Abstract

Background: Uncertainty is a common factor in every real-life decision-making problem. Possibility theory is one uncertainty theory in Fuzzy sets (FS). The possibility-based decision-making under a fuzzy environment is a significant multi-criteria decision-making (MCDM) method.

Methods: A bipolar FS is an extension of a fuzzy set. With the bipolarity concept, we can handle both positive and negative thoughts. In this study, we have provided a possibility mean of a bipolar fuzzy number. We have developed a ranking method for bipolar fuzzy numbers using this possibility concept. A novel possibility MCDM method is suggested for solving the water resources management (WRM) in the Nagpur area, Maharashtra State, India.

Results: The MCDM technique is an effective tool for solving WRM problems in an area. Many uncertainties and bipolarities occur together in the Nagpur water resources systems. WRM technique with fuzzy is one approach that can be used to solve the area's water problem. We have used the proposed MCDM to address the water-related issues of this district. With this proposed MCDM method, numerically, we employed water resource problems under a bipolar fuzzy environment.

Conclusion: The Nagpur area is covered by Basaltic rock and faces water shortage. The district is experiencing severe water shortages. Groundwater, surface water, and rainfall are three water resources considered as alternatives. According to the proposed MCDM technique in Nagpur district, Groundwater is the best water source from three flanks: quality of water, affordability, and availability.

Keywords: Possibility theory, bipolar fuzzy number, MCDM, water resource management, basaltic rock, geological formation.