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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Pamucar, D., Deveci, M., Gokasar, I., Delen, D., Köppen, M., & Pedrycz, W. (2023) · Decision Support Systems · doi:10.1016/j.dss.2023.113944 · Cited by 73
Model‐based evaluation for online shopping platform with probabilistic double hierarchy linguistic CODAS method
Lei, F., Wei, G., & Chen, X.-D. (2021) · International Journal of Intelligent Systems · doi:10.1002/int.22514 · Cited by 73
“Then, Equations (15) and (16) calculate the normalized probabilistic double hierarchy linguistic prospect weights.”
Background
A Probabilistic Linguistic Three-Way Decision Method With Regret Theory via Fuzzy c-Means Clustering Algorithm
Zhu, J., Ma, X., Martínez, L. M., & Zhan, J. (2023) · IEEE Transactions on Fuzzy Systems · doi:10.1109/tfuzz.2023.3236386 · Cited by 99
“Facedwiththisscenario,Zadeh[12]initiatedtheconceptof linguisticvariables,whichismorerelevanttopeople’sthinking habits.”
Novel Aczel–Alsina operations-based hesitant fuzzy aggregation operators and their applications in cyclone disaster assessment
Senapati, T., Chen, G.-Y., Mesiar, R., Yager, R., & Saha, A. (2022) · International Journal of General Systems · doi:10.1080/03081079.2022.2036140 · Cited by 71
“As a result, some new methodologies and hypotheses have been considered to be extensions of the FS hypothesis, for example, interval-valued FS (Zadeh 1975), intuitionistic FS (Atanassov 1986), fuzzy multiset (Yager 1986), and Type-2 FS (Dubois and Prade 1980).”
Background
An interval type-2 fuzzy Kano-prospect-TOPSIS based QFD model: Application to Chinese e-commerce service design
Wu, T., Liu, X., Qin, J., & Herrera, F. (2021) · Applied Soft Computing · doi:10.1016/j.asoc.2021.107665 · Cited by 79
Application of Choquet integral in interval type‐2 Pythagorean fuzzy sustainable supply chain management under risk
Mondal, A., & Roy, S. (2021) · International Journal of Intelligent Systems · doi:10.1002/int.22623 · Cited by 71
“Steps 3 and 4: The normalized decision matrix is obtained using Equations (31) (for E1, E3 and G2) and (32) (for E2, G1, S1 and S2).”
MethodInfluential
Circular intuitionistic fuzzy TOPSIS method with vague membership functions: Supplier selection application context
Kahraman, C., & Alkan, N. (2021) · Notes on Intuitionistic Fuzzy Sets · doi:10.7546/nifs.2021.27.1.24-52 · Cited by 70
“Type-2 fuzzy sets have been introduced by Zadeh [43] to handle the vagueness in membership functions as an extension of ordinary fuzzy sets.”
MethodInfluential
Offshore wind power station (OWPS) site selection using a two-stage MCDM-based spherical fuzzy set approach
Wang, C.-N., Nguyen, N.-A.-T., & Dang, T.-T. (2022) · Scientific Reports · doi:10.1038/s41598-022-08257-2 · Cited by 69
Fuzzy Deep Learning for the Diagnosis of Alzheimer's Disease: Approaches and Challenges
Tanveer, M., Sajid, M., Akhtar, M., Quadir, A., Goel, T., Aimen, A., Mitra, S., Zhang, Y., Lin, C., & Ser, J. D. (2024) · IEEE Transactions on Fuzzy Systems · doi:10.1109/tfuzz.2024.3409412 · Cited by 86
“The focal points in fuzzy systems research involve three primary fuzzy techniques: the fuzzy set (referred to as type-1 fuzzy set) [28], the type-2 fuzzy set [34], and the linguistic variable [35].”
Background
Circular Intuitionistic Fuzzy Decision Making and Its Application
Çakır, E., & Taş, M. (2023) · Expert systems with applications · doi:10.1016/j.eswa.2023.120076 · Cited by 68
Extended CODAS method for multi-attribute group decision-making based on 2-tuple linguistic Fermatean fuzzy Hamacher aggregation operators
Akram, M., Niaz, Z., & Feng, F. (2022) · Granular Computing · doi:10.1007/s41066-022-00332-3 · Cited by 68
“To present the verbal preference, Zadeh (1975) introduced the concept of linguistic variables (LVs).”
