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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“According to prior studies (Zadeh, 1975; Zhang & Su, 2019), triangular fuzzy numbers (TFNs) and extension principals are characterized by the following operational laws.”
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Method
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Background
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Method
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“Some FS extensions already exist, including Zadeh’s [2] interval-valued fuzzy set.”
Method
Retracted
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“…concepts and condition construction that are adopted in the consensus modeling of linguistic distribution assessments are described as follows: Zadeh (1975) innovatively proposed that the linguistic variable, which is in the form of words or sentences with a natural or artificial language,…”
Background
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“This approach allows us to mathematically model events or statements, which can be semantically assigned to multiple parameter values simultaneously [21,22].”
BackgroundMethod
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“Zadeh [21] had initiated fuzzy sets and fuzzy logic (FL).”
Background
A likelihood‐based ORESTE method for failure mode and effect analysis (FMEA) based risk analysis problem under interval type‐2 fuzzy environment
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Statistical depth for fuzzy sets
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“The definition of type-n fuzzy sets was proposed by Zadeh in 1975 [39], followed by the definition of type-2 fuzzy sets in 1976 [40].”
Method
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“Zadeh [20] discovered another idea called linguistic variables (LV) which portray the subjective data for realistic decision problems.”
Background
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An integrated fuzzy decision-making framework for autonomous mobile robot selection: balancing subjective and objective measures with fuzzy TOPSIS and picture fuzzy CoCoSo approach
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“Zadeh (1975) introduced fuzzy set theory to handle problems lacking precise criteria.”
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“So, Zadeh (1975) introduced fuzzy set theory (FS) to treat this problem effectively using a membership function.”
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Nafei, A., Huang, C.-Y., Javadpour, A., Garg, H., Azizi, S., & Chen, S.-C. (2024) · International Journal of Fuzzy Systems · doi:10.1007/s40815-023-01640-9 · Cited by 16
Computerized segmentation of MR brain tumor: an integrated approach of multi-modal fusion and unsupervised clustering
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An integrated risk and productivity assessment model for public–private partnership projects using fuzzy inference system
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On basic arithmetic operations for interval-valued intuitionistic fuzzy sets using the Hamming distance with their application in decision making
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Parametric families of continuous belief functions based on generalized Gaussian random fuzzy numbers
Denoeux, T. (2023) · Fuzzy Sets Syst. · doi:10.1016/j.fss.2023.108679 · Cited by 16
“Let (Ω , Σ Ω , P, Θ , Σ Θ , (cid:101) X ) be a RFS, and ψ : Θ → Λ a one-to-one mapping from Θ to some set Λ. Zadeh’s extension principle [29] allows us to extend mapping ψ to fuzzy subsets of Θ; speciﬁcally, we can deﬁne a mapping ψ :”
An integrated assessment of food waste model through intuitionistic fuzzy cognitive maps
Emir, O., & Ekici, Ş. Ö. (2023) · Journal of Cleaner Production · doi:10.1016/j.jclepro.2023.138061 · Cited by 17
An improved MULTIMOORA with CRITIC weights based on new equivalent transformation functions of nested probabilistic linguistic term sets
Xiao, J.-L., Xu, Z., & Wang, X.-X. (2023) · Soft Computing - A Fusion of Foundations, Methodologies and Applications · doi:10.1007/s00500-023-08218-5 · Cited by 16
“Zadeh (1975) deﬁned linguistic variables which is close to people’s expression habits.”
Background
Stock Selection System Through Suitability Index and Fuzzy-Based Quantitative Characteristics
Syu, J., Lin, J. C.-W., Wu, C.-J., & Ho, J. (2023) · IEEE transactions on fuzzy systems · doi:10.1109/tfuzz.2022.3187192 · Cited by 16
“Therefore, Zadeh [12] proposed a higher-order fuzzy-set of type-2, which is able to state uncertainty and collect more information than a unique membership value.”
Background
Group decision making with hesitant fuzzy linguistic preference relations based on multiplicative DEA cross-efficiency and stochastic acceptability analysis
Song, J., Wu, P., Liu, J.-P., & Chen, H. (2023) · Engineering applications of artificial intelligence · doi:10.1016/j.engappai.2022.105595 · Cited by 16
Triangular norms on bounded trellises
Zedam, L., & Baets, B. D. (2022) · Fuzzy Sets Syst. · doi:10.1016/j.fss.2023.01.003 · Cited by 16
“Researchers in the ﬁeld of fuzzy set theory replaced the hitherto used standard minimum operation by a t-norm, and this in virtually any theoretical development (such as Zadeh’s extension principle [28, 47]) or practical application (like in fuzzy optimization).”
