A Quantum Probabilistic Linguistic Term Framework to Multi-attribute Decision-Making for Battlefield Situation Assessment

The decision-making process is always associated with uncertainty and vagueness because of the incomplete decision data and unpredictable decision-making behavior. The concurrence of the epistemic uncertainty and the aleatory uncertainty, especially when only the qualitative data are accessible, poses more challenges to the decision-making. The probabilistic linguistic term set provides a flexible tool for data representation in such an environment. However, most of the existing decision-making methods for the probabilistic linguistic term sets depend on the aggregation operator. The subjectivity of the decision-makers and the decision-making behaviors are not fully considered. To solve this problem, a quantum-like probabilistic linguistic term decision-making framework is proposed, in which the quantum state, quantum data processing, and quantum interference effect are analyzed in detail. The decision-making beliefs of decision-makers are in a superposition state and their subjective relationships are depicted in the interference term. A multi-attribute decision-making method in this framework is then proposed for practical applications. Then the applications for sea-battlefield situation assessment are presented as the illustration and validation. A comparative analysis is also provided to depict the advantages of the proposed method, based on which appropriate conclusions and remarks are drawn.