Intuitionistic fuzzy approach in multi-objective optimization for KRBMC irrigation system, India

ABSTRACT

In the present study, a new optimization approach, intuitionistic fuzzy optimization (IFO), has been proposed for optimal cropping pattern in the Kakrapar Right Bank Main Canal command area of Ukai Kakrapar Water Resources Project in India. The IFO is an extension of the fuzzy optimization technique which considers, apart from the degree of acceptance, the degree of rejection and hesitation index as the performance measures of the model. The IFO multi-objective fuzzy linear programming (IFO MOFLP) solution for three objectives, i.e. maximization of net irrigation benefits, employment generation and cost of cultivation, with sets of constraints, resulted in the optimal cropping pattern in the command area with irrigation intensity of 76.92%. The results of IFO MOFLP have been found to be similar to multi-objective fuzzy linear programming (MOFLP), in terms of the irrigation intensity of command area. The MOFLP gave the overall degree of satisfaction ($\lambda$= 0.503) for the chosen command area; however, IFO MOFLP gives the additional parameters, i.e. degree of rejection, $\beta$= 0.282 and degree of hesitation, $\pi$= 0.215 with overall acceptance of $\alpha$= 0.503 for $S_f$(Scaling factor) = 0.3. The sensitivity of model parameters with scaling factor indicated that the degree of acceptance has been found to be fairly constant with $S_f$ while the degree of rejection and hesitation index have shown the contrasting trends with $S_f$.

KEYWORDS:

• Intuitionistic fuzzy set
• membership function
• non-membership function
• optimal irrigation planning
• Kakrapar Right Bank Main Canal

Notations

Table

Disclosure statement

No potential conflict of interest was reported by the authors.