Ranked soft sets

This article defines ranked soft sets and establishes their fundamental theory. This new model of uncertain knowledge is a non-numerical yet powerful improvement of soft sets. The model relies on a qualitative improvement of the basic parameterized description posed by soft sets. We define relations between ranked soft sets and some existing models (N-soft sets, fuzzy soft sets, probabilistic soft sets) that enhance the soft set spirit with the help of additional quantities. Primary contributions to their development include set-theoretic operations and representation theorems, at a theoretical level; and scores and aggregation operators, at a practical level. Finally we design a multi-person decision-making strategy for data in the form of ranked soft sets that takes advantage of these elements.