Fixed Point Theorem on Fuzzy Metric Space

Metric that are commonly understood as functions of distance have an important role in analysis and applied mathematics. However, metric (for example Euclid) which are based on the Crisp concept, are not suitable for certain cases such as the definition of the distance between two pixels in image analysis which is often interpreted as two pixel resemblance. Therefore, in this paper the concept of fuzzy metric is developed based on fuzzy concepts. This fuzzy metric is then applied to convergence problems and fixed point problems. It was concluded that some properties in ordinary metric still apply to fuzzy metric.