Multi-objective optimization of the KRBMC irrigation system using intuitionistic fuzzy approach with non-linear membership functions

In the present study, a novel optimization framework is developed by integrating non-linear membership and non-membership functions within an Intuitionistic Fuzzy Optimization-based Multi-Objective Fuzzy Linear Programming (IFO MOFLP) model for irrigation planning. The framework is applied to the Kakrapar Right Bank Main Canal (KRBMC) command area of the Ukai -Kakrapar Water Resources Project, Gujarat, India. Unlike conventional fuzzy optimization, the IFO approach incorporates the degree of acceptance, rejection, and hesitation, improving decision quality under uncertainty. The model considers three objectives: (i) maximization of net irrigation benefits, (ii) maximization of employment generation, and (iii) minimization of cultivation cost, subject to constraints. This study demonstrates, for the first time, the applicability of non-linear membership and non-membership functions in a real-world water resources system. For a selected scaling factor of 0.33, the corresponding acceptance, rejection, and hesitation values were 0.503, 0.282, and 0.215. Under these conditions, the model achieved a net irrigation benefit of Rs. 3585.05 million, employment generation of 10,189.21 thousand man-days, and a cultivation cost of Rs. 2260.13 million, with an irrigation intensity of 76.92%. The results indicate that the non-linear IFO MOFLP framework provides balanced crop allocation and effectively handles conflicting objectives under uncertainty.