Classification of Rainfall Data in the Region of Serres using Fuzzy Logic

The aim of this paper is the classification of rainfall data using fuzzy logic in order to examine whether there are similarities among rainfall stations. The data was taken from 7 rainfall stations in the region of Serres in Northern Greece and was used to calculate correlation coefficients. In order to obtain this similarity, a matrix R called tolerance matrix was created, having the properties of reflexivity and symmetry. This tolerance relation R, can be reformed into an equivalence relation by at most ( n − 1) compositions with itself, where n is the cardinal number of the set defining R. The relation R is an equivalence relation if it has the following three properties: a) reflexivity, b) symmetry, and c) transitivity. From the equivalence matrix R the α-cut sets are used in order to generate the equivalent classes. This last has the following three properties: a) Reflexivity, b) do not overlap and c) the union of all equivalent classes exhaust the Universe. In our research the objective was to find comparable classes of rainfall stations depending on the degree of confidence. Due to the complexity of the problem, an algorithm was created in Matlab environment, which receives the rainfall data, calculates the correlation coefficients, converts the tolerance matrix in equivalence matrix, gives the α-cut sets-classes and creates graphs.