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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“To represent qualitative aspect by using linguistic variables (LVs), linguistic approach (Zadeh 1975) is one of the best technique.”
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“We have fuzzy -neighborhoods, for example, In Zadeh (1975), Zadeh proposed the extension principle, which has become an important tool in fuzzy set theory and its applications.”
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“introduced the fuzzy linguistic approach in which the experts express their opinions in terms of linguistic terms, such as low, high, weak, strong, very good, and excellent [39].”
Background
A New Picture Fuzzy Entropy and Its Application Based on Combined Picture Fuzzy Methodology with Partial Weight Information
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“A linguistic variable is a variable whose values are words or phrases commonly used in a natural language or an artificial language (Zadeh 1975).”
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Background
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“Definition 2.2 (Zadeh 1975a) Let S ¼ sjjj ¼ 0; 1; :::; s be a finite linguistic term set with odd cardinality. sj has the following features: (1) Ordered set: sj [ sk; if j[ k; (2) negation ðsjÞ ¼ sk such that jþ k ¼ s: (3) max sj; sk ¼ sj if j k (4) min sj; sk ¼ sj if j k Definition 2.3 (Jin et…”
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Xu, X.-Q., Xie, J.-L., Wang, H.-H., & Lin, M.-W. (2022) · Applied intelligence (Boston) · doi:10.1007/s10489-022-03289-7 · Cited by 28
“Concerning uncertain linguistic information, Zadeh [4] introduced the fuzzy linguistic approach, which uses the linguistic variables to represent the qualitative information and enhance the adaptability and reliability of decision models.”
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A stochastic cross-efficiency DEA approach based on the prospect theory and its application in winner determination in public procurement tenders
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“Thefuzzylinguisticapproach(Zadeh,1975)isaﬂexibletooltorep-resentqualitativeinformationsinceitisclosetopeople’scognition.”
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Xiong, S.-H., Chen, Z.-S., Chiclana, F., Chin, K., & Skibniewski, M. (2021) · International Journal of Intelligent Systems · doi:10.1002/int.22714 · Cited by 28
“Zadeh 35 introduced the concept of linguistic variable as an approximate technique that represents qualitative information by means of linguistic labels.”
Background
A novel deep interval type-2 fuzzy LSTM (DIT2FLSTM) model applied to COVID-19 pandemic time-series prediction
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Background
Probabilistic linguistic q‐rung orthopair fuzzy Generalized Dombi and Bonferroni mean operators for group decision‐making with unknown weights of experts
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Towards interval uncertainty propagation control in bivariate aggregation processes and the introduction of width-limited interval-valued overlap functions
Asmus, T. D. C., Dimuro, G., Bedregal, B., Sanz, J., Mesiar, R., & Bustince, H. (2021) · Fuzzy Sets Syst. · doi:10.1016/j.fss.2021.09.005 · Cited by 28
“One possible solution is the adoption of interval-valued fuzzy sets (IVFSs) [21, 22, 23], where the membership degrees are represented by intervals.”
Background
Inclusion and similarity measures for interval-valued fuzzy sets based on aggregation and uncertainty assessment
Pe¸kala, B., Dyczkowski, K., Grzegorzewski, P., Grzegorzewski, P., & Bentkowska, U. (2021) · Information Sciences · doi:10.1016/j.ins.2020.09.072 · Cited by 28
A global optimization feedback model with PSO for large scale group decision making in hesitant fuzzy linguistic environments
Zhao, M., Guo, J., Wu, J., & Xu, Z.-S. (2023) · Expert systems with applications · doi:10.1016/j.eswa.2023.120320 · Cited by 27
A Type-3 Fuzzy Parameter Adjustment in Harmony Search for the Parameterization of Fuzzy Controllers
Peraza, C., Castillo, O., Melin, P., Castro, J. R., Yoon, J., & Geem, Z. (2023) · International Journal of Fuzzy Systems · doi:10.1007/s40815-023-01499-w · Cited by 27
“Interval type-2 fuzzy theory [11] has shown that its applicability has been quite successful in a plethora of areas, such as traffic problems [12], energy [13], medicine [14], control problems [15, 16], adaptation of parameters in & Zong Woo Geem geem@gachon.”
