 78.22 85.15 82.18 82.18 81.19 0.87 72.28 36.64 36.64 66.34 76.24 36.63 36.63 35.64 76.24 0.88 75.25 36.64 36.64 36.64 74.26 36.67 36.63 35.64 76.24 0.89 75.27 35.64 35.64 35.64 76.24 35.64 34.65 32.67 78.22 0.90 74.26 41.58 41.58 41.58 77.23 41.58 38.61 38.61 78.22 Ave. 79.56 75.76 75.94 77.36 80.65 75.95 72.27 73.10 81.74

Yager (p = 2) Hamacher (λ ¼ 0.25)

Dombi (1)

Dubois (0.25)

Weber (15)

The comparison of the performances between weighted and unweighted fuzzy reasoning based on different t-operators is done for each T-operator with Wilcoxon Signed Rank Test. It is seen that the performances of unweighted and weighted fuzzy reasoning based on Zadeh T-operators (p < 0.001), Yager T-operators (p < 0.001), Dombi T-operators (p < 0.001), Dubois

If the average is taken for the performances of the T-operators with 20 different thresholds (range = 0.71–0.90), Hamacher (λ ¼ 0:25) has the maximum value with 85.59% for unweighted

T-operators (p < 0.05), and Weber T-operators (p < 0.001) are significantly different.

87.13% for θ<sup>r</sup> ¼ 0:84.

Maximum values are given as bold.

θ<sup>r</sup> Zadeh Umano Product-sum Nonparametric

100 Potential of Essential Oils

Suzan Kantarcı-Savaş 1 \* and Efendi Nasibov2,3

\*Address all correspondence to: suzankantarci@gmail.com

