Cited by 12,187Fuzzy Logic and Control SystemsAdvanced Algebra and LogicMathematical Control Systems and Analysis

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The concept of a linguistic variable and its application to approximate reasoning—I

Zadeh, L.A.·1975·Information Sciences

DOI 10.1016/0020-0255(75)90036-5

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“The notion of sup-J extension principle (Carlsson et al. 2004; Zadeh 1975) consists of a generalization of the Zadeh’s extension principle to deal with functions with two or more arguments given by fuzzy numbers.”
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“It is the generalization of classical set Type 2 fuzzy sets (Zadeh 1975) Its membership function is a fuzzy function It is one kind of generalization of fuzzy sets Intuitionistic fuzzy sets (Atanassov 1999) Every element of this set has a membership value as well as a non-membership value It is…”
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Background
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“Zadeh then expanded the idea of FS to interval-valued fuzzy sets in 1975 [2].”
Background
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Background
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“[13] in 1975, and proposed Interval-valued fuzzy sets (IVFS) that are a variation of fuzzy sets that allow the membership degrees to be represented as intervals rather than precise values.”
Background
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Background
A novel approach based on neutrosophic Bonferroni mean operator of trapezoidal and triangular neutrosophic interval environments in multi-attribute group decision making
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“Zadeh, L.A.”
Background
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“A1 ’ A2 ’ = aU11 aU24, aU12 aU23, aU13 aU22, aU14 aU21; min H1 A U 1 ; ; H1 A U 2 ; , min H2 A U 1 ; ; H2 A U 2 ; , aL11 aL24, aL12 aL23, aL13 aL22, aL14 aL21; min H1 A L 1 ; ; H1 A L 2 ; , min H2 A L 1 ; ; H2 A L 2 ; : ð5Þ Definition 3: The multiplication operation for the two trapezoidal IT2FSs A1 ’ and A2 ’ is desc…”
Influential
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“After that, for describing the qualitative information more intuitively, linguistic term set (LTS) is developed by Zadeh (Zadeh 1975).”
Background
A Review of Various Controller Techniques Designed for the Operational Control of DC and Servo Motors
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“To quantify uncertain information, different theories are used, such as fuzzy sets (Zadeh 1965) and various generalizations of fuzzy theory.”
Background
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“Fuzzy relations have been applied in many fields [8] such as clustering with a covariance matrix [9], L1-norm based clustering [10], clustering with partial supervision,controlling a dynamic plant, mathematical programming and reasoning [11] including mathematical modeling.”
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Singh, Y., & Bisht, D. (2021) · International Journal of Modelling and Simulation · doi:10.1080/02286203.2021.1983079 · Cited by 13
“To overcome from such uncertainties fuzzy set theory is a good tool to use [6–9].”
Method
Fuzzy Based Prediction Model for Air Quality Monitoring for Kampala City in East Africa
Katushabe, C., Kumaran, S., & Masabo, E. (2021) · Applied System Innovation · doi:10.3390/asi4030044 · Cited by 13
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Retracted
Multiplicative consistency analysis of linguistic preference relation with self‐confidence level and self‐doubting level and its application in a group decision making
Mandal, P., Samanta, S., & Pal, M. (2021) · International Journal of Intelligent Systems · doi:10.1002/int.22516 · Cited by 13
“In Reference [15], fuzzy linguistic approach for qualitative knowledge was analyzed and discussed extensively.”
BackgroundInfluential
Double-hierarchy hesitant fuzzy linguistic information-based framework for green supplier selection with partial weight information
Krishankumar, R., Arun, K., Kumar, A. R., Rani, P., Ravichandran, K. S., & Gandomi, A. H. (2021) · Neural Computing and Applications · doi:10.1007/s00521-021-06123-2 · Cited by 13
“Zadeh [3] framed the basis for linguistic decision-making, which reduced the transformation overhead and promoted flexible decision-making.”
Background
Matrix games with linguistic intuitionistic fuzzy Payoffs : Basic results and solution methods
Verma, R., & Aggarwal, A. (2021) · Artificial Intelligence Review · doi:10.1007/s10462-021-10014-2 · Cited by 13
“The theory of fuzzy sets (FSs), proposed by Zadeh (1975), provides an efficient tool to deal with uncertainty and fuzziness occurred in many organizational decision making and game-related problems.”
