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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Vydáno v:	IEEE transactions on fuzzy systems Ročník 30; číslo 8; s. 2800 - 2812
Hlavní autoři:	Banerjee, Romi, Pal, Sankar K., Pal, Jayanta Kumar
Médium:	Journal Article
Jazyk:	angličtina
Vydáno:	New York IEEE 01.08.2022 The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Témata:	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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Abstract	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.
AbstractList	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.
Author	Pal, Sankar K. Pal, Jayanta Kumar Banerjee, Romi
Author_xml	– sequence: 1 givenname: Romi orcidid: 0000-0001-6416-6438 surname: Banerjee fullname: Banerjee, Romi email: rm.banerjee@gmail.com organization: Department of Computer Science and Engineering, Indian Institute of Technology Jodhpur, Jodhpur, India – sequence: 2 givenname: Sankar K. orcidid: 0000-0003-3301-4751 surname: Pal fullname: Pal, Sankar K. organization: Center for Soft Computing Research, Indian Statistical Institute, Kolkata, India – sequence: 3 givenname: Jayanta Kumar orcidid: 0000-0001-6940-3842 surname: Pal fullname: Pal, Jayanta Kumar organization: Machine Intelligence Unit, Indian Statistical Institute, Kolkata, India
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SubjectTerms	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
Title	A Decade of the Z-Numbers
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