The problem of city garbage disposal was investigated under an environment of polymorphic uncertainty. In some settings, a class of management of solid garbage disposal was formulated as an interval fuzzy optimization model. Possibility degree operator for the order of interval numbers was firstly defined in axiomatic method, and for given weight coefficients and confidence levels, a deterministic equivalent formulation for the original model was obtained on the basis of such a definition. Then the problem was solved in the ordinary linear programming method. The model and the solution method were applied into a practical management problem, and the results indicate that the model and the solution method are effective.