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Groundwater resources have become the main resources for water supply due to the unavailability of surface water in arid zones. Arid zone’s damage to groundwater resources will have a high impact on human life in arid zones comparing to other regions. Due to the lack of surface water resources in these arid zones, groundwater is used as a resource for drinking and sanitation purposes due to the lack of surface water resources in these arid zones. Water desalination facilities are set up in locations where there is both sufficient amount of water (quantitative criteria) and the extracted water has adequate quality (qualitative criteria). Therefore, an optimization model should be used to locate optimal places for water desalination facilities. Multi-criteria decision-making models are mathematical techniques that, by using the geographic information system, are able to evaluate the options under complicated and indefinite geographic conditions. This research prepares information and factor maps to assign weights to qualitative water maps which were combined in the form of an inductive network. Therefore, by employing the concept of fuzzy fusion models, this article presents a method for solving multi-criteria geographically-indeterminate problems, and finally finds an appropriate location for the construction of a water desalination system in the desert region of Birjand in Iran.