Background
A new last aggregation fuzzy compromise solution approach for evaluating sustainable third-party reverse logistics providers with an application to food industry
Mohammadkhani, A., & Mousavi, S. (2022) · Expert systems with applications · doi:10.1016/j.eswa.2022.119396 · Cited by 27
BIM-aided large-scale group decision support: Optimization of the retrofit strategy for existing buildings
Chen, Z.-S., Yang, L.-P., Rodríguez, R. M., Zhu, Z., Pedrycz, W., & Skibniewski, M. (2022) · Applied Soft Computing · doi:10.1016/j.asoc.2022.109790 · Cited by 27
T-spherical uncertain linguistic MARCOS method based on generalized distance and Heronian mean for multi-attribute group decision-making with unknown weight information
Wang, H., & Ullah, K. (2022) · Complex & Intelligent Systems · doi:10.1007/s40747-022-00862-y · Cited by 27
“Especially when assessing system performance, the decision-makers prefer to use linguistic evaluation [3, 4], such as “good”, “very likely”, “low”, etc.”
Background
COVID-19 medical waste transportation risk evaluation integrating type-2 fuzzy total interpretive structural modeling and Bayesian network
Tang, J., Liu, X.-W., & Wang, W. (2022) · Expert systems with applications · doi:10.1016/j.eswa.2022.118885 · Cited by 27
“To describe the different opinions about the same word, Zadeh (1975) proposed the type-2 fuzzy sets (T2FS).”
Background
A new maximal flow algorithm for solving optimization problems with linguistic capacities and flows
Akram, M., Habib, A., & Allahviranloo, T. (2022) · Information Sciences · doi:10.1016/j.ins.2022.08.068 · Cited by 27
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“To increase the interpretability of these variables, we propose the use of fuzzy linguistic variables which were originally proposed by Zadeh [8].”
Integrated BWM-Entropy weighting and MULTIMOORA method with probabilistic linguistic information for the evaluation of Waste Recycling Apps
Ma, Y., Zhao, Y., Wang, X.-Y., Feng, C., Zhou, X.-Y., & Lev, B. (2022) · Applied intelligence (Boston) · doi:10.1007/s10489-022-03377-8 · Cited by 27
A Fuzzy Inference System for the Assessment of Indoor Air Quality in an Operating Room to Prevent Surgical Site Infection
Colella, Y., Valente, A., Rossano, L., Trunfio, T., Fiorillo, A., & Improta, G. (2022) · International Journal of Environmental Research and Public Health · doi:10.3390/ijerph19063533 · Cited by 27
“All the designed clinical linguistic variables, membership functions, and rules have been included in a Mamdani FIS [40,41].”
BackgroundMethod
An improved type-reduction algorithm for general type-2 fuzzy sets
Wu, L., Qian, F., Wang, L.-Z., & Ma, X.-H. (2022) · Information Sciences · doi:10.1016/j.ins.2022.01.078 · Cited by 27
Sustainable industrialization performance evaluation of European Union countries: an integrated spherical fuzzy analytic hierarchy process and grey relational analysis approach
Candan, G., & Toklu, M. C. (2022) · International Journal of Sustainable Development and World Ecology · doi:10.1080/13504509.2022.2027293 · Cited by 27
An extended gained and lost dominance score method based risk prioritization for Fine-Kinney model with interval type-2 fuzzy information
Wang, W., Jiang, W., Han, X., & Liu, S. (2022) · Human and Ecological Risk Assessment · doi:10.1080/10807039.2021.2023807 · Cited by 27
“The type-2 fuzzy sets (T2FSs), originally proposed by Zadeh (1975), is a more effective and useful technique to depict the complex uncertain information, compared with the type-1 fuzzy sets (T1FSs).”
Background
Multi-criteria prioritization of the renewable power plants in Australia using the fuzzy logic in decision-making method (FMCDM)
Aryanfar, A., Gholami, A., Ghorbannezhad, P., Yeganeh, B., Pourgholi, M., Zandi, M., & Stevanovic, S. (2021) · Clean Energy · doi:10.1093/ce/zkab048 · Cited by 27
“Thus, the mentioned influential parameters are generally expressed using linguistic variables [26].”
