The DOI matches its Crossref record; 43 of the 43 references it cites were found in a registry or an index.
Fuzzy set theory
Open accessAbstract
Since its inception in 1965, the theory of fuzzy sets has advanced in a variety of ways and in many disciplines. Applications of this theory can be found, for example, in artificial intelligence, computer science, medicine, control engineering, decision theory, expert systems, logic, management science, operations research, pattern recognition, and robotics. Mathematical developments have advanced to a very high standard and are still forthcoming to day. In this review, the basic mathematical framework of fuzzy set theory will be described, as well as the most important applications of this theory to other theories and techniques. Since 1992 fuzzy set theory, the theory of neural nets and the area of evolutionary programming have become known under the name of ‘computational intelligence’ or ‘soft computing’. The relationship between these areas has naturally become particularly close. In this review, however, we will focus primarily on fuzzy set theory. Applications of fuzzy set theory to real problems are abound. Some references will be given. To describe even a part of them would certainly exceed the scope of this review. Copyright © 2010 John Wiley & Sons, Inc. This article is categorized under: Statistical Learning and Exploratory Methods of the Data Sciences > Clustering and Classification
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Cites
Zadeh, L. A. (1965) · Information and Control · doi:10.1016/s0019-9958(65)90241-x · Cited by 67,855
Zadeh, L. A. (1996) · Cited by 46,844
Pattern Recognition with Fuzzy Objective Function Algorithms
Bezdek, J. C. (1981) · doi:10.1007/978-1-4757-0450-1 · Cited by 9,881
Outline of a New Approach to the Analysis of Complex Systems and Decision Processes
Zadeh, L. A. (1973) · IEEE Transactions on Systems, Man, and Cybernetics · doi:10.1109/tsmc.1973.5408575 · Cited by 8,721
Fuzzy Set Theory—and Its Applications
Zimmermann, H.-J. (2001) · Springer eBooks · doi:10.1007/978-94-010-0646-0 · Cited by 7,526
Self-citationDecision-Making in a Fuzzy Environment
Bellman, R. E., & Zadeh, L. A. (1970) · Management Science · doi:10.1287/mnsc.17.4.b141 · Cited by 6,813
An experiment in linguistic synthesis with a fuzzy logic controller
Mamdani, E. H., & Assilian, S. (1975) · International Journal of Man-Machine Studies · doi:10.1016/s0020-7373(75)80002-2 · Cited by 5,785
An Experiment in Linguistic Synthesis with a Fuzzy Logic Controller
MAMDANI, E. H., & ASSILIAN, S. (1999) · International Journal of Human-Computer Studies · doi:10.1006/ijhc.1973.0303 · Cited by 5,603
Decision Making in a Fuzzy Environment
(2007) · Advances in Fuzzy Systems — Applications and Theory · doi:10.1142/9789812770622_0004 · Cited by 5,320
A Fuzzy Relative of the ISODATA Process and Its Use in Detecting Compact Well-Separated Clusters
Dunn, J. C. (1973) · Journal of Cybernetics · doi:10.1080/01969727308546046 · Cited by 5,049
Cited by
Mariani, M. M., Perez‐Vega, R., & Wirtz, J. (2022) · Psychology & Marketing · doi:10.1002/mar.21619 · Cited by 631
Intuitionistic Fuzzy Information Aggregation Using Einstein Operations
Wang, W., & Liu, X. (2012) · IEEE Transactions on Fuzzy Systems · doi:10.1109/tfuzz.2012.2189405 · Cited by 416
Hassan, S., Wang, J., Kontovas, C., & Bashir, M. (2022) · Journal of Loss Prevention in the Process Industries · doi:10.1016/j.jlp.2021.104616 · Cited by 67
Recycled construction and demolition waste material: a cost–benefit analysis under uncertainty
Tseng, M.-L., Jeng, S.-Y., Lin, C.-W., & Lim, M. K. (2021) · Management of Environmental Quality: An International Journal · doi:10.1108/meq-08-2020-0175 · Cited by 19
Aleksić, A., Tadić, D., Komatina, N., & Nestić, S. (2025) · Mathematics · doi:10.3390/math13132216 · Cited by 11
Metadata
- Authors
- Zimmermann, H. ‐.
- Venue
- WIREs Computational Statistics
- Publisher
- Wiley
- Published
- 2010-05
- Volume
- 2
- Issue
- 3
- Pages
- 317-332
- ISSN
- 1939-0068 (ISSN-L)
- 1939-5108
- OpenAlex
- W2076556084
- Cited by
- 744
- References
- 43
- FWCI
- 21.43
- Type
- journal article
- Language
- en
- Open access
- green
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Contains information from the Semantic Scholar Academic Graph Datasets, made available under the ODC Attribution License (ODC-BY 1.0).
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