Open AccessFuzzy topology and fuzzy geometry of the topological concepts
Author(s) -
Djavanshir Gadjiev,
Aligadzhi Rustanov
Publication year - 2020
Publication title -
iop conference series. materials science and engineering
Language(s) - English
Resource type - Journals
eISSN - 1757-899X
pISSN - 1757-8981
DOI - 10.1088/1757-899x/1001/1/012071
Subject(s) - geometry , social connectedness , topology (electrical circuits) , mathematics , fuzzy logic , convexity , adjacency list , computer science , artificial intelligence , algorithm , combinatorics , psychology , financial economics , economics , psychotherapist
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.