عنوان مقاله [English]
نویسندگان [English]چکیده [English]
Introduction: Social, technical and economic factors in addition to environmental, soil and climate factors affect crop yield and cultivation. This study was implemented to know the impact of age, experience and literacy level of farmers as social factors and access to water supply, roads, silo, labor, tractors and machinery and conservation tillage as technical-mechanization factors on crop yield. Fuzzy rule-based inference system converts the complex decision-making problems to the smaller criteria and makes easier the multi-criteria evaluation process. So we decided to use fuzzy approach to modeling the social and technical-mechanization indices. The main disadvantage of fuzzy systems is their inability to learn. So, the optimization of fuzzy systems is the most important step in its implementation. Genetic algorithm (GA) approach is used as a complementation of fuzzy model to optimize fuzzy rules. One method to optimize the fuzzy rules is Pittsburgh method in GA. In this method, one gene is used for every rule and the gene value finds out the rule.The kind of membership function will have a great impact on the result. The kinds of membership function for fuzzy sets involve triangular, trapezoidal, generalized bell, Gaussian, Gaussian combination, Sigmoidal, product of two sigmoidal, difference between two sigmoidal, Π, Z and S shapes. The objectives of this study are: 1- providing two fuzzy models for the social and technical-mechanization indices for wheat production 2- optimizing the fuzzy rules and the type of membership function for the fuzzy set.
Materials and Methods: Fuzzy toolbox of MATLAB software ver. 7.8.0 (R2009a) was used to design fuzzy model. Fuzzy inference system (FIS) used in this study was Mamdani type that is based on if-then rules. The age, experience and literacy level of farmers were selected as input data for fuzzy social model. Access to water supply, roads, silage, labor, tractors and machinery and conservation tillage equipment were selected as input data for fuzzy technical-mechanization model. Mamdani fuzzy inference system was used to design models. Fuzzy rules were written by a mechanization expert knowledge. To correct written rules, the method of Pittsburgh in GA was used to optimize the fuzzy rules for all FISs. Then, a program was written in MATLAB software to get the best combination of membership functions to achieve the best result. The program tested 24 kinds of combined membership functions for medial and side fuzzy sets of input variables. The result was the best when the relationship between obtained index and crop yield had the highest value of the correlation coefficient (R2), minimum value of mean square error (MSE) and mean absolute error (MAE). So the fuzzy-GA model will produce the social and technical-mechanization indices while the fuzzy rules of model have been optimized and the best combination of membership functions has been selected.
Results and Discussion: The coefficients of determination were obtained 0.11 for fuzzy social model and 0.51 for technical-mechanization model before optimization of fuzzy rules. The error of fitness function decreased with rising generation numbers of GA until the best answer was obtained. After optimization of fuzzy rules by genetic algorithm, these values increased to 0.50 and 0.71 for the fuzzy social and technical-mechanization models, respectively. This result showed that optimizing the fuzzy rules had a significant impact on results of models. After implementation of the written program, to select the best type of membership functions for fuzzy input variables, coefficient of determination varied from 0.14 to 0.51 and 0.1 to 0.73 for the fuzzy social and technical- mechanization models, respectively. This result showed that the effect of social factors on wheat yield was less than technical-mechanization factors and yield can be predicted by technical-mechanization factors with more accuracy than social factors.
In the social model for input of experience, the lowest MSE and the highest R2 belong to a FIS with three fuzzy sets and S, Π and Z-shaped membership functions for the right, medial and left fuzzy sets, respectively. In the technical model for input of road availability, the lowest MSE and the highest R2 belong to a FIS with three fuzzy sets and s, trapezoid and z- shaped membership functions for the right, medial and left fuzzy sets, respectively. These results showed that the type of membership functions for fuzzy sets had considerable importance for the accuracy of the model.
Conclusion: It can be concluded that the accuracy of the fuzzy model with optimized rules by GA and the best type of membership function for fuzzy sets are considerable. Effect of technical-mechanization factors on wheat yield was more than social factors. This result also showed the strength of fuzzy–GA method in modeling of such issues.