A class of semicontinuous fuzzy mappings

The concept of upper and lower semicontinuity of fuzzy mappings introduced by Bao and Wu [Y.E. Bao, C.X. Wu, Convexity and semicontinuity of fuzzy mappings, Comput. Math. Appl., 51 (2006) 1809–1816] is redefined by using the concept of parameterized triples of fuzzy numbers. On the basis of the linear ordering of fuzzy numbers proposed by Goetschel and Voxman [R. Goetschel, W. Voxman, Elementary fuzzy calculus, Fuzzy Sets and Systems 18], we prove that an upper semicontinuous fuzzy mapping attains a maximum (with respect to this linear ordering) on a nonempty closed and bounded subset of the n -dimensional Euclidean space R n , and that a lower semicontinuous fuzzy mapping attains a minimum (with respect to this linear ordering) on a nonempty closed and bounded subset of R n .