The semantics of N-soft sets, their applications, and a coda about three-way decision

This paper presents the first detailed analysis of the semantics of N-soft sets. The two benchmark semantics associated with soft sets are perfect fits for N-soft sets. We argue that N-soft sets allow for an utterly new interpretation in logical terms, whereby N-soft sets can be interpreted as a generalized form of incomplete soft sets. Applications include aggregation strategies for these settings. Finally, three-way decision models are designed with both a qualitative and a quantitative character. The first is based on the concepts of V-kernel, V-core and V-support. The second uses an extended form of cardinality that is reminiscent of the idea of scalar sigma-count as a proxy of the cardinality of a fuzzy set.(c) 2022 The Author(s). Published by Elsevier Inc. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/).

Automated summary

This paper presents a detailed analysis of the semantics of N-soft sets for the first time. The two benchmark semantics associated with soft sets are a perfect fit for N-soft sets. N-soft sets allow for a new interpretation in logical terms, where they can be seen as a generalized form of incomplete soft sets. The study also introduces aggregation strategies and designs three-way decision models with qualitative and quantitative features.