Considering the image processing field, neural networks in all of their forms have become state-of-the-art due to their universality and ability to discover semantic features of images. On the other hand, their long training times and non-interpretability of results have been neglected over the years. Moreover, neural networks are still limited by the requirement of a reasonably big dataset. In our work, we are focusing on the problem of extending a dataset. This is done by enriching the original data by adding new information, which cannot be extracted by the network itself. The enriching is based on substituting a standard image representation by a new one, called Image Represented by a Fuzzy Function, which replaces original crisp values of pixel intensities by a fuzzy sets given by their triangular membership function. The membership function for a certain pixel is established from intensities of the spatial neighborhood of the given pixel, which is motivated by the center-surrounding mechanism and by modeling the absolute intensity contrast, used for handling visual saliency. Based on the benchmarks, we show that such new representation can increase the accuracy of the network by providing, otherwise unavailable, information. The another added value is that the new representation is realized as a preprocessing and does not require a modification of neural network architecture and so can be easily integrated into existing networks.