Background
The Impact of the COVID-19 Pandemic on College Students: An Online Survey
Tran, T. K., Dinh, H. M., Nguyen, H., Le, D., Nguyen, D.-K., Tran, A. C., Việt, N. H., Thu, H. N. T., Hung, D., Tieu, S., et al. (2021) · Sustainability · doi:10.3390/su131910762 · Cited by 33
Linguistic single‐valued neutrosophic soft sets with applications in game theory
Kamacı, H. (2021) · International Journal of Intelligent Systems · doi:10.1002/int.22445 · Cited by 27
A Clinical Decision Support System based on fuzzy rules and classification algorithms for monitoring the physiological parameters of type-2 diabetic patients
Colella, Y., Chiara, D. L., Improta, G., Rossano, L., Vecchione, D., Spinosa, T., Giordano, V., Ciro, V., & Santini, S. (2021) · Mathematical Biosciences & Engineering · doi:10.3934/mbe.2021135 · Cited by 81
Linguistic interval-valued q-rung orthopair fuzzy TOPSIS method for decision making problem with incomplete weight
Khan, M. S. A., Khan, A. S., Khan, I., Mashwani, W. K., & Hussain, F. (2021) · Journal of Intelligent & Fuzzy Systems · doi:10.3233/jifs-200845 · Cited by 27
“To overcome this limitation, the idea of linguistic term set (LTS) was ﬁrst introduced by Zadeh [36, 37].”
Advancements and Challenges in Mobile Robot Navigation: A Comprehensive Review of Algorithms and Potential for Self-Learning Approaches
Mahmud, S. A., Kamarulariffin, A., Ibrahim, A., & Mohideen, A. J. H. (2024) · Journal of Intelligent and Robotic Systems · doi:10.1007/s10846-024-02149-5 · Cited by 26
“One extensively utilized approach is fuzzy logic, which was presented by Zadeh [34], and has been shown to be quite useful in operating mobile robots.”
Trust Risk Test-Based Group Consensus With Probabilistic Linguistic Preference Relations Under Social Networks
Han, X.-R., Zhan, J.-M., Xu, Z.-S., & Martínez, L. (2024) · IEEE transactions on fuzzy systems · doi:10.1109/tfuzz.2024.3377126 · Cited by 26
“Introduced by Zadeh [23], the fuzzy linguistic method employed linguistic term sets (LTS) to capture the vagueness and plurality of concepts.”
Method
BWM Integrated VIKOR method using Neutrosophic fuzzy sets for cybersecurity risk assessment of connected and autonomous vehicles
Tanaji, B. A., & Roychowdhury, S. (2024) · Applied Soft Computing · doi:10.1016/j.asoc.2024.111628 · Cited by 32
Three-way group consensus method based on probabilistic linguistic preference relations with acceptable inconsistency
Han, X.-R., Zhan, J.-M., Bao, Y.-K., & Sun, B. (2024) · Information Fusion · doi:10.1016/j.inffus.2023.102100 · Cited by 26
A Type-2 fuzzy hybrid preference optimization methodology for electric vehicle charging station location
Men, J., & Zhao, C. M. (2024) · Energy · doi:10.1016/j.energy.2024.130701 · Cited by 28
A Review on Intelligent Control Theory and Applications in Process Optimization and Smart Manufacturing
Lee, M. R. (2023) · Processes · doi:10.3390/pr11113171 · Cited by 37
“This introduces a more intricate layer to address greater uncertainties than type-1 systems [107,108].”
Background
Group decision-making method based on advanced aggregation operators with entropy and divergence measures under 2-tuple linguistic Pythagorean fuzzy environment
Verma, R., & Álvarez‐Miranda, E. (2023) · Expert systems with applications · doi:10.1016/j.eswa.2023.120584 · Cited by 26
When content-centric networking meets multi-criteria group decision-making: Optimal cache placement policy achieved by MARCOS with q-rung orthopair fuzzy set pair analysis
Peng, X.-D., Garg, H., & Luo, Z. (2023) · Engineering applications of artificial intelligence · doi:10.1016/j.engappai.2023.106231 · Cited by 26
2-tuple Linguistic Decision-making with Consistency Adjustment Strategy and Data Envelopment Analysis
Jin, F.-F., Guo, S.-Y., Cai, Y., Liu, J.-P., & Zhou, L.-G. (2023) · Engineering applications of artificial intelligence · doi:10.1016/j.engappai.2022.105671 · Cited by 26
Intelligent Fractional Order Sliding Mode Based Control for Surgical Robot Manipulator
Sachan, S., & Swarnkar, P. (2023) · Electronics · doi:10.3390/electronics12030729 · Cited by 28
Design of an interval type-2 fuzzy neural network sliding mode robust controller for higher stability of magnetic spacecraft attitude control.
Liu, X., Zhao, T.-Y., Cao, J.-T., & Li, P. (2023) · ISA transactions · doi:10.1016/j.isatra.2023.01.011 · Cited by 26
The Evaluation of Creditworthiness of Trade and Enterprises of Service Using the Method Based on Fuzzy Logic
Makhazhanova, U., Kerimkhulle, S., Mukhanova, A., Bayegizova, A., Aitkozha, Z., Mukhiyadin, A., Tassuov, B., Saliyeva, A., Taberkhan, R., & Azieva, G. (2022) · Applied Sciences · doi:10.3390/app122211515 · Cited by 26
“In the general case, we assume that any parameter takes values on a certain interval of real numbers [18].”
