Fuzzy Topological Spaces

Fuzzy mathematics as fuzzy sets and fuzzy logics is a new branch of mathematics which has been found multiple uses across numerous fields such as control systems, engineering, image processing, power engineering, industrial automation, robotics, consumer electronics, and optimization. Fuzzy concept is considered to be an important aspect in the field of mathematics that interprets the uncertainties, and deals with the unreliable information and vagueness of data. Fuzzy set theory is a particularly useful tool to describe situations in which the data are imprecise or vague. The main goal of this chapter is to introduce basic and standard properties often required for fuzzy spaces.