About a definition of metric over an abelian linearly ordered group

Abstract

A G-metric over an abelian linearly ordered group G = (G,⊙,≤) is a binary operation, d G , verifying suitable properties. We consider a particular G metric derived by the group operation ⊙ and the total weak order ≤, and show that it provides a base for the order topology associated to G.

Keywords

• G-metric, abelian linearly ordered group, multi-criteria decision making.