Comparison of Applying Uncertainty Theory and Probability Theory in Calculating Uncertainty Measures of Revenue of Major Crops in Sari Goharbaran

Document Type : Research Article

Authors

• F. Kashiri Kolaei ¹
• S.A. Hosseini Yekani ²
• S.M. Mojaverian ²

¹ Sari University of Agricultural Sciences and Natural Resources, Sari. Sari. Iran

² Department of Agricultural Economics, Sari University of Agricultural Sciences and Natural Resources, Sari, Iran

https://doi.org/10.22067/jead2.vi0.82584

Abstract

Introduction: Selecting suitable crops for cultivation in a non-certain environment is considered as an important management topic in the agricultural sector. Despite the multiple application of probability theory in quantifying uncertainty in the form of risk programming, validity of this theory depends on the existence of frequency for uncertain variable. For events that cannot be measured by frequency, the only solution is to use subjective judgment of persons in the domain field rather than historical data. Some experts have mistakenly considered subjective judgmentl as a subjective probability and thus used the probability theory to quantify subjective judgmental. But based on existing evidence, the quantification of subjective judgment should be carried out in another theory called the uncertainty theory. In uncertainty theory, in addition to using the belief degree rather than frequency for calculating mathematical moments, the expected value of multiplicative variables will be different with their corresponding relations in the probability theory. Considering these conditions and having in mind that the agricultural sector is always faced with uncertain variables such as price of crops and weather conditions like rainfall, in this study the revenue uncertainty measures of major crops in the Goharbaran region of Sari have been calculated and compared. There are different measures for uncertainty, which in the present study variance and Tail Value at Risk (TVaR) have been used.
Materials and Methods: The first step in the application of the uncertainty theory is the elicitation of the belief degree or subjective judgments of the farmers about the crop's price and rainfall during the crop season. To elicit the uncertainty distribution of these variables based on the subjective judgments of farmers, 120 farmers were randomly selected in 2018. After eliciting the farmers' beliefs about uncertain rainfall and prices in the cdf method, it was necessary to select the number of belief degree which current practice was based on previous studies in this field. After calculating the above subjective judgments, while assuming linear, zigzag, normal and normal forms for uncertainty distribution, the parameters of each function were calculated using the least squares method. Among the forms of uncertainty distribution functions, the best form of the uncertainty distribution for each crop's price and rainfall was selected by comparing the RMSE indexes. Subsequently, by calculating a causal relationship between rainfall and crop yield, inverse uncertainty distribution of yield was also extracted. Given the inverse uncertainty distribution functions of crop price and yield, required parameters such as expected revenue, variance and TVaR of revenue at 95% confidence were calculated based on operational laws of uncertainty theory and probability theory. Eviews and Matlab software were used to estimate the yield response function and the uncertainty distribution functions, respectively.
Results and Discussion: In this study, after collecting the belief degree of farmers in the studied area about different levels of price and rainfall, three groups of comprehensive beliefs about prices and rainfall were determined by goodness of fit test. Then, according to the relationship between crop yield and rainfall, the inverse function uncertainty distribution is also calculated. With the uncertainty distribution function of crops price and yield, the expected revenue, variance (standard deviation) and TVaR measure for revenue per hectare of crops were calculated and compared with the uncertainty theory as well as probability theory. Based on the results of this study, the amount of the above measures varied in different belief degree groups,    which is due to differences in the uncertainty distribution parameters. Also, based on the results of this study in all groups of beliefs for all crops, the probability theory compared to the uncertainty theory has estimated the variance approximately more than 30% less, which is a significant result. In other words, applying probability theory to belief modeling will lead to erroneous and misleading results. In the case of the TVaR measure in binary multiplicative variable conditions, the use of probability theory and uncertainty theory in calculating TVaR does not yield conflicting results.
Conclusion: The purpose of this study was to compare the results of applying probability theory for modeling belief degree rather than uncertainty theory in order to illustrate the necessity of using uncertainty theory in belief degree modeling. Studying the effect of probability theory in modeling the belief degree also suggests that the application of probability theory in the presence of two uncertain variables has no significant effect on expected values and TVaR but has a significant effect on variance size. Based on the results of the present study, assuming the binary multiplicative variable, in calculating higher mathematical moments such as variance, the results of probability theory and uncertainty theory make a considerable difference. This demonstrates the need to promote the uncertainty theory in belief degree modeling. In other words, basic training in the belief degree modeling method should be considered.

Keywords

• Belief degree
• Price
• Rainfall
• Uncertainty
• Yield

20.1001.1.20084722.1399.34.1.4.7

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