Metric on L-Fuzzy Real Line

In this study, the concept of L-fuzzy real numbers which is given in [14] is extended by presenting the definition from both-sided. For each side, different functions are defined and it is proved that these functions are metrics. For that, it is shown that for a complete lattice L, given conditions in [14] for an equivalence relation ~ on mdR (L) are equivalent. So condition is weakened in our work. A metric which is consistent with the Euclidean metric is defined by using two-sided metrics. Also, an example is given for L-Fuzzy metric.