RECONSTRUCTABILITY ANALYSIS OF MULTI-DIMENSIONAL RELATIONS: A Theoretical Basis for Computer-Aided Determination of Acceptable Systems Models †

Abstract

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 situation. Some classes or structure systems, each of which emerges either from computational considerations or from various investigative contexts, are introduced and examined. The ultimate result of the paper is a set of eight schematically described generative procedures which provide a comprehensive basis for developing two computationally efficient software packages for reconstructability analysis, one for interactive processing and one for batch processing.