Mathematical Morphology on Soft Sets for application to Metabolic Networks

Abstract

In this paper, we introduce mathematical morphological operators such as dilation and erosion on soft sets. Rather than the common approach which is based on expressing soft set analogues of the classical theory, we use the classical theory to morphologically analyse a soft set. The main goal of our study is to apply this morphological concepts to metabolic networks to derive an algebraic picture of chemical organizations. For this purpose we first introduce various types of complete lattices on soft sets which represent metabolic networks, then study morphological operations respect to corresponding lattice structure. We also give the concept of duality on soft sets.