RELATIONSHIP BETWEEN TRUE AND ESTIMATED POSSIBILISTIC SYSTEMS AND THEIR RECONSTRUCTIONS†

Abstract

This paper is a theoretical contribution to reconstructability analysis of possibilistic systems. A method to estimate a given possibility distribution from the associated observations is derived based on the one-to-one correspondence between possibility distributions and their basic probability assignments. It is shown that in this estimation the possibility value for a state is proportional to the frequency of the state in the observations which are drawn from nested state subsets. The order preservation relationship between a given (true) possibility distribution and its estimation is derived. Based on this preservation property, it is shown that the order in the distance from an original possibilistic overall system of their unbiased reconstructions from two alternative reconstruction hypotheses (structures) is preserved in the estimated systems domain. Particularly, it is proved that systems conceptualized in terms of possibility theory possess an important property: if a possibilistic system is perfectly reconstructable from a specific reconstruction hypothesis, then a system estimated from any data produced by the former system is also perfectly reconstructable from the same hypothesis.

INDEX TERMS:

• Reconstructability analysis
• possibility theory
• reconstruction hypothesis
• possibilistic system
• perfect reconstruction
• possibilistic data

Notes

†This work was supported by the National Science foundation under Grant No. IST 85-44191.