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Equity principles are embedded within a multiple objective framework for obtaining optimal solutions to a generic allocation problem, such as the fair distribution of water, energy, or other types of key resources among users in society. Because of the great import of fresh water as a scarce and diminishing resource within and among many nations of the world, the equity concepts are used in the allocation of water rights and subsequent water transfers or trades among users to improve the economic efficiency of water utilization. More specifically, water allocation is formulated as a generalized multiple objective problem and then the measurable fairness principles are used in the development of two approaches for equitable water rights allocation. In particular, the proposed priority-based maximal multiperiod network flow programming method has a social aggregation function satisfying the monotonicity and priority principles, and thus is a priority equitable allocation approach. The lexicographic minimax water shortage ratios method, which satisfies the principles of monotonicity, impartiality, and equitability, generates perfectly equitable solutions. The priority ranks and weights used in the two proposed approaches, respectively, are designed to achieve fair treatment of all the competitors for access to limited water resources and constitute important parameters. The capabilities of the approaches are tested and demonstrated in applications to the Aral Sea Basin in Central Asia and the South Saskatchewan River Basin in Western Canada.