Mapping a Fuzzy Pattern onto a String

The problem of segmentation of a given string to match a fuzzy pattern is considered in this paper. The fuzzy pattern is defined as a sequence of fuzzy properties. It is assumed that each string can match a fuzzy property in some measure. Being increasing, decreasing, or oscillating are examples of fuzzy properties of a numerical sequence. The problem we consider is how to split the given string (sequence) into sufficiently long substrings (contiguous subsequences) to match the pattern as well as possible. This problem can be considered in the frame of the fuzzy clustering problem that has many applications in such areas as image processing, bioinformatics, etc. It can also be viewed as a special case of the fuzzy string matching problem. In this paper, we propose the optimal solution to the fuzzy segmentation problem and consider its application to the decomposition of a given function.