In many respects, water resources allocation problems have fuzzy characteristics owing to uncertainty and imprecision not only as numerical data but also as linguistic data, in addition to the political nature of resource allocation. All classical techniques require numerical data and cannot treat linguistic data, but fuzzy inference systems (FIS) can deal with both types of data. Hence, it is suitable to reflect the dynamic nature of country benefits, reflective variations in the main drainage and subdrainage basin flows, and various system parameters in search of a coalition among a few riparian countries. The size of core, which is generated from a series of linear programming (LP) optimization models and game theory concepts, shows the potential extra benefit advantage of being in grand coalition to all parties, but it does not provide a sufficient condition to assemble a robust coalition unless an agreeable allocation scheme or principle is provided. In this respect, there is a fuzzy link between being in the grand coalition and percentage share received from a core. Hence, a proper FIS is proposed, and the necessary steps are developed with the Shapley value and the core as game theory methods, which provide a methodological base in the evaluation of possible allocation schemes among the parties. The application of the methodology is presented to search for coalition possibilities among the riparian countries: Turkey, Syria, and Iraq. Basic results are generated over the application of the Inter-Temporal Euphrates and Tigris River Basin Model, which is an optimization model for the allocation of scarce water resources considering agricultural and urban uses, energy generation, and conveyance costs in the Euphrates-Tigris basin.