Application of Fuzzy Sets to the Determination of Sunspot Areas

Abstract

The computation of sunspot areas is important for many applications in solar physics. Some uncertainty is, however, inherent to this determination, since there is uncertainty in defining the limits of sunspots, as well as their umbrae and penumbrae, particularly in high-resolution images where large variations in intensity are observed, mainly in the penumbrae and photosphere regions. In this paper a methodology based on the classical histogram method is presented that enables the generation of fuzzy sets that correspond to the umbrae and penumbrae of sunspots, as well as to the complete sunspots, which enable the representation of the uncertainty in their locations. The areas of the sunspots and of their umbrae and penumbrae are then obtained by computing the areas of the fuzzy sets used to represent them. Two operators are used: the Rosenfeld Area operator, which generates a real number for the area, and the Fuzzy Area operator, which generates a fuzzy number, providing more information about the uncertainty of the area. A comparison of the obtained results with the area values given by the classical cumulative histogram method is made and the differences analyzed.