Using adaptive neuro‐fuzzy inference system and multiple linear regression to estimate orange taste

Abstract In this research, some characteristic qualities of orange fruits such as vitamin C and acid content; weight; fruit and skin diameter; and red (R), green (G), and blue (B) values of the RGB color model for 70 samples were used to predict the taste of orange grown in Darab, southeast of Fars Province, Iran, by multiple linear regression (MLR) and adaptive neuro‐fuzzy inference system (ANFIS). To use MLR, firstly the most important input data were selected, and then, the best model to predict the taste of orange was applied. In this research, methodology of ANFIS consisted of selection of dependent orange taste, fuzzification, fuzzy inference rule, membership function, and defuzzification process. The predictive capability of these models was evaluated by various descriptive statistical indicators such as mean square error (MSE) and determination coefficient (R 2). The results showed that the prediction performance of the MLR model has a strong significant relationship between orange taste and vitamin C (0.897**), red color (0.901**), and blue color (0.713*). Also, the results of ANFIS model showed that with low error for train and check data increased the most accuracy for prediction of orange taste. Moreover, the results indicated that the success rate of taste determination for orange is higher by using ANFIS compared to the MLR. This research was to provide valuable information for orange taste.


| Data
In order to predict orange taste, these parameters (acid, fruit weight, vitamin C, fruit diameter, skin diameter, red, green, and blue values of the RGB color) from 70 samples in different months were measured in Darab gardens, Fars Province, Iran. The summaries of them are shown in Table 1. For measurement of vitamin C and acid was used titration method. For weight were applied GF-3000 model digital scales. Fruit diameter and skin diameter were measured by S-R 400 model digital coliseum. Finally, by using MATLAB software, orange images were converted to a matrix.

| Multiple regression models
The general aim of multiple regressions is to determine the relationship between independent (vitamin C, acid, weight, fruit and skin diameter, red [R], green [G], and blue [B]) and dependent (orange taste) parameters for the investigation of designated goal. The regression equations were computed based on Equation 1: where M is the dependent variable, S 0 is the intercept, S 1 … bn are regression coefficients, and X 1 -X n are independent factors referring to basic orange characteristics.
The ANFIS is one of the ANN models that is a combination of fuzzy systems and ANN. The stage of ANFIS method is shown in To forecast fuzzy rules, for eight inputs, a typical rule set with eight fuzzy rules and eight membership functions (MF) can be expressed as follows (Bui, Bui, Zou, Van Doan, & Revhaug, 2017): where x 1 , x 2 , … x n are inputs; f j (j = 1 n) are output.
For definition, membership function was used as Gaussian function. The Gaussian function is distinguished using the central value m and a standard deviation k more than 0. The membership function is shown in the following: where m and k are arbitrary real constants. The membership function of Gaussian function shows that in Figure 3.
Membership function for eight input data and the rules are shown in the following: The normalized firing strength (N) is computed in j-th node of this layer. Moreover, the overall output (µ) obtained by ANFIS method is calculated in this layer.
In total, ANNs consist of computing the outputs, compare the outputs with the desired target values, adjust the weights, and repeat the process.
One of the most widely used algorithms in the field of orange taste properties is the basic backpropagation, FCM, and hybrid (4)

| Network design
The ANFIS used in the study contains an eight-layer feedforward neural network and implements TS (Takagi Sugeno) fuzzy inference system for a systematic method to making fuzzy rules from a given

| Performance evaluation criteria
For determination of the precision of the forecasting capacity of the models, mean square error (MSE) and the coefficient (R 2 ) were used that can be calculated using Equations 7 and 8: In Equations 7 and 8, T depicts the number of data, y i is the desired output, and ŷ i is the predicted output.

| Orange analysis
In order to predict orange taste, 70 samples in different months were used (Figure 4). In addition, 70% of the whole data were used for training procedure, while it is 30% to test the obtained results (Tables 2 and 3).

| Relationships between orange variables
The calculated R between orange taste and independent variables was investigated by means of SPSS V.22 software that are shown in Table 4. It was found that there was a positive and highly significant correlation between taste and vitamin C (0.897 ** ), red color (0.901 ** ), and blue color (0.713 * ) content.
(7)  The results of them showed that the ANFIS method was suitable to predict fruit quality.

| CON CLUS ION
In this research, an attempt was made to predict the taste of or-

ACK N OWLED G M ENT
The authors would like to thank Shiraz University for providing financial support (238726-121) for this study.

CO N FLI C T O F I NTE R E S T
The authors declare that they have no competing interests.

E TH I C A L A PPROVA L
Not applicable.

CO N S E NT FO R PU B LI C ATI O N
Not applicable.

I N FO R M E D CO N S E NT
Written informed consent was obtained from all study participants.

DATA AVA I L A B I L I T Y S TAT E M E N T
The datasets used and analyzed during the current study are available from the corresponding author on reasonable request.