Reconstruction families of possibilistic structure systems

A method is presented for characterizing the family of overall systems reconstructable from a given possibilistic structure system. The technique is elaborated in terms of fuzzy relation equations.It is demonstrated that the reconstruction family of a given structure system is equivalent to the set of solutions of a special type of fuzzy relation equation. The solution set is partially ordered, and contains both minimal solutions and a unique maximum solution. When these elements are identified, all members of the reconstruction family are determined.Another characteristic of the reconstruction family is its reconstruction uncertainty, a measure of which is also developed in this paper. This measure is used to define an identifiability quotient that expresses the degree of confidence with which we may identify a single overall system given a particular structure system.