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Based on a large number of multi-attribute decision making problems with interval numbers in the social economy and engineering system, this paper defines and analyses the basic operation rules of interval numbers, standardized methods, sequence comparison strategy, interval number distance and the formulas of interval number sequence distance. It also gives the decision making model of weighted gray relational analysis(GRA) based on interval number operation rule, then this model solves many key problems, such as the solution of standardized matrix in the decision making system, the selection of reference sequence, and the calculation of gray relational coefficient with interval numbers. The model improves the insufficiency of weighted GRA which only applies to real number type primitive attribute matrix, and improves the effectiveness, practicability and the adapting surface. Besides, the optimized location of the fire station can be solved well by this model. The decision making model of weighted gray relational analysis based on interval number operation rule provides a scientific, practical ways and means to solve the multi-objective decision making problems with interval number.