A Characterization of Convex Fuzzy Mappings

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Preliminaries

Letdenote the -dimensional Euclidean space. A fuzzy set ofis defined to be a function frominto. The support,, of a fuzzy setis defined by:

.

For, the -level setof a fuzzy setis defined by:

wheredenotes the closure of. A fuzzy number considered in this paper is a fuzzy setwith the following properties:

• (1)is normal, i.e.,,

• (2)is fuzzy convex, i.e.,, for anyand for any,

• (3)is upper semicontinuous, i.e., for any,is a closed subset of, and

• (4)is bounded.