Grey Fractional Programming A New Experimental Approach in Sustainable Agriculture

Different approaches are used to explain sustainable agriculture. Grey programming is one of the approaches that has been used widely in this field. A new version of this method in the form of Fractional Fuzzy programming with and without multiple goals has been used in different fields. However, this method is not planned in the form of gray programming. In this study, first grey fractional programming is introduced and an application has been shown for cropping pattern in line with sustainable agriculture. Results showed that dry and rain fed wheat area in the region is between (7135/5, 17331/6) and (4702/6, 12687/2) acres, respectively. Also, dry and rain fed barely area are changed between (0, 1232/8) and (1032/3) acres, respectively. Upper bound of alfalfa and sugar beet area in sustainable pattern is 3804/3 and 1854, respectively that is less than the current cropping pattern and would cause profit reduction of the current pattern. Results showed that the sustainability index with respect to nitrate fertilizer in fractional programming case is in the range of grey fractional interval model and has improved than the current pattern. Also, the current area of wheat is in the range of sustainable agriculture.