A Decade of the Z-Numbers

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Research Article

Publication Title

IEEE Transactions on Fuzzy Systems


In this article, we present a study on the development in the theory and application of the Z-numbers since its inception in 2011. The review covers the formalization of Z-number-based mathematical operators, the role of Z-numbers in computing with words, decision-making, and trust modeling, application of Z-numbers in real-world problems such as multisensor data fusion, dynamic controller design, safety analytics, and natural language understanding, a brief comparison with conceptually similar paradigms, and some potential areas of future investigation. The paradigm currently has at least four extensions to its definition: multidimensional Z-numbers, parametric Z-numbers, hesitant-uncertain linguistic Z-numbers, and Z∗-numbers. The Z-numbers have also been used in conjunction with rough sets and granular computing for enhanced uncertainty handling. While this decade has seen a plethora of theoretical initiatives toward its growth, there remains a major work scope in the direction of practical realization of the paradigm. Some challenges yet unresolved are automated translation of (imprecise, sarcastic, and metaphorical) linguistic expressions to their Z-number forms, discernment of probability-possibility distributions to map real-world situations under consideration, analysis of linguistic equivalents of Z-operator results to intuitive human responses, the endogenous arousal of belief in intelligent agents, and analysis of biases embedded in expert-belief values that are primary inputs to Z-number-based expert systems. After a decade of the Z-numbers, the paradigm has proved to be of use in expert-input-based decision-making systems and initial value problems. Its applicability in high-risk, high-precision areas, such as deep-sea exploration and space science, remains unexplored.

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