Ranked soft sets

Abstract

AbstractThis 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.