The notion of similarity and relations with other metrics

In this study, the relations between metric, partial metric, quasi metric and similarity metric is investigated. First, the basic notions and definitions of metric, partial metric and quasi metric are studied. Also, explicit examples of these structures are given. In the next section, the relations between these metrics examined. Then, the notion of similarity metric function and its properties are studied. In the last section, which is also the main section of this study, the relations between similarity metric and other metrics are evaluated. Moreover, we focused to construct one metric from each other and state theorems about these construction. Also, some examples of the results obtained are given.