<p>This article deals with a new solution procedure to solve a news vendor problem where the demand and cost parameters are assumed to be uncertain in nature. First of all, we develop a news vendor model where the total demand may or may not exceeds the order quantity. Basically, the demand function assumes a decreasing function over the unit selling price. Due to the market uncertainty (may be random or non-random) and nature of stock level with respect to the demand, the model itself has been split into two different sub-models and they are analysed under several uncertain environments. Considering all parameters random -fuzzy approximate reasoning, the model has been developed extensively. Initially, the model is solved in a traditional approach, then to find the best solution of the model, we further extend the model into non-linear stochastic programming problem and the problem of primal–dual model of fuzzy approximate reasoning via some evolutionary algorithms. For numerical computation and to validate the model, we consider a case study. Environmental cost is also computed to study the effect of total average system profit. Numerical study suggests that the dual cut approach provides the best optimum solution with respect to other methods whenever the demand gets value below the order quantity and the environmental cost varies with the items to be stocked. However, if the demand assumes greater than order quantity then the primal—dual cuts models give better results than other approaches. Indeed, sensitivity analysis and graphical illustrations are done for model justification. Finally, managerial insights, a concluding remark of the proposed study have been done followed by a scope of future work.</p>