In real situations, it is often too restrictive and difficult for experts to give precise (crisp) assessments for parameters such as inflation. This would become more serious especially for some international exporters or other companies in some pendulous situations. To deal with these situations, this paper develops a dependence-based evidential reasoning approach. This study employs the effects of imperfect production process for deteriorating/ameliorating products, considering inspection in an inflationary inventory system with time dependent demand rate. Different from the previous studies, which considered inflation rate as constant and well-known, stochastic or fuzzy, this model involves inflation with uncertainty of belief structure type. A genetic algorithm is adopted, which deals with interval parameters, and a numerical example is provided to illustrate how the proposed algorithm will be performed and the results indicate that the performance of the proposed algorithm is superior to that of a heuristic approach.