Aggregation of fuzzy quasi-metrics

In the last years fuzzy (quasi-) metrics and indistinguishability operators have been used as a mathematical tool in order to develop appropriate models useful applied sciences as, for instance, image processing, clustering analysis multi-criteria decision making. The both aforesaid similarities allow us fuzzify crisp notion of equivalence relation when certain degree similarity can be only provided between compared objects. However, applicability is reduced because difficulty generating examples. One technique generate new binary relations based on merging collection them into one by means use function. Inspired, part, preceding fact, this paper devoted study which functions merge single one. We present characterization such terms ∗-triangular triplets also isotonicity ∗-supmultiplicativity, where ∗ t-norm. show that does not depend symmetry quasi-metrics. same problem stationary studied and, consequence, characterizations those aggregating preorders are obtained.