A multi-objective, multi-item fuzzy stochastic inventory model is constructed for deteriorating items under limited storage space as well as capital investment. Demand is considered as a function of price and frequency of advertisements. In this model, some parameters are considered to be vague and some are random. The vagueness of parameters is represented by membership function, and randomness of parameters is represented by a probability distribution. In the inventory model, if some parameters are vague and some are probabilistic, then the model is called a fuzzy stochastic model. Here, parameters such as purchasing cost, shortage costs as well as a capital investment are considered to be random in nature and storage space is considered as imprecise. The randomness of a parameter is represented by a normal distribution, and the impreciseness of parameters is expressed using linear membership function. By using fuzzy nonlinear programming (FNLP) and intuitionistic fuzzy optimization (IFO) techniques, a solution for the multi-objective fuzzy stochastic inventory model is obtained. The major goal of the paper is to find an optimal quantity to be replenished. The objective of this work is to study the effect of capital investment and warehouse space on profit as well as shortage cost through sensitivity analysis. The other objective is to compare the efficiency of FNLP and IFO techniques for obtaining solutions through numerical results. This paper shows that FNLP works better than IFO in case of minimizing shortage cost.