Computing with words =? New mathematical theory of descriptions. Part 1: description of paths (spiral data, Kolmogorov theorem and neural networks, chess, salesman)

The method of description introduced by F. Karbou and F. Karbou (2000) had as a goal the recognition of handwritten characters. This description defines rules of recognition which are simples, generals and especially locals to each object. These rules were based on a special interval's utilization where one situates intervals and numbers positions (or empty intervals and full intervals position) in a predefined order. This processing defines discriminant rules. The article proposes a similar approach to human path description. This approach is based on fuzzy spatial primitive relationships (left, right, bottom, below) (F. Karbou and F. Karbou, 2000) and a recursive sense of the covered path following these directions. So, computing with words (L.A. Zadeh, 1996) is introduced differently. We explain how computing of words can be useful and general. In addition, the paper is an introduction. It is difficult to master notations, to give precise definitions and to define a pluridisciplinary theory based on human perception. In fact, we had to give precise tools of descriptions, the limit of each tool, the role of the goal in a description or in a particular form of description. Nevertheless, the role of intervals is very important. Thus, one can for example, describe the position of intervals where a curve or a path is decreasing to the right or increasing to the right compared to a reference. And therefore, one returns to the type of description made in handwritten recognition where one has described relatively the respective position of intervals end numbers in a predefined order.