Applications of Quantum Probability Amplitude in Decision Support Systems

Establishing various frameworks for managing uncertainties in decision-making systems have been posing many fundamental challenges to the system design engineers. Quantum paradigm has been introduced to the area of decision and control communities as a possible supporting platform in such uncertainty management. This paper presents an overview of how a quantum framework and, in particular, probability amplitude has been proposed and utilized in the literature to complement two classical probabilistic decision-making approaches. The first such framework is based in the Bayesian network, and the second is based on an element of Dempster–Shafer (DS) theory using the definition of mass function. The paper first presents a summary of these classical approaches, followed by a review of their preliminary enhancements using the quantum model framework. Particular attention was given on how the notion of probability amplitude is utilized in such extensions to the quantum-like framework. Numerical walk-through examples are combined with the presentation of each method in order to better demonstrate the extensions of the proposed frameworks. The main objective is to better define and develop a common platform in order to further explore and experiment with this alternative framework as a part of a decision support system.