<p>A joint replenishment problem (JRP) considering multiple types of uncertainties and carbon emission cost under a carbon cap-and-trade policy is studied in this paper. In particular, a novel fuzzy JRP is primarily formulated, in which the influences on the budget control arising from uncertainties of product defective rate and fuzzy cost parameters, and the carbon emission during the replenishment are for the first time taken into account simultaneously. Accordingly, a fuzzy dependent-chance programming (DCP) with the aim of maximizing the credibility of budget control is constructed. Following that, improved hybrid intelligent algorithms named BIS-DE and Exact-DE are designed to solve the proposed novel fuzzy JRP efficiently by employing the bisection fuzzy simulation method and the differential evolution algorithm. Furthermore, based on advanced inverse operational laws, the novel fuzzy DCP model is transformed into an equivalent deterministic counterpart which could be solved with the intelligent algorithm without any simulation process. The effectiveness and superiority of both treatments for the novel fuzzy JRP are illustrated by performing numerical experiments and sufficient comparisons.</p>