Possibility Set-valued Mapping And Its Application

Based on the falling shadows of random sets and possibility theory, a concept of possibility set-valued mapping is given in this paper. The definition of falling shadows of possibility set-valued mapping is presented. By the use of the operations of possibility set-valued mapping and the idea of falling shadows of random set, a theoretical approach to define the operations of fuzzy sets and implication operators of fuzzy sets is introduced. Zadeh operators,probability product operators and bounded product operators is acquired under certain conditions.