4. Experimental study on fuzzy rule-based approach to geographic classification of virgin olive oil using T-operators

In this section, fuzzy rule-based approach to geographic classification of virgin olive oil problem is summarized. And, the solution is given step by step. Then, we describe the experimental study. Firstly, the description of the olive oil samples and the methodology used in chemical analyses of olive oil samples are explained in detail. Secondly, we explain performance measure and statistical tests. Fuzzy reasoning methods with nonparametric operators are examined. The behavior of fuzzy ID3 weighted fuzzy reasoning method based on different T-operators is observed. Then, the weighted and unweighted fuzzy reasoning methods based on different T-operators are compared.

#### 4.1. Olive oil samples

The adaptation of generalized model with weighted fuzzy reasoning based on T-operators. The steps are given below combined with FID3 reasoning based on T-operators:

<sup>¼</sup> <sup>T</sup> <sup>μ</sup>Aj<sup>1</sup> xp<sup>1</sup>

bl <sup>j</sup> xp

<sup>¼</sup> <sup>T</sup><sup>∗</sup> bl

Class ¼ arg max

4. Experimental study on fuzzy rule-based approach to geographic

conf <sup>l</sup> xp

classification of virgin olive oil using T-operators

<sup>¼</sup> <sup>T</sup> <sup>μ</sup>Aj

μAj xp

computed

96 Potential of Essential Oils

where μAj

where bl

<sup>j</sup> xp

predicted one [2, 27].

to the j.th rule.

xpi

consequent classes (Eq. (16))

T-conorm (listed in Table 1) [2, 27].

the number of antecedents of the rule.

Step 1: Antecedent degree of a rule: In this step, the strength of activation of the if-part for all rules handled from each path of the fuzzy decision tree in the RB with the pattern xp is

is handled from a leaf node at the end of each path. T is a T-norm (listed in Table 1) and nj is

Step 2: Consequent degree for a class: The consequent degree favor of class l by the rule Rj for the pattern xp is computed as follows where RWjl the weight is computed according to the multiple

Step 3: Confidence degree for a class: In this stage, the confidence degree for the class l according to all rules in RB is computed. To obtain the confidence degree of a class, the association degrees of the rules of that class are aggregated by using conjunction operators, where T\* is a

> <sup>1</sup> xp ; b<sup>l</sup>

Step 4: Classification: The class is obtained with the highest confidence degree assign as the

In this section, fuzzy rule-based approach to geographic classification of virgin olive oil problem is summarized. And, the solution is given step by step. Then, we describe the experimental study. Firstly, the description of the olive oil samples and the methodology used in chemical analyses of olive oil samples are explained in detail. Secondly, we explain performance measure and statistical tests. Fuzzy reasoning methods with nonparametric operators are examined. The behavior of fuzzy ID3 weighted fuzzy reasoning method based on different

xp ;RWjl 

> <sup>2</sup> xp ;…::; b<sup>l</sup>

, <sup>j</sup> <sup>¼</sup> <sup>1</sup>, <sup>2</sup>, …, R, is the association degree of the pattern xp, to the class <sup>l</sup>, according

<sup>l</sup>¼<sup>1</sup>, <sup>2</sup>…, <sup>m</sup> conf <sup>l</sup> xp

<sup>R</sup> xp (19)

(20)

 ;……:μAj<sup>1</sup> xpnj 

is the matching degree of the example with ith antecedent of the rule Rj, which

(17)

(18)

Olives were collected from certain trees of the cultivars, which were determined subject matter of this work: Ayvalik, Memecik, Kilis Yaglik, and Nizip Yaglik. The samples collected in 2002– 2003, 2004–2005, and 2005–2006 harvest seasons. About 101 olive oil samples [47] were used for the experimental study. These samples were collected from different regions [North Aegean (33), South Aegean (53), Mediterranean (4), and South East (11)]. The detail information about the chemical analysis of the samples was given in pioneer studies [27, 47, 48]. PCA was applied in SPSS 20.0, partition coefficients and fuzzy c-means algorithm were handled in MATLAB 2015. The software is designed named as OliveDeSoft in the Visual C# for the experimental study (intel i7, 2.4 GHz, 4 Gb RAM) [48]. The data fuzzification process was applied by using fuzzy c-means (FCM). Partition coefficient determined the number of clusters [19, 20]. The calculated partition coefficient value for each cluster is given in former study [27].

