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<p>Uncertainty is an intrinsic feature of real-world decision environments, manifesting as vagueness, imprecision, and ambiguity that classical probability theory cannot adequately model. Fuzzy set theory provides a rigorous mathematical framework for representing graded membership and linguistic uncertainty and has subsequently evolved into a rich family of generalizations including intuitionistic, type-2, neutrosophic, hesitant, Pythagorean, Fermetean, T-spherical, picture and q-rung orthopair fuzzy sets. This paper presents a comprehensive bibliometric and systematic review, derived from fully screened Web of Science corpus of more than 3200 publications following a PRISMA 2020-compliant search, screening and extraction protocol, of fuzzy set theory and its real-life applications from 2000 to 2024. Through analysis of publication trends, collaborative networks, productive authors, institutions and countries and keyword clustering, we map the evolution of the field across three phases: foundational consolidation (2000–2009), rapid theoretical expansion (2010–2017) and interdisciplinary application explosion (2018–2024). The review identifies primary application domains- control systems, multi-criteria decision-making, medical diagnosis, supply chain management, environmental assessment and finance, robotics and autonomous systems, smart cities and industry 4.0 and examines the most impactful methods and representative studies within each. Three cutting-edge application frontiers are highlighted: the integration of fuzzy logic with deep learning, smart city infrastructure management and quantum-inspired fuzzy computing. The paper also provides quantitative comparison of fuzzy set theory with related uncertainty frameworks, synthesizing key findings and identifies promising future research directions. This review serves as a comprehensive reference for researchers and practitioners seeking to harness fuzzy methodologies for complex real-world uncertainty problems.</p>

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ComputaTional Fuzzy Methods For Engineering Uncertainty: A State-of-the-Art Bibliometric And Systematic Review

  • 期刊论文

  • 发表日期：

    2026年8月4日

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  • Muhammad Asif,
  • Jianli Cao

摘要

Uncertainty is an intrinsic feature of real-world decision environments, manifesting as vagueness, imprecision, and ambiguity that classical probability theory cannot adequately model. Fuzzy set theory provides a rigorous mathematical framework for representing graded membership and linguistic uncertainty and has subsequently evolved into a rich family of generalizations including intuitionistic, type-2, neutrosophic, hesitant, Pythagorean, Fermetean, T-spherical, picture and q-rung orthopair fuzzy sets. This paper presents a comprehensive bibliometric and systematic review, derived from fully screened Web of Science corpus of more than 3200 publications following a PRISMA 2020-compliant search, screening and extraction protocol, of fuzzy set theory and its real-life applications from 2000 to 2024. Through analysis of publication trends, collaborative networks, productive authors, institutions and countries and keyword clustering, we map the evolution of the field across three phases: foundational consolidation (2000–2009), rapid theoretical expansion (2010–2017) and interdisciplinary application explosion (2018–2024). The review identifies primary application domains- control systems, multi-criteria decision-making, medical diagnosis, supply chain management, environmental assessment and finance, robotics and autonomous systems, smart cities and industry 4.0 and examines the most impactful methods and representative studies within each. Three cutting-edge application frontiers are highlighted: the integration of fuzzy logic with deep learning, smart city infrastructure management and quantum-inspired fuzzy computing. The paper also provides quantitative comparison of fuzzy set theory with related uncertainty frameworks, synthesizing key findings and identifies promising future research directions. This review serves as a comprehensive reference for researchers and practitioners seeking to harness fuzzy methodologies for complex real-world uncertainty problems.