THE CUT SETS, DECOMPOSITION THEOREMS AND REPRESENTATION THEOREMS ON (R-)-FUZZY SETS

摘要

In this paper, some kinds of cut sets for (R-)-fuzzy sets are introduced and their properties are given. Moreover, the decomposition theorems and representation theorems on (R-)-fuzzy sets are obtained based on different cut sets. Finally, the axiomatic definition of cut set for (R-)-fuzzy set is introduced which characterizes the common properties of cut set.