#### 4.2. Performance measure and statistical tests

In former study [27], principal component analysis is performed on this data set in order to explore the data structure. It is seen that the geographic origin of virgin olive oils on the results handled from the chemical analyses are explained clearly. Yet one region (Mediterranean) has less data than the other regions, so it is not explained. The data implementation is done in IBM SPSS 20. The chemical measurements have fuzziness. So, we prefer to use fuzzy ID3 algorithm based on fuzzy logic for the classification in our study. In classical case, ID3 algorithm works with categorical variables. It is an advantage of fuzzy ID3 algorithm. This algorithm carries out numerical variables via fuzzy variables. Each numeric variable is converted to fuzzy variable. Fuzzy c-means algorithm is performed for the fuzzification. This proposed approach displays eight different T-operators in the reasoning procedure. The performances of standard fuzzy ID3 represented in [2, 27] and C4.5 [49] algorithms are examined in the experimental study. Leave one out validation procedure was performed for the performances measurement of the algorithms. Accuracy rate is preferred to test different methods [13]. In experimental study, threshold value for fuzzy decision tree is set to θ<sup>r</sup> ¼ 0:75. Parameters of parametric operators are fixed as Yager p = 2, Hamacher p = 0.25, Dombi = 1, Dubois = 0.25, and Weber = 15 for fuzzy reasoning procedure. The comparison of the performances of unweighted and weighted fuzzy reasoning approaches is performed.

Studying fuzzy reasoning method with nonparametric operators: C4.5 algorithm also uses entropy as splitting criteria. It is the improved version of ID3 algorithm. It was presented by Quinlan in 1994 to work on the numerical data [27]. The performance of it is 86.14%. Then, it is observed that the performance of fuzzy ID3 algorithm with reasoning method in [2] is 86.14% too [27].

The performance results of nonparametric approaches given in Table 2 shows that the result handled from three nonparametric operators have the same performance value with handled from C4.5 algorithm. Yet, the accuracy handled with Zadeh T-operators is smaller value with 82.18%.


The results of pairwise comparisons for weighted fuzzy ID3 reasoning based on different Toperators [27] with 20 different thresholds (range = 0.71-0.90) via adjusted significance values

A Fuzzy Rule Based Approach to Geographic Classification of Virgin Olive Oil Using T-Operators

Friedman aligned ranks test shows that p-value is equal to zero. It means that there are significant differences among the results. Then, the pairwise comparisons are performed. The results are shown in Table 4. These nonparametric tests were performed in IBM SPSS 20.

The comparison of the weighted and unweighted fuzzy reasoning methods based on different Toperators: Accuracy rates handled for different thresholds within unweighted fuzzy reasoning method based on different T-operators are given in Table 5. It is seen that maximum value has Dombi T-operators handled for θ<sup>r</sup> ¼ 0:85 with 88.11%. As a result, it is observed that we can

On the other hand, accuracy rates handled for different thresholds within weighted fuzzy reasoning method based on different T-operators are given in Table 6. It is seen that Umano

Hamacher (λ ¼ 0)

0.71 85.15 85.15 85.15 84.16 85.15 85.15 85.15 82.18 51.48 0.72 85.15 85.15 85.15 84.16 85.15 85.15 85.15 82.18 51.48 0.73 85.15 85.15 85.15 84.16 85.15 85.15 85.15 82.18 85.15 0.74 85.15 85.15 85.15 84.16 85.15 85.15 85.15 82.18 85.15 0.75 86.14 86.14 86.14 85.15 86.14 86.14 86.14 83.16 86.14 0.76 86.14 86.14 86.14 85.15 86.14 86.14 86.14 83.16 86.14 0.77 84.16 84.16 84.16 83.17 84.16 84.16 84.16 82.18 84.16 0.78 82.18 82.18 82.18 81.19 82.18 82.18 82.18 82.18 82.18 0.79 86.14 84.16 84.16 85.15 84.16 86.14 84.16 84.16 84.16 0.80 86.14 84.16 84.16 85.15 84.16 86.14 84.16 84.16 84.16 0.81 86.14 84.16 84.16 85.15 84.16 86.14 84.16 84.16 84.16 0.82 86.14 84.16 84.16 85.15 84.16 86.14 84.16 84.16 84.16 0.83 86.14 84.16 84.16 85.15 84.16 86.14 84.16 84.16 84.16 0.84 87.13 87.13 87.13 86.14 87.13 87.13 87.13 87.13 87.13 0.85 87.13 86.14 86.14 86.14 86.14 87.13 86.14 88.11 86.14 0.86 87.13 86.14 86.14 86.14 86.14 87.13 86.14 86.14 86.14 0.87 86.14 83.17 83.17 85.15 83.17 86.14 83.17 86.14 83.17 0.88 85.15 36.63 36.63 84.16 36.63 85.15 36.63 36.63 36.63 0.89 84.16 37.62 37.62 83.17 37.62 86.14 37.62 35.64 37.62 0.90 84.16 42.57 42.57 83.17 42.57 83.17 42.57 40.59 42.57 Ave. 85.54 77.97 77.97 84.46 77.97 85.59 77.97 77.03 74.60