Background
Interpretable Mamdani neuro-fuzzy model through context awareness and linguistic adaptation
Navarro-Almanza, R., Sanchez, M. A., Castro, J. R., Mendoza, O. D., & Licea, G. (2021) · Expert Systems with Applications · doi:10.1016/j.eswa.2021.116098 · Cited by 26
The Bioeconomy in emerging economies: a study of the critical success factors based on Life Cycle Assessment and Delphi and Fuzzy-Delphi methods
Rampasso, I. S., Quelhas, O. L. G., Anholon, R., Silva, D. A. L., Pontes, A. T., Miranda, J. D. A., & Dias, J. O. (2021) · The International Journal of Life Cycle Assessment · doi:10.1007/s11367-021-01913-1 · Cited by 31
“Initially proposed by Zadeh (1965, 1975), the fuzzy set theory can capture answers’ uncertainties (Shen et al.”
Background
Interval-valued Fuzzy Logic approach for overloaded hosts in consolidation of virtual machines in cloud computing
Moura, B. M. P., Schneider, G., Yamin, A., Santos, H., Reiser, R., & Bedregal, B. (2021) · Fuzzy Sets Syst. · doi:10.1016/j.fss.2021.03.001 · Cited by 26
The trust incentive mechanism by trust propagation to optimize consensus in social network group decision making
Xing, Y., Wang, S., Dong, Y., Liu, Y., & Wu, J. (2024) · Expert systems with applications · doi:10.1016/j.eswa.2024.125111 · Cited by 25
Towards green logistics: An innovative decision support model for zero-emission transportation modes development
Moktadir, M. A., & Ren, J. (2024) · Transportation Research Part E: Logistics and Transportation Review · doi:10.1016/j.tre.2024.103648 · Cited by 25
Novel similarity measure between hesitant fuzzy set and their applications in pattern recognition and clustering analysis
Gupta, R., & Kumar, S. (2024) · Journal of engineering and applied sciences · doi:10.1186/s44147-023-00329-y · Cited by 25
“Consequently, some new strategies for-instance Intuitionistic fuzzy set (IFS) suggested by Atanassov [3], interval-valued fuzzy set by Zadeh [4], Type 2 fuzzy set introduced by Dubois [5] and fuzzy multi-set by Yager [6] were suggested which are the expansion of FS.”
Method
Data-Driven Interval Type-2 Fuzzy Inference System Based on the Interval Type-2 Distending Function
Dombi, J., & Hussain, A. (2023) · IEEE transactions on fuzzy systems · doi:10.1109/tfuzz.2022.3224793 · Cited by 25
“Type-2 fuzzy systems (T2FSs) were developed to handle the uncertainty in type-1 fuzzy sets [21], [22].”
Background
Extended group decision-making methods with 2-tuple linguistic Fermatean fuzzy sets
Akram, M., Shahzadi, S., Bibi, R., & Santos-García, G. (2023) · Soft Computing - A Fusion of Foundations, Methodologies and Applications · doi:10.1007/s00500-023-08158-0 · Cited by 25
A Framework of Intelligent Mental Health Monitoring in Smart Cities and Societies
Chakraborty, A., Banerjee, J., Bhadra, R., Dutta, A., Ganguly, S., Das, D., Kundu, S., Mahmud, M., & Saha, G. (2023) · Journal of the Institution of Electronics and Telecommunication Engineers · doi:10.1080/03772063.2023.2171918 · Cited by 25
“As an expansion of the idea of a typical fuzzy set, or a type-1 fuzzy set, Zadeh [41] developed the idea of type-2 fuzzy sets.”
Method
An integrated decision support method for strategic planning and tactical management of regional biomass power plants under uncertainties
Ji, L., Zheng, Z.-X., Huang, Y.-N., Xie, Y.-L., Sun, L.-J., & Huang, G.-H. (2023) · Journal of Cleaner Production · doi:10.1016/j.jclepro.2023.135968 · Cited by 25
A Granular Computing-Driving Hesitant Fuzzy Linguistic Method for Supporting Large-Scale Group Decision Making
Zheng, Y., Xu, Z.-S., & Pedrycz, W. (2022) · IEEE Transactions on Systems, Man & Cybernetics. Systems · doi:10.1109/tsmc.2021.3093467 · Cited by 25
“During the comparison process, qualitative expression in the form of linguistic variables [36] such as “a little better than” or “much worse than” is more straightforward for experts to express opinions.”
