Multi-Objective Fuzzy Probabilistic Programming Approach for Obtaining Optimum Crops Pattern with Water Replenishment

This research paper is concerned with the solution procedure of a multi-objective fuzzy probabilistic problem (MOFPP), taking different crop patterns as the objective functions and water requirements of crops as constraints, which is then solved using fuzzy programming technique. In order to handle fuzzy probabilistic constraints, a transformation technique is developed for fuzzy uniform distribution. As the study area receives less rainfall, the cultivation is mainly dependent on irrigation water. A continual use of underground water for irrigation led to a substantial decrease in the water level of the surrounding area. So, to uplift the underground water level, a proper selection of crops can play a vital role in the replenishment of underground water without compensating the farmer’s income. To illustrate the above technique, a case study is provided with the cultivated area of different crops as a decision variable. The two objective functions are taken as the yield of crops taken as fuzzy number and profit obtained by the farmers after selling the products. A comparison table is furnished in the result section for making better decisions. The study reveals that planting a combination of beans, bitter-gourd, and cabbages will yield maximum profit.