Multivalued continuum systems

This paper deals with continuum systems, where a continuous degree of performance levels between perfect functioning and complete failure is allowed. Here the authors shall assume that the system can be modeled as a structure function given by a mapping from the n-dimensional unit hypercube into a k-dimensional unit hypercube, in such a way that the performance of the system is described according to k single continuum-valued criteria. Some basic concepts relative to these continuum multivalued systems are discussed and general reliability bounds are obtained based upon the minimal paths and minimal cuts of the k associated single-valued continuum systems.