Closed-loop supply chain (CLSC) is a prominent concept emphasizing on both economic and environmental aspects. Since a CLSC comprises of forward and reverse supply chains, there are a variety of internal and external factors associated with its total expected profit. In a forward flow, volatility in transportation cost, holding cost, and forecasting the market's demand are the most challenging issues for decision makers, while determining the rate of returned products and efficiency in recycling the returned products are crucial parameters to predict in reverse flow. In this paper, it is aimed to develop and apply a fully fuzzy programming (FFP) method to determine the possible upper, middle, and lower ranges of profit for a multi-echelon battery CLSC with multi-components, multi-product in multi-period under imprecise information. In addition, we extend the proposed model to multi-objective to consider the green factors related to plants and battery recovery centers. Fuzzy analytic network process (Fuzzy ANP) is utilized to alter the qualitative measurements to the measurable parameters. Then, distance technique and ε-constraint method are utilized for solving the multi-objective problem. We illustrate the application of the model in Vancouver, Canada using maps.