Karim SORKHEH, Ahmad KAZEMIFARD, Shakiba RAJABPOOR

A comparative study of fuzzy linear regression and multiple linear regression in agricultural studies: a case study of lentil yield management

This study investigates the advantages of two fuzzy linear regression (FLR) models, namely the Tanaka and the Savic andPedrycz models, over multiple linear regression (MLR) for lentil yield management. We used a fuzzy approach to model the yieldof lentil genotypes in which the input is crisp and the output fuzzy. Moreover, after finding FLR equations, we estimated the outputcorresponding to the collection of fuzzy inputs by using fuzzy algebraic operations and an appropriate defuzzification method knownas the center of area method. Results showed the superiority of the Tanaka model over MLR because of reducing the included variables,especially variables available after harvest. The study also emphasizes the advantage of the Savic and Pedrycz model in comparison tothe other two models with a smaller error rate.

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Agresti A (1996). An Introduction to Categorical Data Analysis. New York, NY, USA: John Wiley & Sons, Inc.
Ayyub BM, Gupta MM (1997). Uncertainty Analysis in Engineering and Sciences: Fuzzy Logic, Statistics, and Neural Network Approach. Dordrecht, the Netherlands: Kluwer Academic.
Bardossy A (1990). Note on fuzzy regression. Fuzzy Set Syst 5: 65-75.
Bojadziev G (2007). Fuzzy Logic for Business, Finance, and Management (Vol. 23). Singapore: World Scientific.
Canan İ, Gündoğdu M, Seday U, Oluk CA, Karaşahin Z, Eroğlu EÇ, Yazıcı E, Ünlü M (2016). Determination of antioxidant, total phenolic, total carotenoid, lycopene, ascorbic acid, and sugar contents of Citrus species and mandarin hybrids. Turk J Agric For 40: 894-899.
Chang PT, Lee ES (1994). Fuzzy linear regression with spreads unrestricted in sign. Comp Math Appl 28: 61-70.
Diamond P, Korner R (1997). Extended fuzzy linear models and least squares estimates. Comput Math Appl 33: 15-32.
Ercisli S (2009). Apricot culture in Turkey. Sci Res Essays 4: 715-719.
Erturk Y, Ercisli S, Haznedar A, Cakmakci R (2010). Effects of plant growth promoting rhizobacteria (PGPR) on rooting and root growth of kiwifruit (Actinidia deliciosa) stem cuttings. Biol Res 43: 91-98.
Fortin JG, Anctil F, Parent LÉ, Bolinder MA (2010). A neural network experiment on the site-specific simulation of potato tuber growth in Eastern Canada. Comput Electron Agr 73: 126-132.
Hricova A, Fejer J, Libiakova G, Szabova M, Gazo J, Gajdosova A (2016). Characterization of phenotypic and nutritional properties of valuable Amaranthus cruentus L. mutants. Turk J Agric For 40: 761-771.
Huang Y, Lan Y, Thomson SJ, Fang A, Hoffmann WC, Lacey RE (2010). Development of soft computing and applications in agricultural and biological engineering. Comput Electron Agr 71: 107-127.
Ishibuchi H (1992). Fuzzy regression analysis. Fuzzy Theo Syst 4: 137-148.
Jiang P, Thelen KD (2004). Effect of soil and topographic properties on crop yield in a north-central corn-soybean cropping system. Agro J 96: 252-258.
Kitchen NR, Drummond ST, Lund ED, Sudduth KA, Buchleiter GW (2003). Soil electrical conductivity and topography related to yield for three contrasting soil-crop systems. Agro J 95: 483- 495.
Kravchenko AN, Bullock DG (2000). Correlation of corn and soybean grain yield with topography and soil properties. Agro J 92: 75-83.
Kutner M, Nachtsheim C, Neter J, Li W (2004). Applied Linear Statistical Models. 5th ed. New York, NY, USA: McGraw-Hill/ Irwin.
Mann KK, Schumann AW, Obreza TA (2011). Delineating productivity zones in a citrus grove using citrus production, tree growth and temporally stable soil data. Precis Agric 12: 457-472.
Ministry of Jihad-e-Agriculture of Iran (2014). Annual Agricultural Statistics. Tehran, Iran: Ministry of Jihad-e-Agriculture of Iran.
Ni Y (2005). Fuzzy Correlation and Regression Analysis. Norman, OK, USA: University of Oklahoma Graduate College.
Park SJ, Hwang CS, Vlek PLG (2005). Comparison of adaptive techniques to predict crop yield response under varying soil and land management conditions. Agri Syst 85: 59-81.
Peters G (1994). Fuzzy linear regression with fuzzy intervals. Fuzzy Sets Syst 63: 35-43.
Redden DT, Woodal WH (1994). Properties of certain fuzzy linear regression methods. Fuzzy sets Syst 64: 361-375.
Rousseeuw PJ, Van Alest S, Van Driessen K, Agulló J (2004). Robust multivariate regression. Technometrics 46: 293-305.
Savic D, Pedrycz W (1991). Evaluation of fuzzy regression models. Fuzzy Sets Syst 39: 51-63.
Shapiro AF (2005). Fuzzy Regression Models. State College, PA, USA: Pennsylvania State University.
Singh AK, Meena MK, Bharati RC, Gade RM (2013). Effect of sulphur and zinc management on yield, nutrient uptake, changes in soil fertility and economics in rice (Oryza sativa)–lentil (Lens culinaris) cropping system. Indian J Agri Sci 83: 344-348.
Taheri SM, Kelkinnama M (2012). Fuzzy linear regression based on least absolutes deviations. Iranian J Fuzzy Syst 9: 121-140.
Tanaka H, Uejima S, Asai K (1982). Linear regression analysis with fuzzy model. IEEE T Syst Man Cyb 12: 903-907.
Torres J, Rutherfurd SM, Muñoz LS, Peters M, Montoya CA (2016). The impact of heating and soaking on the in vitro enzymatic hydrolysis of protein varies in different species of tropical legumes. Food Chem 194: 377-382.
Wu HC (2003). Linear regression analysis for fuzzy input and output data using the extension principle. Comput Math Appl 45: 1849-1859.
Yazıcı K, Şahin A (2016). Characterization of pomegranate (Punica granatum L.) hybrids and their potential use in further breeding. Turk J Agric For 40: 813-824.
Yuan HY, Saha S, Vandenberg A, Bett KB (2017). Flowering and growth responses of cultivated lentil and wild lens germplasm toward the differences in red to far-red ratio and photosynthetically active radiation. Front Plant Sci 8: 386.
Zadeh LA (1965). Fuzzy sets. Information Control 8: 338-353.
Zadeh LA (1975a). The concept of linguistic variables and its application to approximate reasoning I. Inform Sciences 8: 199-249.
Zadeh LA (1975b). The concept of linguistic variables and its application to approximate reasoning II. Inform Sciences 8: 301-357.
Zadeh LA (1975c). The concept of linguistic variables and its application to approximate reasoning III. Inform Sciences 9: 43-80.