Computational prediction of the drilling rate of penetration (ROP): A comparison of various machine learning approaches and traditional models
Brenjkar, E., & Delijani, E. B. (2021) · Journal of Petroleum Science and Engineering · doi:10.1016/j.petrol.2021.110033 · Cited by 75
An optimisation-based method to conduct consistency and consensus in group decision making under probabilistic uncertain linguistic preference relations
Song, Y., Li, G.-X., Ergu, D., & Liu, N. (2021) · Journal of the Operational Research Society · doi:10.1080/01605682.2021.1873079 · Cited by 68
“The use of linguistic terms or fuzzy numbers to evaluate qualitative variables is an intuitive and flexible approach, because they conform to people’s cognitive process and reasoning (Li, Kou, Lin et al., 2015; Li, Kou & Peng, 2015; Zadeh, 1975; Zhao et al., 2018).”
Method
An Incentive Mechanism-Based Minimum Adjustment Consensus Model Under Dynamic Trust Relationship
Xing, Y., Wu, J., Chiclana, F., Liang, C., & Yager, R. R. (2024) · IEEE Transactions on Cybernetics · doi:10.1109/tcyb.2023.3349257 · Cited by 67
“…pair ξ = In GDM, experts may express their preferences using terms from a set of ordinal linguistic terms: S = { s 0 , s 1 , . . . , s r } ( r even) such that s 0 s 1 · · · s r , s ( r / 2 ) represents indifference of preference, and negator operator neg ( s a ) = s r − a [57], [58], [59].”
Method
Efficiency evaluation with regret-rejoice cross-efficiency DEA models under the distributed linguistic environment
Jin, F.-F., Cai, Y., Pedrycz, W., & Liu, J.-P. (2022) · Computers & industrial engineering · doi:10.1016/j.cie.2022.108281 · Cited by 67
Analysis of evolutionary process in intuitionistic fuzzy set theory: A dynamic perspective
Yu, D., Sheng, L.-B., & Xu, Z.-S. (2022) · Information Sciences · doi:10.1016/j.ins.2022.04.019 · Cited by 67
Circular intuitionistic fuzzy TOPSIS method: pandemic hospital location selection
Alkan, N., & Kahraman, C. (2021) · Journal of Intelligent & Fuzzy Systems · doi:10.3233/jifs-219193 · Cited by 67
“Later, q-rung orthopair fuzzy sets (Q-ROFSs) have been proposed as a general class of IFSs and PFSs by Yager [52].”
Retracted
A novel interval-valued fuzzy soft decision-making method based on CoCoSo and CRITIC for intelligent healthcare management evaluation
Peng, X.-D., Krishankumar, R., & Ravichandran, K. (2021) · Soft Computing - A Fusion of Foundations, Methodologies and Applications · doi:10.1007/s00500-020-05437-y · Cited by 67
“Definition 1 (Zadeh 1975) An interval-valued fuzzy set (IVFS) I in U is given by I = {< χ, [I−(χ), I+(χ)] >| χ ∈ U }, (1) where 0 ≤ I−(χ) ≤ I+(χ) ≤ 1.”
An integrated MCDM framework for evaluating the environmental, social, and governance (ESG) sustainable business performance
Yu, K., Wu, Q., Chen, X., Wang, W.-Z., & Mardani, A. (2023) · Annals of Operations Research · doi:10.1007/s10479-023-05616-8 · Cited by 66
“However, because the traditional type-1 fuzzy sets (T1FSs) have unavoidable limitations in dealingwithuncertaininformation,Zadeh(1975)proposedtype-2fuzzysets(T2FSs)tosolve theproblemofuncertainty.”
A hybrid decision-making method using robust programming and interval-valued fuzzy sets for sustainable-resilient supply chain network design considering circular economy and technology levels
Foroozesh, N., Karimi, B., Mousavi, S., & Mojtahedi, M. (2023) · Journal of Industrial Information Integration · doi:10.1016/j.jii.2023.100440 · Cited by 66
Unit consensus cost-based approach for group decision-making with incomplete probabilistic linguistic preference relations
Liu, P.-D., Dang, R., Wang, P., & Wu, X.-M. (2023) · Information Sciences · doi:10.1016/j.ins.2022.12.114 · Cited by 66
A new approach for spherical fuzzy TOPSIS and spherical fuzzy VIKOR applied to the evaluation of hydrogen storage systems
Sharaf, I. (2022) · Soft Computing - A Fusion of Foundations, Methodologies and Applications · doi:10.1007/s00500-022-07749-7 · Cited by 66
“Several researchers developed other types of fuzzy sets besides Zadeh’s type 1 (T1FSs) and type 2 (T2FSs) ordinary fuzzy sets (Zadeh 1965, 1975).”
