Reconstructability analysis is viewed as a process of investigating the possibilities of reconstructing desirable properties or overall systems from the knowledge of the corresponding properties of their various subsystems. Overall systems are represented by n-dimensional relations, each of which is viewed as a finite set of aggregate states (n-tuples) formed by individual stales of n variables. Depending on the context or investigation, the relations may include various measures defined on them, such as probability distributions or fuzzy set membership functions. Each subsystem is defined as a projection of the overall relation into k or its n dimensions (k < n). Every set of subsystems or an overall system is referred to as a structure system and is viewed as a possible basis for reconstructing specified properties of the overall system This paper focuses on the problem of generating, in an orderly fashion, all meaningful structure systems of a given overall system which ore desirable in each particular...