Soft set

Mathematics

Algorithm

Data mining

Artificial intelligence

Semantics (computer science)

Programming language

Computer science

Theoretical computer science

Cardinality (data modeling)

Fuzzy logic

Information Sciences

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.

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