Background
An outranking approach with 2-tuple linguistic Fermatean fuzzy sets for multi-attribute group decision-making
Akram, M., Bibi, R., & Deveci, M. (2023) · Engineering applications of artificial intelligence · doi:10.1016/j.engappai.2023.105992 · Cited by 65
Possibilistic classification by support vector networks
Hao, P.-Y., Chiang, J.-H., & Chen, Y. (2022) · Neural Networks · doi:10.1016/j.neunet.2022.02.007 · Cited by 71
Numerical approach in the Hilbert space to solve a fuzzy Atangana-Baleanu fractional hybrid system
Hasan, S., Al-Smadi, M., El-Ajou, A., Momani, S., Hadid, S., & Al-Zhour, Z. (2021) · doi:10.1016/j.chaos.2020.110506 · Cited by 65
Evaluation of Sustainable Development and Utilization-Oriented Renewable Energy Systems based on CRITIC-SWARA-CODAS Method Using Interval Valued Picture Fuzzy Sets
Alkan, N. (2023) · Sustainable Energy, Grids and Networks · doi:10.1016/j.segan.2023.101263 · Cited by 64
Measuring sustainability, resilience and livability performance of European smart cities: A novel fuzzy expert-based multi-criteria decision support model
KUTTY, A. A. K. A., Küçükvar, M., Onat, N. C., Ayvaz, B., & Abdella, G. M. (2023) · Cities · doi:10.1016/j.cities.2023.104293 · Cited by 81
An intuitionistic fuzzy multi-distance based evaluation for aggregated dynamic decision analysis (IF-DEVADA): Its application to waste disposal location selection
Alkan, N., & Kahraman, C. (2022) · Engineering applications of artificial intelligence · doi:10.1016/j.engappai.2022.104809 · Cited by 64
A MCDM framework for site selection of island photovoltaic charging station based on new criteria identification and a hybrid fuzzy approach
Dang, R., Li, X.-M., Li, C.-T., & Xu, C. (2021) · doi:10.1016/j.scs.2021.103230 · Cited by 64
An extended hesitant fuzzy set using SWARA-MULTIMOORA approach to adapt online education for the control of the pandemic spread of COVID-19 in higher education institutions
Saraji, M. K., Mardani, A., Köppen, M., Mishra, A., & Rani, P. (2021) · Artificial Intelligence Review · doi:10.1007/s10462-021-10029-9 · Cited by 64
“Recently, it is worth mentioning that the HFSs have powerfully related to the existing FSs, namely, Intuitionistic Fuzzy Sets (IFSs) (Atanassov 1986), Type-2 Fuzzy Sets (T2FSs) (Zadeh 1975), Fuzzy Multi-Sets (FMSs) (Yager 1986).”
Background
RETRACTED ARTICLE: The optimal project selection in portfolio management using fuzzy multi-criteria decision-making methodology
Mohammed, H. J. (2021) · Journal of Sustainable Finance & Investment · doi:10.1080/20430795.2021.1886551 · Cited by 64
“RE TR AC TE D compositional rule of inference (Zadeh 1975) to draw conclusions from the fuzzy rule sets.”
BackgroundInfluential
Retracted
Achieving a Balance Between Privacy Protection and Data Collection: A Field Experimental Examination of a Theory-Driven Information Technology Solution
Liu, B., Pavlou, P. A., & Cheng, X. (2021) · Information Systems Research · doi:10.1287/isre.2021.1045 · Cited by 73
Deep learning in economics: a systematic and critical review
Zheng, Y., Xu, Z., & Xiao, A. (2023) · Artificial Intelligence Review · doi:10.1007/s10462-022-10272-8 · Cited by 73
“Meanwhile, the combination of linguistic variables and economics assists to collect much natural linguistic information and reveal some undiscovered laws of economic motion (Zadeh, 1975).”
Background
A framework of LR fuzzy AHP and fuzzy WASPAS for health care waste recycling technology
Chakraborty, S., & Saha, A. K. (2022) · Applied Soft Computing · doi:10.1016/j.asoc.2022.109388 · Cited by 62
Risk assessment of renewable energy-based island microgrid using the HFLTS-cloud model method
Wu, Y., Hu, M., Liao, M., Liu, F., & Xu, C. (2020) · Journal of Cleaner Production · doi:10.1016/j.jclepro.2020.125362 · Cited by 64
A reliability-based consensus model and regret theory-based selection process for linguistic hesitant-Z multi-attribute group decision making
Mondal, A., Roy, S., & Zhan, J.-M. (2023) · Expert systems with applications · doi:10.1016/j.eswa.2023.120431 · Cited by 61

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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