با همکاری انجمن اقتصاد کشاورزی ایران

نوع مقاله : مقالات پژوهشی

نویسندگان

1 دانشگاه علوم کشاورزی و منابع طبیعی ساری، ساری، ایران

2 گروه اقتصاد کشاورزی، دانشگاه علوم کشاورزی و منابع طبیعی ساری، ساری، ایران

چکیده

با وجود اینکه فعالیت در بخش کشاورزی توأم با عدم حتمیت می­باشد، مدل­سازی مناسبی برای سنجش عدم­حتمیت­های این بخش صورت نگرفته است. سنجش عدم حتمیت در درجه اول مستلزم استخراج درجه باور بوده و در درجه دوم، استفاده از تئوری عدم حتمیت در مدل­سازی آن ضروری به­نظر می­رسد. در مطالعه حاضر به­منظور شناسایی لزوم به­کارگیری تئوری عدم حتمیت به جای تئوری احتمال در کمی­سازی درجه باور، محاسبه سنجه­های عدم حتمیت همچون واریانس و ارزش در معرض خطر دنباله­دار برای درآمد غیرحتمی محصولات زراعی عمده، در منطقه گهرباران ساری مدنظر قرار داده شد. درآمد غیرحتمی نیز از حاصلضرب دو متغیر غیرحتمی قیمت و عملکرد محاسبه شد. نتایج حاکی از آن بود که علی­رغم اختلاف ناچیز ارزش در معرض خطر دنباله­دار محاسبه شده در تئوری احتمال و تئوری عدم حتمیت، میزان واریانس بیش از 30 درصد در تئوری احتمال نسبت به تئوری عدم حتمیت، کمتر سنجیده شده است. این نتیجه لزوم ترویج تئوری عدم حتمیت را در مدل­سازی درجه باور نمایان می­سازد.

کلیدواژه‌ها

عنوان مقاله [English]

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

نویسندگان [English]

  • 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

چکیده [English]

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.

کلیدواژه‌ها [English]

  • Belief degree
  • Price
  • Rainfall
  • Uncertainty
  • Yield
  1. Abdolahi Ezzatabadi M., and Bakhshoodeh M. 2007. Investigation of the possibility of using area yield agricultural insurance in Iran: A case study of pistachio. Scientific Journal of Agriculture 30(1): 37-50. (In Persian with English abstract)
  2. Agricultural Jihad Service Center of Goharbaran, 2017. (In Persian with English abstract)
  3. Alvanchi M., Mahmoud Sabouhi Sabouni M., and Rastegaripour F. 2011. Determination of agricultural programming in Fars Province using utility-efficient programming approach. Agricultural Economics 5(4): 89-106.
  4. Artzner Ph., Delbaen F., Eber J.M., and Heath D. 1997. Thinking coherently. Risk 10: 68–71.
  5. Chen L. Peng J. Zhang B. and Rosyida I. 2016. Diversified models for portfolio selection based on uncertain semivariance. International Journal of Systems Science 48(3): 1-11.
  6. Chirima J., and Matete C. 2018. On uncertain programming and the farm planning problem. Scholars Journal of Physics, Mathematics and Statistics 5(2): 124-129.
  7. Cochran C.B. 1977. Sampling techniques. John Wiley, New York.
  8. Dalman H. 2016. Uncertain programming model for multi-item solid transportation problem. International Journal of Machine Learning and Cybernetics 1-9.
  9. Hazell P.B.R. 1990. The proper functioning of agricultural insurance in developing countries In: Agricultural insurance in Asia (APO), Mohsen, H. Translation. Agricultural Economic, Planning and Research Development center 47-67.
  10. Hesamian G., Peng Z., and Chen X. 2011. Goodness of fit test: A hypothesis test in uncertain statistics. Proceedings of the Twelfth Asia Pacific Industrial Engineering and Management Systems Conference, Beijing, China, October 14-16, 978-982.
  11. Holly S., and Hughes Hallett A. 1991. Optimal control, expectation and uncertainty. The Economic Journal 101(407): 976-978.
  12. Huang X., and Zhao T. 2014. Mean-chance model for portfolio selection based on uncertain measure. Insurance, Mathematics and Economics 59: 243–250.
  13. Huang X. 2011. Mean-risk model for uncertain portfolio selection. Fuzzy Optimization and Decision Making 10: 71–89.
  14. Kahneman D., and Tversky A. 1979. Prospect theory: An analysis of decision under risk. Econometrica 47: 263–292.
  15. Kay R.D. 2012. Farm Management, translated by Arslanbad, M. R., Urmia University Press. (In Persian with English abstract)
  16. Liu B. 2007. Uncertainty Theory. 2nd edn, Springer-Verlag, Berlin.
  17. Liu B. 2009. Some research problems in uncertainty theory. Journal of Uncertain Systems 3(1): 3-10.
  18. Liu B. 2015. Uncertainty theory. 5th Edition, Springer-Verlag Berlin.
  19. Liu J., Li Y.P., Huang G.H., Zhuang X.W., and Fu H.Y. 2017. Assessment of uncertainty effects on crop planning and irrigation water supply using a Monte Carlo simulation based dual-interval stochastic programming method. Journal of Cleaner Production 149: 945-967
  20. Moschini G., and Hennessy D.A. 2001. Uncertainty, risk aversion, and risk management for agricultural producers. In Gardner, B.L. and Rausser, G.C., Eds., Handbook of Agricultural Economics, 1, Elsevier 88-153.
  21. Peng J. 2013. Risk metrics of loss function for uncertain system. Fuzzy Optimization and Decision Making 12(1): 53-64.
  22. Shaik S., Coble K.H., Knight T.O., Baquet A.E., and Patrick G.F. 2008. Crop revenue and yield insurance demand: A subjective probability approach. Journal of Agricultural and Applied Economics 40(3): 757–766.
  23. Torkamani J. 2006. Measuring and incorporating farmers’ personal beliefs and preferences about uncertain events in decision analysis: A stochastic programming experiment. Indian Journal of Agricultural Economics 61(2): 185-199.
  24. Yao K. 2015. A formula to calculate the variance of uncertain variable. Soft Computing 19(10): 2947–2953.
  25. Zarakani F., Chizari A., and Kamali G. 2014. The effect of climate change on the economy of rain fed wheat (a case study in Northern Khorasan). Journal of Agroecology 6(2): 301-310. (In Persian with English abstract)
CAPTCHA Image