An Algorithmic Research Analysis of Fuzziness in

Mathematical Morphology is a theory and technique for the analysis and the processing of geometrical structures based on set theory, lattice theory, topology and random functions. It can be applied on graphs, surface meshes, solids and many other spatial structures. Fuzzy Mathematical morphology aims to extend the binary morphology operators to grey level images. Mathematical Morphology is the methodology for the quantitative analysis of spatial structures based on concepts of shape and form. Mathematical Morphology is based on set theory, commonly applying to digital images. It is a foundation of Morphological image processing which consists of set operators that transform images. In this paper, we present two articles on the subject. In the first article, membership functions, fuzzy set theory, fuzzy logic, fuzzy mathematical morphology fuzzy operators such as erosion, dilation, opening & closing will be explained in detail. In the second article, there will be an innovative study of construction of Mathematical Morphology on fuzzy sets and their properties.