Background
Generalized hesitant fuzzy knowledge measure with its application to multi-criteria decision-making
Singh, S., & Ganie, A. H. (2021) · Granular Computing · doi:10.1007/s41066-021-00263-5 · Cited by 13
“These extensions are Atanassov’s (1986) intuitionistic fuzzy sets (IFSs), type-2 fuzzy sets given by Zadeh (1975), etc.”
Background
An approach to construct entropies on interval-valued intuitionistic fuzzy sets by their distance functions
Che, R., Suo, C.-F., & Li, Y. (2021) · Soft Computing - A Fusion of Foundations, Methodologies and Applications · doi:10.1007/s00500-021-05713-5 · Cited by 13
“Fuzzy set (FS) and interval-valued fuzzy set (IVFS) were proposed by Zadeh (1965), Zadeh (1975).”
BackgroundMethodInfluential
Addition and subtraction of interactive fuzzy numbers via family of joint possibility distributions
Esmi, E., Wasques, V., & Barros, L. (2021) · Fuzzy Sets Syst. · doi:10.1016/j.fss.2021.03.005 · Cited by 13
A fuzzy approach for assessment of smart socio-cultural attributes of a historic urban landscape: Case study of Alwar walled city in India
Dhingra, M., & Chattopadhyay, S. (2021) · Sustainable Cities and Society · doi:10.1016/j.scs.2021.102855 · Cited by 19
Spatial relation learning for explainable image classification and annotation in critical applications
Pierrard, R., Poli, J.-P., & Hudelot, C. (2020) · Artificial Intelligence · doi:10.1016/j.artint.2020.103434 · Cited by 21
Security synchronization protocol for IT2 stochastic fuzzy multiplex complex networks via fuzzy hybrid control.
Luo, M.-Z., Cheng, J., Shi, K.-B., Hu, C., & Lan, J. (2021) · ISA transactions · doi:10.1016/j.isatra.2021.02.010 · Cited by 13
Unbalanced probabilistic linguistic decision-making method for multi-attribute group decision-making problems with heterogeneous relationships and incomplete information
Teng, F., Liu, P.-D., & Liang, X. (2021) · Artificial Intelligence Review · doi:10.1007/s10462-020-09927-1 · Cited by 13
“Zadeh has pioneered the use of linguistic variables to present qualitative information (Zadeh 1975).”
Background
A numerical method to solve a fuzzy differential equation via differential inclusions
Liu, X.-M., Jiang, J., & Hong, L. (2021) · Fuzzy Sets Syst. · doi:10.1016/j.fss.2020.04.023 · Cited by 13
Fuzzy multi-criteria decision-making approach to prioritization of space debris for removal
Bazzocchi, M. C. F., Sánchez-Lozano, J., & Hakima, H. (2021) · Advances in Space Research · doi:10.1016/j.asr.2020.11.006 · Cited by 13
An interval type-2 fuzzy MCDM model for work package subcontractor prequalification
Afshar, M., Shahhosseini, V., & Sebt, M. (2021) · Soft Computing - A Fusion of Foundations, Methodologies and Applications · doi:10.1007/s00500-020-05173-3 · Cited by 13
Induced OWA Operator for Group Decision Making Dealing with Extended Comparative Linguistic Expressions with Symbolic Translation
He, W., Dutta, B., Rodríguez, R. M., Alzahrani, A. A., & Martínez, L. (2020) · Mathematics · doi:10.3390/math9010020 · Cited by 13
Alpha-cut based fuzzy cognitive maps with applications in decision-making
Baykasoğlu, A., & Gölcük, I. (2020) · Computers & industrial engineering · doi:10.1016/j.cie.2020.107007 · Cited by 13
Advancing Hazardous Materials Transport Safety: Systematic Insights on Risks, Challenges, and Research Gaps
Gholamizadeh, K., Rostami, C., Zarei, E., Yazdi, M., & Moslem, S. (2025) · Journal of Safety Science and Resilience · doi:10.1016/j.jnlssr.2025.100226 · Cited by 12
A multi-criteria decision-making framework using spherical trapezoidal fuzzy harmonic mean aggregation and the best–worst method for selecting an electric vehicle charging station location
Irvanizam, I., Zahara, N., Fikri, A., & Junaidi, H. (2025) · Journal of Supercomputing · doi:10.1007/s11227-025-07372-x · Cited by 12
An Adaptive-switching Fuzzy Structural Vibration Control System: Theory and Experiment
Zhang, C.-W., Pei, S., & Mohammadzadeh, A. (2025) · Journal of Vibration Engineering & Technologies · doi:10.1007/s42417-025-01881-y · Cited by 12
“The concept of type-2 fuzzy set was ﬁrst proposed by Professor Zadeh [41].”
