Soft to Hard Data Transformation Using Uncertainty Balance Principle

The paper advances our on going work in the area of uncertainty alignment and transformation between fuzzy (soft, human generated, possibilistic) and random (hard, machine generated, probabilistic) data. As reported in our previous papers, the Uncertainty Balance Principle was defined to express uncertain data vagueness as represented by a fuzzy data models, with a non uniqueness of related random data distributions. The underlying assumption is that both fuzzy and random data are described in terms of the same independent uncertain variables. The connection between fuzzy and random data is done via cumulative rather than probability density functions. In this paper we clarify and extend our previous work whereas an initial fuzzy distributions (membership functions) are supplied and the aim is to determine corresponding and related random distributions. The next step in this analysis will focus on Bayesian data mining to determine random distributions from a given large set (data base) of soft data modeled as fuzzy (triangular, trapezoidal or other convex) distributions. This work has been inspired by an ever increasing need to fuse human and machine data in order to perform decision making procedures. Areas of applications include Bank Risk Assessment in financial industry as well as Command and Control Integration in defense industry and any other applications where soft and hard data fusion is required.