Method
Cross-platform hotel evaluation by aggregating multi-website consumer reviews with probabilistic linguistic term set and Choquet integral
Zhang, Y., Liang, D., & Xu, Z. (2022) · Annals of Operations Research · doi:10.1007/s10479-022-05075-7 · Cited by 21
“The PLTS theory proposed by Pang et al. (2016) is an extension of the linguistic term set theory (Zadeh, 1975; Zhou & Xu, 2018).”
Type-2 intuitionistic fuzzy TODIM for intelligent decision-making under uncertainty and hesitancy
Shukla, A. K., Prakash, V., Nath, R., & Muhuri, P. K. (2022) · Soft Computing - A Fusion of Foundations, Methodologies and Applications · doi:10.1007/s00500-022-07482-1 · Cited by 16
“On the other hand, type-2 fuzzy sets developed by Zadeh (1975) can handle these uncertainties by blurring the membership function boundaries called foot-print of uncertainty (FOU).”
Background
Retracted
An empirical study on how humans appreciate automated counterfactual explanations which embrace imprecise information
Stepin, I., Alonso, J. M., Catalá, A., & Pereira-Fariña, M. (2022) · Information Sciences · doi:10.1016/j.ins.2022.10.098 · Cited by 22
Fuzzy Controllers of Antilock Braking System: A Review
Amirkhani, A., & Molaie, M. (2022) · International Journal of Fuzzy Systems · doi:10.1007/s40815-022-01376-y · Cited by 16
“Ten years later, in 1975, Zadeh [30] presented an upgraded version of his proposed system, which was termed as T2-FSs.”
Background
Hesitant fuzzy linguistic iterative method for consistency and consensus-driven group decision making
Ren, P., Wang, X.-X., Xu, Z.-S., & Zeng, X.-J. (2022) · Computers & industrial engineering · doi:10.1016/j.cie.2022.108673 · Cited by 16
Bipolar Complex Fuzzy Subgroups
Yang, X.-P., Mahmood, T., & Rehman, U. U. (2022) · Mathematics · doi:10.3390/math10162882 · Cited by 16
“Various researchers generalized this basic conception of FS such as intuitionistic FS [8], interval-valued FS [9], soft sets [10], etc.”
Background
Collaborative hospital supply chain network design problem under uncertainty
Dorgham, K., Nouaouri, I., Nicolas, J.-C., & Goncalves, G. (2022) · Operational Research · doi:10.1007/s12351-022-00724-y · Cited by 16
“Since the appearance of fuzzy theory (Zadeh 1965, 1974, 1978), the incorporation of fuzziness in the field of combinatorial optimization becomes a challenging problem in terms of modeling and solution.”
Background
Evaluation of Network Security Service Provider Using 2‐Tuple Linguistic Complex q‐Rung Orthopair Fuzzy COPRAS Method
Naz, S., Akram, M., Al-Shamiri, M. M. A., & Saeed, M. R. (2022) · Complex · doi:10.1155/2022/4523287 · Cited by 16
“To describe the uncertainties, Zadeh [1] introduced the fuzzy set (FS) as a generalization of the crisp set, and the value of FS lies between [ 0 , 1 ] .”
Background
A Survey on Uncertainty Reasoning and Quantification for Decision Making: Belief Theory Meets Deep Learning
Guo, Z., Wan, Z., Zhang, Q., Zhao, X.-J., Chen, F., Cho, J.-H., Zhang, Q., Kaplan, L. M., Jeong, D.-H., & Jøsang, A. (2022) · arXiv.org · doi:10.48550/arxiv.2206.05675 · Cited by 16
Evaluating readiness degree for Industrial Internet of Things adoption in manufacturing enterprises under interval-valued Pythagorean fuzzy approach
Sumrit, D. (2022) · Production & Manufacturing Research · doi:10.1080/21693277.2022.2064931 · Cited by 16
“The combination of MCDM and fuzzy set theory, namely, ‘Fuzzy Multi-Criteria Decision-Making’ (FMCDM) is an effective tool to deal with such issues (Seiti et al., 2019; Zadeh, 1975).”
Method
Computing and Clustering in the Environment of Order-2 Information Granules
Pedrycz, W. (2022) · IEEE Transactions on Cybernetics · doi:10.1109/tcyb.2022.3163350 · Cited by 16
“The term was coined in [1] and it generalizes information granules formulated in the space expressed over the space consisting of individual elements (namely, information granules of order-1).”
