Parametric 0–1 processes and extensive fuzzy sets

AbstractIn this paper the methods of random processes are used to establish the rigorous mathematical concepts of fuzzy sets and set up the concepts of extensive fuzzy sets. A 0–1 process determined by C on an index set T is called an extensive fuzzy set in T. As a special case, an independent 0–1 process is a fuzzy set. An example shows that the extensive fuzzy sets may portray fuzzy phenomena more precisely. The proofs of a decomposition theorem and an extension theorem are given