Soft order topology and graph comparison based on soft order

Soft sets provide a suitable framework for representing and dealing with vagueness. A scenario for vagueness can be that alternatives are composed of specific factors and these factors have specific attributes. Towards this scenario, this paper introduces soft order and its associated order topology on the soft sets with a novel approach. We first present the definitions and properties of the soft order relations on the soft sets via soft elements. Next, we define soft order topology on any soft set and provide some properties of this topology. In order to implement what we introduced about the soft orders, we describe soft preference and soft utility mapping on the soft sets and we finally demonstrate a decision-making application over the soft orders intended for comparing graphs.