A probabilistic uncertain linguistic MCDM model based on regret theory and MULTIMOORA method
Fan, J., Jin, Z., & Wu, M. (2025) · Computational and Applied Mathematics · doi:10.1007/s40314-025-03217-8 · Cited by 12
“Tobettercapturefuzzyevalua-tioninformation,Zadeh(1965)introducedfuzzysets(FSs),laterextendedtofuzzylinguistic sets(FLSs)(Zadeh1975),inwhichnaturallanguagereplacesprecisenumbers.”
Modeling linguistic intuitionistic fuzzy preference into the consensus and dissent framework of graph model for conflict resolution and its application
Tang, G.-L., Zhang, T.-Z., Lv, Y., & Liu, P.-D. (2025) · Information Sciences · doi:10.1016/j.ins.2025.122288 · Cited by 12
Multi-criteria decision making with Hamacher aggregation operators based on multi-polar fuzzy Z-numbers
Ullah, I., Akram, M., & Allahviranloo, T. (2025) · Information Sciences · doi:10.1016/j.ins.2024.121707 · Cited by 12
Possibilistic C-means with novel image representation for image segmentation
Cui, H.-S., Wang, H., Zeng, W., Liu, Y., & Zhao, B. (2024) · Artificial Intelligence Review · doi:10.1007/s10462-024-11057-x · Cited by 12
“Therefore, various types of fuzzy sets have been introduced for different scenarios, including the interval-valued fuzzy set (Zadeh 1975a, b , c ), intuitionistic fuzzy set (Atanassov 1986, 1989), fuzzy multisets (Miyamoto 2000; Yager 1986), and hesitant fuzzy set (Torra and Narukawa 2009).”
Intuitionistic Fuzzy Ordinal Priority Approach with Grey Relational Analysis
Majumder, P., & Salomon, V. (2024) · Mathematics · doi:10.3390/math12193156 · Cited by 12
Enhancing group decision-making: Maximum consensus aggregation for fuzzy cross-efficiency under hesitant fuzzy linguistic information
Song, H.-H., Wang, Y.-M., & Martínez, L. (2024) · Computers & industrial engineering · doi:10.1016/j.cie.2024.110622 · Cited by 12
Machine Learning for Optimizing Macro-ergonomics in Pharmaceutical Supply Chain
Jamali, N., Gharib, M. R., Moayyedian, M., & Hedayati-Dezfooli, M. (2024) · International Journal of Computational Intelligence Systems · doi:10.1007/s44196-024-00513-9 · Cited by 14
“Some research [24–26] has used the fuzzy data envelopment analysis (FDEA) method to analyze the efficiency of healthcare systems [7, 11, 27].”
Group decision making based on dice similarity measure and 2-dimension linguistic fuzzy weighted arithmetic aggregation operator for 2-dimension linguistic fuzzy variables
Zhu, H., Rodríguez, R., & Zhao, J. (2024) · Engineering applications of artificial intelligence · doi:10.1016/j.engappai.2024.108845 · Cited by 12
Dynamic portfolio optimization with the MARCOS approach under uncertainty
Yu, P., Ge, Z., Gong, X., & Cao, X. (2024) · International Review of Financial Analysis · doi:10.1016/j.irfa.2024.103565 · Cited by 11
A hybrid decision-making technique based on extended entropy and trapezoidal fuzzy rough number
Fatima, S., Akram, M., & Zafar, F. (2024) · Journal of Applied Mathematics and Computation · doi:10.1007/s12190-024-02150-z · Cited by 12
“In 1975, he additionally presented the concept of a linguistic variable and how it could be used in approximate reasoning [66].”
A Binary Risk Linguistic Fuzzy Behavioral TOPSIS Model for Multi-attribute Large-Scale Group Decision-Making Based on Risk Preference Classification and Adaptive Weight Updating
Huang, A., Yang, Y., & Liu, Y. (2024) · International Journal of Fuzzy Systems · doi:10.1007/s40815-024-01710-6 · Cited by 12
Modeling of limit order book data with ordered fuzzy numbers
Marszałek, A., & Burczyński, T. (2024) · Applied Soft Computing · doi:10.1016/j.asoc.2024.111555 · Cited by 12
A Fuzzy Inference Model to Identify the Current Industry Maturity Stage in the Transformation Process to Industry 4.0
Gomes, A. D. O., & Basilio, J. C. (2024) · IEEE Transactions on Automation Science and Engineering · doi:10.1109/tase.2023.3242225 · Cited by 12
“Truth is actually a linguistic variable whose truth-values are taken from fuzzy numbers representing terms such as true, not true, completely true, essentially true, fairly true, more or less true, etc. [20], [21].”