Table 5. Accuracy rates handled for different thresholds (%) unweighted fuzzy reasoning based on different T-operators.

Yager (p = 2) Hamacher (p = 0.25)

Dombi (1)

http://dx.doi.org/10.5772/intechopen.79962

Dubois (0.25)

Weber (15)

99

also reach better results by using different threshold values.

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

Maximum values are given as bold.

are given in Table 4.

Table 2. The performance results of each algorithm for nonparametric operators [27].

Study of the behavior of fuzzy ID3 weighted fuzzy reasoning method based on different T-operators: We have made use of the Friedman aligned ranks as a nonparametric statistical procedure to discover statistical differences among a group of results for 20 threshold (θr) values in Table 3.


Table 3. Friedman aligned ranks for weighted Fuzzy ID3 reasoning based on different T-operators.


Table 4. The results of pairwise comparisons for weighted Fuzzy ID3 reasoning based on different T-operators with 20 different thresholds (range = 0.71–0.90) via adjusted significance values.

The results of pairwise comparisons for weighted fuzzy ID3 reasoning based on different Toperators [27] with 20 different thresholds (range = 0.71-0.90) via adjusted significance values are given in Table 4.

Friedman aligned ranks test shows that p-value is equal to zero. It means that there are significant differences among the results. Then, the pairwise comparisons are performed. The results are shown in Table 4. These nonparametric tests were performed in IBM SPSS 20.

The comparison of the weighted and unweighted fuzzy reasoning methods based on different Toperators: Accuracy rates handled for different thresholds within unweighted fuzzy reasoning method based on different T-operators are given in Table 5. It is seen that maximum value has Dombi T-operators handled for θ<sup>r</sup> ¼ 0:85 with 88.11%. As a result, it is observed that we can also reach better results by using different threshold values.

Study of the behavior of fuzzy ID3 weighted fuzzy reasoning method based on different T-operators: We have made use of the Friedman aligned ranks as a nonparametric statistical procedure to discover statistical differences among a group of results for 20 threshold (θr) values in Table 3.

Product-Sum 6.80 Total N 20 Nonparametric Hamacher ðλ ¼ 0) 6.88 Test Statistic 76.396

Hamacher 6.80 Degrees of Freedom 8

Table 3. Friedman aligned ranks for weighted Fuzzy ID3 reasoning based on different T-operators.

Weber Zadeh Yager Hamacher Nonparametric

Dubois 0.399 1.000 1.000 0.001 0.001 0.001 0.009

Umano 1.000 0.004 0.036 1.000 1.000 1.000

Product sum 1.000 0.000 0.006 1.000 1.000

different thresholds (range = 0.71–0.90) via adjusted significance values.

1.000 0.000 0.004 1.000

Dombi 0.128 1.000 1.000 0.000 0.000 0.000 0.002 1.000

Table 4. The results of pairwise comparisons for weighted Fuzzy ID3 reasoning based on different T-operators with 20

Dubois 3.22 Asymptotic Sig. (2 sided test) 0.000

Algorithms Accuracy rate (%)

<sup>1</sup> 82.18

<sup>2</sup> 86.14

Hamacher (λ ¼ 0)

Product sum

Umano Dubois

<sup>3</sup> 86.14

C4.5 86.14 FuzzyID3\_reasoning with Weighted Product Sum\_Umano 86.14

FuzzyID3\_ reasoning with Weighted T-Operators T<sup>1</sup> & T<sup>∗</sup>

98 Potential of Essential Oils

FuzzyID3\_ reasoning with Weighted Product-Sum T<sup>2</sup> & T<sup>∗</sup>

Zadeh 3.02 Umano 6.40

Yager 3.55

Dombi 2.90

Weber 5.42

Hamacher 1.000 0.000 0.006

Yager 1.000 1.000

Zadeh 0.201

Non parametric Hamacher (λ ¼ 0)

FuzzyID3\_ reasoning with Weighted Non Parametric Hamacher (<sup>λ</sup> <sup>¼</sup> 0) <sup>T</sup><sup>3</sup> & <sup>T</sup><sup>∗</sup>

Table 2. The performance results of each algorithm for nonparametric operators [27].

