Issues in Possibilistic Reliability Theory

Recently, alternative models for the classical reliability theory based upon fuzzy set theory and related theories, are proposed to solve the problems of the classical approach. Our model is based upon a combination of multistate structure functions and possibility theory. In this paper, we present a congruence relation on the complete lattice of structure functions, that links several concepts of the theory of multistate structure functions and the possibilistic reliability theory. Some important possibilistic reliability bounds are established and, finally, we apply the theoretic concepts to some concrete examples.