Background
Interval type-2 generalized fuzzy hyperbolic modelling and control of nonlinear systems
Tahamipour-Z., S. M., Akbarzadeh-T., M., & Baghbani, F. (2022) · Applied Soft Computing · doi:10.1016/j.asoc.2022.108859 · Cited by 16
ENF-S: An Evolutionary-Neuro-Fuzzy Multi-Objective Task Scheduler for Heterogeneous Multi-Core Processors
Abdi, A., & Salimi-Badr, A. (2022) · IEEE Transactions on Sustainable Computing · doi:10.1109/tsusc.2023.3244081 · Cited by 16
“Since these systems are built upon fuzzy logic, they can model uncertainty mathematically in the input variables considering them as linguistic variables [68, 47, 23].”
Background
Consensus Building for Uncertain Large-Scale Group Decision-Making Based on the Clustering Algorithm and Robust Discrete Optimization
Li, Y., Ji, Y., & Qu, S. (2022) · Group Decision and Negotiation · doi:10.1007/s10726-022-09774-1 · Cited by 16
“Many studies introduced the basic symbols and operation rules of language variables (Herrera et al. 2008; Zadeh 1975).”
Background
On computing the similarity of trapezoidal fuzzy sets using an Automated Area Method
Mendel, J. (2022) · Information Sciences · doi:10.1016/j.ins.2021.12.057 · Cited by 16
Type-2 fuzzy logic based transit priority strategy
Jovanović, A., & Teodorovic, D. (2022) · Expert systems with applications · doi:10.1016/j.eswa.2021.115875 · Cited by 16
A New TOPSIS Approach Using Cosine Similarity Measures and Cubic Bipolar Fuzzy Information for Sustainable Plastic Recycling Process
Riaz, M., Pamucar, D., Habib, A., & Riaz, M. (2021) · Mathematical Problems in Engineering · doi:10.1155/2021/4309544 · Cited by 16
“An intervalvalued fuzzy set (IVFS) [2] is the generalization of FS that assigns an interval of membership grades to the elements in the universe.”
Background
Site selection of nursing homes based on interval type-2 fuzzy AHP, CRITIC and improved TOPSIS methods
Zhang, H.-G., Bai, X., & Hong, X.-P. (2021) · Journal of Intelligent & Fuzzy Systems · doi:10.3233/jifs-212010 · Cited by 16
“In [30], Zadeh ﬁrst proposes a new fuzzy set, which complements the type 1 fuzzy set in previous literature [31].”
Solutions of matrix games involving linguistic interval-valued intuitionistic fuzzy sets
Naqvi, D. R., Verma, R., Aggarwal, A., & Sachdev, G. (2021) · Soft Computing - A Fusion of Foundations, Methodologies and Applications · doi:10.1007/s00500-022-07609-4 · Cited by 16
Heronian Mean Operators Based on Novel Complex Linear Diophantine Uncertain Linguistic Variables and Their Applications in Multi-Attribute Decision Making
Ali, Z., Mahmood, T., & Santos-García, G. (2021) · Mathematics · doi:10.3390/math9212730 · Cited by 16
“To put together it, Zadeh [1] alluded the guideline of fuzzy sets (FSs), to deal with the concerns in the information, using the TG (“Truth grade”) to explain the agreement.”
MethodInfluential
A graph model for conflict resolution with inconsistent preferences among large-scale participants
Tang, M., & Liao, H.-C. (2021) · Fuzzy Optimization and Decision Making · doi:10.1007/s10700-021-09373-w · Cited by 16
“Zadeh (Zadeh, 1975) pointed out some properties for any two linguistic terms sα and sβ : (1) The set is ordered: sα > sβ if α > β; (2) Negation operator: Neg(sα) sβ, α g − β(g + 1 is the cardinality); (3) Maximization operator: max(sα, sβ ) sα if sα ≥ sβ ; (4) Minimization operator: min(sα, sβ ) sα if sα ≤ sβ .”
MethodInfluential
Rural Fire Risk Assessment in GIS Environment Using Fuzzy Logic and the AHP Approaches
Erdin, C., & Çağlar, M. (2021) · Polish Journal of Environmental Studies · doi:10.15244/pjoes/136009 · Cited by 20
Associated Probabilities in Interactive MADM under Discrimination q-Rung Picture Linguistic Environment
Sirbiladze, G. (2021) · Mathematics · doi:10.3390/math9182337 · Cited by 16
“As is well-known, Zadeh’s linguistic variables [20] have these features to perform high quality modeling, although as Wang and Li [21] noted, linguistic variables can only describe the qualitative side of DMs’ intellectual activity.”
Method
A Type-2 Fuzzy Approach to Driver-Automation Shared Driving Lane Keeping Control of Semi-Autonomous Vehicles Under Imprecise Premise Variable
Liu, Y., Xu, Q., Guo, H.-Y., & Zhang, H. (2021) · Chinese Journal of Mechanical Engineering · doi:10.1186/s10033-022-00706-3 · Cited by 16
“The conception of type-2 fuzzy system was proposed by Zadeh in [19].”
Method

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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