Algorithm Rank Friedman aligned ranks

On the other hand, accuracy rates handled for different thresholds within weighted fuzzy reasoning method based on different T-operators are given in Table 6. It is seen that Umano


Table 5. Accuracy rates handled for different thresholds (%) unweighted fuzzy reasoning based on different T-operators.


fuzzy reasoning approach and Weber (λ ¼ 15) has the maximum value with 81.74% for weig-

A Fuzzy Rule Based Approach to Geographic Classification of Virgin Olive Oil Using T-Operators

http://dx.doi.org/10.5772/intechopen.79962

101

Geographical classification of olive oil is an important topic. This topic has crucial manner for the human health from past to present. In addition, this topic is the main topic for the traceability of designation of origin olive oil. In pioneer study, we were interested in geographic classification system of olive oil. In accordance of this paper, chemical measurements were used for the experimental study. Chemical measurements contain imprecise information. In order to deal with imprecise information, fuzzy ID3 classifier was selected for the classification of olive oil samples. In addition, fuzzy ID3 reasoning method based on T-operators has been suggested. We made the experiments for the performances of proposed fuzzy reasoning method in order to solve geographic classification problem. In this paper, we propose weighted fuzzy reasoning approach based T-operators. Three nonparametric operators [Product-Sum\_Umano, Product-Sum, and Nonparametric Hamacher (λ ¼ 0)] have the same performance value with handled from C4.5 algorithm. Yet, the accuracy handled with Zadeh T-operators is smaller value with 82.18%. Then, we have checked the performance of parametric operators. Statistical procedure was performed in order to detect statistical differences among a group of results for 20 threshold (θr) values. It is observed that there are significant differences among the results between unweighted and weighted fuzzy reasoning based approaches. It is seen that weighted fuzzy reasoning approach based on Umano 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%. So, we claim that by using different parameters and weights for each rule, we can

The authors would like to thank Erden Kantarcı for his valuable support and Mrs. Ummuhan

3 Institute of Control Systems, Azerbaijan National Academy of Sciences, Baku, Azerbaijan

Tibet and Dr. Aytac Gumuskesen for allowing us to use the data set.

\* and Efendi Nasibov2,3

1 Department of Econometrics, Kırklareli University, Kırklareli, Turkey

2 Department of Computer Science, Dokuz Eylul University, İzmir, Turkey

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

hted fuzzy reasoning approach.

handle better reasoning performances.

1

Acknowledgements

Author details

Suzan Kantarcı-Savaş

5. Conclusion

Maximum values are given as bold.

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

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 87.13% for θ<sup>r</sup> ¼ 0:84.

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

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 fuzzy reasoning approach and Weber (λ ¼ 15) has the maximum value with 81.74% for weighted fuzzy reasoning approach.

## 5. Conclusion

Geographical classification of olive oil is an important topic. This topic has crucial manner for the human health from past to present. In addition, this topic is the main topic for the traceability of designation of origin olive oil. In pioneer study, we were interested in geographic classification system of olive oil. In accordance of this paper, chemical measurements were used for the experimental study. Chemical measurements contain imprecise information. In order to deal with imprecise information, fuzzy ID3 classifier was selected for the classification of olive oil samples. In addition, fuzzy ID3 reasoning method based on T-operators has been suggested. We made the experiments for the performances of proposed fuzzy reasoning method in order to solve geographic classification problem. In this paper, we propose weighted fuzzy reasoning approach based T-operators. Three nonparametric operators [Product-Sum\_Umano, Product-Sum, and Nonparametric Hamacher (λ ¼ 0)] have the same performance value with handled from C4.5 algorithm. Yet, the accuracy handled with Zadeh T-operators is smaller value with 82.18%. Then, we have checked the performance of parametric operators. Statistical procedure was performed in order to detect statistical differences among a group of results for 20 threshold (θr) values. It is observed that there are significant differences among the results between unweighted and weighted fuzzy reasoning based approaches. It is seen that weighted fuzzy reasoning approach based on Umano 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%. So, we claim that by using different parameters and weights for each rule, we can handle better reasoning performances.