Background
An extended COPRAS method based on complex q-rung orthopair fuzzy 2-tuple linguistic Maclaurin symmetric mean aggregation operators
Naz, S., Mehreen, R., Abbas, T., Piñeres-Espitia, G., & Butt, S. A. (2024) · Journal of Ambient Intelligence and Humanized Computing · doi:10.1007/s12652-023-04742-2 · Cited by 12
“…problems, linguistic variables (LVs) offer a feasible solution since DMs may ﬁnd it challenging to provide crisp numbers for MD and NMD associated with some LVs. Linguistic MAGDM problems have witnessed many developments since Zadeh Zadeh (1975) established LV theory to address such problems.”
A dynamic system‐based model for analyzing human factors: Enhanced AcciMap with spherical fuzzy dynamic Bayesian network approach
Ghalenoei, M., Zarei, E., Tohidizadeh, K., Yazdi, M., & Kolivand, K. (2024) · Human Factors and Ergonomics in Manufacturing & Service Industries · doi:10.1002/hfm.21029 · Cited by 12
“In addition to conventional fuzzy sets, various other types have emerged, such as type 2 fuzzy sets (Zadeh, 1975), distance value fuzzy sets (Sambuc, 1975), multiple fuzzy sets (Yager, 1986), and intuitive fuzzy sets (Szmidt & Kukier, 2008).”
Method
Optimizing traveling salesman problem using tabu search metaheuristic algorithm with Pythagorean fuzzy uncertainty
Habib, A., & Akram, M. (2024) · Granular Computing · doi:10.1007/s41066-023-00424-8 · Cited by 12
“In 1975, Zadeh (1975) introduced these FNs to deal with imprecise numerical quantities.”
A 2-additive Choquet integral-based multi-criterion decision-making method with complex linguistic information in drug value assessment
Fang, R., & Liao, H.-C. (2024) · Applied Soft Computing · doi:10.1016/j.asoc.2023.111198 · Cited by 12
Streamlining apartment provider evaluation: A spherical fuzzy multi-criteria decision-making model
Nguyen, P.-H., Tran, T.-H., Nguyen, L.-A. T., Pham, H., & Pham, M.-A. T. (2023) · Heliyon · doi:10.1016/j.heliyon.2023.e22353 · Cited by 12

Authors: Zadeh, L. A.
Affiliations: University of California, Berkeley (US)
Corresponding author: Zadeh, L.A.
Venue: Information Sciences
Publisher: Elsevier BV
Published: 1975
Volume: 8
Issue: 3
Pages: 199-249
ISSN: 0020-0255 (ISSN-L)
DOI: 10.1016/0020-0255(75)90036-5
OpenAlex: W4245152641
Cited by: 12,187
References: 48
Citations by year: 2026: 309 · 2025: 516 · 2024: 569 · 2023: 707 · 2022: 682 · 2021: 746 · 2020: 693 · 2019: 759 · 2018: 655 · 2017: 598 · 2016: 551 · 2015: 546 · 2014: 484 · 2013: 437 · 2012: 367
FWCI: 13.65
Type: journal article
Language: en
Open access: closed
Licence: www.elsevier.com/tdm/userlicense/1.0/ (tdm)
www.elsevier.com/legal/tdmrep-license (tdm)
Locations: Information Sciences (publishedVersion)
Funders: Army Research Office (DA-ARO-D-31-124-7 l-G1 74)
National Science Foundation (GK-VP-610656X3)
Topics: Physical Sciences › Computer Science › Artificial Intelligence › Fuzzy Logic and Control Systems
Physical Sciences › Computer Science › Computational Theory and Mathematics › Advanced Algebra and Logic
Physical Sciences › Computer Science › Artificial Intelligence › Mathematical Control Systems and Analysis
Keywords: linguistic variables, approximate reasoning, fuzzy logic, compatibility function, hedges, linguistic truth values, nonlinear programming, human decision-making, fuzzy sets, artificial intelligence

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