A Decade of the Z-Numbers

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, applica...

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Veröffentlicht in:IEEE transactions on fuzzy systems Jg. 30; H. 8; S. 2800 - 2812
Hauptverfasser: Banerjee, Romi, Pal, Sankar K., Pal, Jayanta Kumar
Format: Journal Article
Sprache:Englisch
Veröffentlicht: New York IEEE 01.08.2022
The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Schlagworte:
Arousal
Boundary value problems
Computation
Computational modeling
Computing with perceptions (CWP)
computing with words (CWW)
Control systems design
Data integration
Decision making
Deep sea
Expert systems
Fuzzy sets
Intelligent agents
linear programming (LP)
Linguistics
Mathematical model
multicriteria decision-making (MCDM)
multiobjective decision-making (MODM)
Multisensor fusion
Operators (mathematics)
Probability distribution
Reliability
trust modeling
Z-distance
Z-interpolation
Z-number arithmetic
Z-rule base
Z-similarity
ISSN:1063-6706, 1941-0034
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Zusammenfassung: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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ISSN:1063-6706
1941-0034
DOI:10.1109/TFUZZ.2021.3094657