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A multi-objective inventory models of deteriorating items have been developed with Weibull rate of decay allowing shortages, in which demand is taken as a function of time and production is proportional to demand rate. Here objectives are to maximize the profit from different items with space constraint on infinite planning horizon for nonintegrated and integrated business. Objectives are also made fuzzy in nature for non-integrated business. The compromised solutions of the optimization problem are obtained by the application of Zimmermann's technique and Fuzzy Additive Goal Programming technique. Crisp and fuzzy weights are used to incorporate the relative importance of the objective and constraint goals. The models are illustrated numerically and the results of those models each with crisp and fuzzy weights are compared. The results for the model assuming them to be Single House Integrated Business (SHIB) are obtained by using Generalized Reduced Gradient method. The costs like cost per unit items, holding costs, set up costs, shortage costs, selling prices are taken in fuzzy environment as triangular fuzzy numbers and trapezoidal fuzzy numbers also. When costs are imprecise, optimistic and pessimistic equivalent of fuzzy objective function is obtained by using credibility measure of fuzzy event by taking fuzzy expectation. The problems have been solved by formulating them as a single objective with fuzzy costs. The results of fuzzy SHIB model is illustrated with numerical example and those are compared with the best possible solution of the non-integrated business.

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