Theory of Distances in NeutroGeometry

NeutroGeometry is one of the most recent approaches to geometry. In NeutroGeometry models, the main condition is to satisfy an axiom, definition, property, operator and so on, that is neither entirely true nor entirely false. When one of these concepts is not satisfied at all it is called AntiGeometry. One of the problems that this new theory has had is the scarcity of models. Another open problem is the definition of angle and distance measurements within the framework of NeutroGeometry. This paper aims to introduce a general theory of distance measures in any NeutroGeometry. We also present an algorithm for distance measurement in real-life problems. Keywords: NeutroGeometry, path, rectifiable path, single-valued neutrosophic set, Taxicab geometry, Chinese checker metric