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In this paper, we introduce a concept of a granular neural network and develop its comprehensive design process. The proposed granular network is formed on the basis of a given (numeric) neural network whose structure is augmented by the formation of granular connections (being realized as intervals) spanned over the numeric ones. Owing to its simplicity of the underlying processing, the interval connections become an appealing alternative of information granules to clarify the main idea. We introduce a concept of information granularity and its quantification (viewed as a level of information granularity). Being treated as an essential design asset, the assumed level of information granularity is distributed (allocated) among the connections of the network in several different ways so that certain performance index becomes maximized. Due to the high dimensionality nature of some protocols of allocation of information granularity and the nature of the allocation process itself, single-objective versions of particle swarm optimization is considered a suitable optimization vehicle. As we are concerned with the granular output of the network, which has to be evaluated with regard to the numeric target of data, two criteria are considered; namely, coverage of numeric data and specificity of information granules (intervals). A series of numeric studies completed for synthetic data and data coming from the machine learning and StatLib repositories provide a useful insight into the effectiveness of the proposed algorithm.