Fuzzy topology and fuzzy geometry of the topological concepts

Abstract

Abstract The typical approach to analyze the images in terms of recognition and further interpretation is to obtain an extension of the conventional geometry to the fuzzy case. The fuzzy geometry, which consists of the topological and geometrical structures such as connectedness, adjacency, principle of surrounded-ness (areas seen as surrounded by other areas are perceived as figures), convexity, area, perimeter, height, width, adjacency and etc. are essential to reflect the geometrical ambiguity of an image processing. Moreover, the application of the fuzzy geometry properties is important in soft computing decisions to further analyze and interpret a fuzzy image. The properties of fuzzy geometry based on the concepts of the length, breadth, height and methods of measuring a distance between fuzzy numbers are introduced here due to the numerous of applications in engineering problems and other fields.