Purulia district in West Bengal, India, is a well-known drought-prone area. Farmers of the area suffer a lot the whole year and could not plant the crops due to the poor water resources management. During the summer season, the situation becomes worst. Water resource management (WRM) is a potential method to address the available water resources for the district. In this paper, we have developed a multi-criterion water resource management technique for defining available water resources in agriculture. We have introduced a novel ranking method of generalized single-valued non-linear bipolar neutrosophic numbers based on possibility measures. Additionally, we have first defined the possibilistic mean of generalized single-valued non-linear bipolar neutrosophic number. Using the possibilistic mean, we have invented the positive and negative rank expositor for authenticity, hesitate, and falsity membership functions. In the present situation, water resource management in agriculture has become a big problem worldwide. Multi-criteria decision-making (MCDM) technique is necessary for developing this situation. Using the proposed multi-criteria decision-making (MCDM) method, we have solved a real water resource management problem in the Purulia district under GSVnTbN-environment. In this decision-making problem, we have considered the GSVnTbN-environment. Because during the summertime, water demand is very high, and groundwater level declines. At the end of summer, water demand is deficient in the agriculture field of the Purulia district. Sometimes the monsoon season, rainwater does not occur entirely. Even rainfall is uneven over the district. At that time, monsoon crop planting was tough in the agriculture field. So, this district's water scarcity nature is of a non-linear and uncertain type of nature. Therefore, we proposed an MCDM method for water resource management problems under GSVnTbN-environment.
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