Background
Ranked hesitant fuzzy sets for multi-criteria multi-agent decisions
Alcantud, J. (2022) · Expert systems with applications · doi:10.1016/j.eswa.2022.118276 · Cited by 25
Integrated modelling approach for an eco-industrial park site selection
Nuhu, S. K., Manan, Z. A., Alwi, S. R. W., & Reba, M. N. M. (2022) · Journal of Cleaner Production · doi:10.1016/j.jclepro.2022.133141 · Cited by 25
Linguistic information-based granular computing based on a tournament selection operator-guided PSO for supporting multi-attribute group decision-making with distributed linguistic preference relations
Huang, T., Tang, X.-A., Zhao, S.-Y., Zhang, Q., & Pedrycz, W. (2022) · Information Sciences · doi:10.1016/j.ins.2022.07.050 · Cited by 25
An interval type-2 fuzzy axiomatic design method: A case study for evaluating blockchain deployment projects in supply chain
Gölcük, I. (2022) · Information Sciences · doi:10.1016/j.ins.2022.04.034 · Cited by 25
Development, experimental validation, and comparison of interval type-2 Mamdani fuzzy PID controllers with different footprints of uncertainty
Praharaj, M., Sain, D., & Mohan, B. (2022) · Information Sciences · doi:10.1016/j.ins.2022.03.095 · Cited by 25
A two-sided matching decision-making approach based on prospect theory under the probabilistic linguistic environment
Jia, X., Xin-fan, W., Wang, Y., & Zhou, L. (2022) · Soft Computing · doi:10.1007/s00500-022-06737-1 · Cited by 26
“The linguistic variable, initiated by Zadeh (1975), is a typical kind of qualitative information, which was extended to the linguistic term by Xu (2012).”
Background
Lifetime prolongation of a wireless charging sensor network using a mobile robot via linear Diophantine fuzzy graph environment
Prakash, K., Parimala, M., Garg, H., & Riaz, M. (2022) · Complex & Intelligent Systems · doi:10.1007/s40747-022-00653-5 · Cited by 25
“Fuzzy models are gaining popularity as they attempt to reduce the disparities among classical digital prototypes used in engineering, technology, and research and symbolic prototypes used in expert systems [23,26,30,33,44,47,53,54].”
Background
Methodology for integrated multicriteria decision-making with uncertainty: Extending the compromise ranking method for uncertain evaluation of alternatives
Juanpera, M., Domenech, B., Ferrer-Martí, L., García-Villoria, A., & Pastor, R. (2021) · Fuzzy Sets Syst. · doi:10.1016/j.fss.2021.08.008 · Cited by 25
A large-scale group decision-making method for site selection of waste to energy project under interval type-2 fuzzy environment
Pan, X., Wang, Y., & Chin, K. (2021) · Sustainable Cities and Society · doi:10.1016/j.scs.2021.103003 · Cited by 30
Efficiency Analysis with Educational Data: How to Deal with Plausible Values from International Large-Scale Assessments
Aparicio, J., Cordero, J., & Ortiz, L. (2021) · Mathematics · doi:10.3390/math9131579 · Cited by 25
An integrated multi-stage fuzzy inference performance measurement scheme in humanitarian relief operations
Anjomshoae, A., Hassan, A., Wong, K., & Banomyong, R. (2021) · International Journal of Disaster Risk Reduction · doi:10.1016/j.ijdrr.2021.102298 · Cited by 25
Generalized similarity measures under linguistic q-rung orthopair fuzzy environment with application to multiple attribute decision-making
Verma, R. (2021) · Granular Computing · doi:10.1007/s41066-021-00264-4 · Cited by 25
“If the LTS is a set of seven terms, then q ¼ s ¼ 0:8.”
BackgroundMethodInfluential
Improving the urban heritage based on a tourism risk assessment using a hybrid fuzzy MADM method: The case study of Tehran's central district
Hosseini, A., Pourahmad, A., Ayashi, A., Tzeng, G.-H., Banaitis, A., & Pourahmad, A. (2021) · Journal of Multi-Criteria Decision Analysis · doi:10.1002/mcda.1746 · Cited by 25
A new interval type-2 fuzzy logic system under dynamic environment: Application to financial investment
Takahashi, A., & Takahashi, S. (2021) · Engineering applications of artificial intelligence · doi:10.2139/ssrn.3532096 · Cited by 25

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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