An axiomatic approach to scalar cardinalities of fuzzy sets
Generate an AI Snapshot to get a quick, structured summary of this paper.
A concise AI-generated summary of the paper will appear here once you click Generate AI Snapshot.
TL;DR
An axiomatic approach to scalar cardinalities of fuzzy sets which is based on a system of three simple postulates is presented, and a characterization theorem for those cardinalities is given.
Abstract
We present an axiomatic approach to scalar cardinalities of fuzzy sets which is based on a system of three simple postulates. A characterization theorem for those cardinalities is given. The infinite family of possible scalar cardinalities of a fuzzy set generated by the postulates contains as particular cases all standard concepts of scalar cardinality, e.g. the sigma count of a fuzzy set, the cardinality of its core or support, and the cardinality of its t-level set.