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

•We introduce the first eshaustive semantical analysis N-soft sets.•Three interpretations are examined, the third concerns many-valued logics.•Aggregation is justified by these semantical interpretations.•We use this theory for three-way decision.•Qualitative and quantitative approaches generalize t...

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Bibliographic Details
Published in:Information sciences 2022-08, Vol.606, p.837-852
Main Author: R. Alcantud, José Carlos
Format: Article
Language:English
Subjects:
Aggregation
Decision making
Multi-valued logic
N-soft set
Three-way decision
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Summary:•We introduce the first eshaustive semantical analysis N-soft sets.•Three interpretations are examined, the third concerns many-valued logics.•Aggregation is justified by these semantical interpretations.•We use this theory for three-way decision.•Qualitative and quantitative approaches generalize the case of soft sets. 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.
ISSN:0020-0255
1872-6291
DOI:10.1016/j.ins.2022.05.084