Multiple scoring systems (including rank and score functions; MSS) have been widely used in multiple regression, intelligent biometric systems, multiple artificial neural nets, combining pattern classifiers, ensemble methods, machine learning and artificial intelligence (AI), data and information fusion, preference ranking, and deep learning.Combining MSS has achieved numerous successful results in a variety of domain applications.However, the reasons why this happens remains an active area of investigation.Combinatorial fusion analysis Platinum Edition (CFA) combines MSS using the rank-score characteristic (RSC) function and cognitive diversity (CD).
The RSC function was proposed to characterise the predictive behaviour of a scoring system.It was subsequently used to define the notion of “cognitive diversity”, which measures the dissimilarity in the representation of information between two scoring systems.In this article, we first examine characterizations of and diversity between scoring systems.Then, we review combinatorial fusion analysis with a variety of domain applications, including biometric systems in cognitive neuroscience, and joint decision making with visual cognitive systems.
Finally, we demonstrate that multi-layer combinatorial fusion (MCF) on the Kemeny rank space is a viable machine learning and AI framework for preference ranking and Display prom reinforcement learning.This work provides a scientific foundation and technological insights for the use of Combinatorial Fusion in ensemble methods, data and information fusion, preference ranking, and deep reinforcement learning with applications to a variety of domains in data science and informatics for secure and sustainable societies.