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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“Since Zadeh [5] proposed the concept of linguistic term sets, the study of linguistic evaluation information on MADM problems has attached extensive attention.”
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“However, the fuzzy control is based on type-1 fuzzy sets (T1 FSs), which has some limitations in dealing with uncertain problems [24].”
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“A membership function µ M ( z i ) describes a fuzzy set M deﬁned on Z as where the function value µ M ( z i ) is referred to as the degree of membership of z i to M in Z. Deﬁnition 2 ([67,68]) .”
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“…evaluations of experts, several linguistic representation models have been proposed in the existing literature: 1) single linguistic terms [48]; 2) hesitant fuzzy linguistic terms (HFLTs) [30] and unbalanced linguistic assessments (ULAs) [3]; and 3) linguistic distribution assessments…”
Background
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“Fuzzy set (FS) theory has been successfully used to address this problem (Boosothonsatit et al., 2012; Kumar et al., 2013; Zadeh, 1975; Zadeh, 1965).”
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“After that, Zadeh extends type-1 fuzzy sets and presents type-2 fuzz sets [10].”
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“Furthermore, Rodriguez et al. (2012) brought up the hesitant fuzzy LTSs (HFLTSs) with the aid of HFSs (Torra 2010) and LTSs (Zadeh 1975) which allowed DMs to provide some possible LTSs.”
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Method
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BackgroundMethodInfluential
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“So, the concept of type-2 fuzzy sets was invented by Zadeh [39], which extends the ordinary type-1 fuzzy sets.”
Method
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“In the last few years, Zadeh’s fuzzy set theory (FST) [1] and its extensions, i.e., intuitionistic fuzzy set theory (IFST) [2], Pythagorean fuzzy set theory (PFST) [3], hesitant fuzzy set theory (HFST) [4, 5], and intervalvalued fuzzy set theory (IVFST) [6], have been proved to be efficient tools handling uncertainty…”
Method
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“This theory was introduced by Zadeh in 1965 and uses fuzzy sets to try to reproduce human behaviour under certain conditions (L. Zadeh, 1975, L. Zadeh, 1975).”
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“[6] brought up the hesitant fuzzy LTSs (HFLTSs) with the aid of HFSs [7] and LTSs [8] which allowed DMs to provide some possible LTSs.”
Method
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“When assessing or determining something, every-day language can be ambiguous and lack a clear meaning (Zadeh 1975).”
Background
A distance measure for optimistic viewpoint of the information in interval-valued intuitionistic fuzzy sets and its applications
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A novel complex fuzzy N-soft sets and their decision-making algorithm
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“1 Department of Mathematics and Statistics, International Islamic University Islamabad, Islamabad, Pakistan from researchers and got extensions such as interval-valued FSs (IvFSs) [4], intuitionistic FSs (IFSs) [5], interval-valued IFSs (IvIFSs) [6], etc.”
Background
Sustainability evaluation of photovoltaic poverty alleviation projects using an integrated MCDM method: A case study in Guangxi, China
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Multivariate data-based optimization of membrane adsorption process for wastewater treatment: Multi-layer perceptron adaptive neural network versus adaptive neural fuzzy inference system.
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A hybrid method combining three-way decision and DEA game cross-efficiency for procurement mode selection in contract farming
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Sustainable-resilient-responsive supply chain with demand prediction: An interval type-2 robust programming approach
Mondal, A., Giri, B. K., Roy, S., Deveci, M., & Pamucar, D. (2024) · Engineering applications of artificial intelligence · doi:10.1016/j.engappai.2024.108133 · Cited by 49
An automated machine-learning-assisted stochastic-fuzzy multi-criteria decision making tool: Addressing record-to-record variability in seismic design
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A multi-agent digital twin-enabled decision support system for sustainable and resilient supplier management
Li, Y.-L., Tsang, Y., Wu, C.-H., & Lee, C. K. M. (2023) · Computers & industrial engineering · doi:10.1016/j.cie.2023.109838 · Cited by 49
Consensus reaching for social network group decision making with ELICIT information: A perspective from the complex network
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A Hesitant Fuzzy Combined Compromise Solution Framework-Based on Discrimination Measure for Ranking Sustainable Third-Party Reverse Logistic Providers
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“Recently, it is revealing that the HFSs have powerfully associated to the existing concepts, namely, Intuitionistic Fuzzy Sets (IFSs) [9], Type-2 Fuzzy Sets (T2FSs) [10], and Fuzzy Multi Sets (FMSs) [11].”
Background
Multi-criteria group decision-making based on an integrated PROMETHEE approach with 2-tuple linguistic Fermatean fuzzy sets
Akram, M., & Bibi, R. (2023) · Granular Computing · doi:10.1007/s41066-022-00359-6 · Cited by 48
“The fuzzy set (FS) theory, developed by Zadeh (1965), is now more effective DM tool for coping with erroneous, unclear, or insufﬁcient information.”
Method
An efficiency-based interval type-2 fuzzy multi-criteria group decision making for makeshift hospital selection
Chen, Z.-H., Wan, S., & Dong, J.-Y. (2021) · Applied Soft Computing · doi:10.1016/j.asoc.2021.108243 · Cited by 48
“Since interval type-2 fuzzy set (IT2FS) has powerful ability in capturing uncertain and complex information by applying the secondary membership [24,26], it has been extensively concerned and applied to various decision making problems, such as supplier selections [27,28], stock selection [29], etc.”
Interval Type-2 Fuzzy Logic Controlled Shunt Converter Coupled Novel High-Quality Charging Scheme for Electric Vehicles
Balasundar, C., Sundarabalan, C. K., Srinath, N. S., & Guerrero, J. M. (2020) · IEEE Transactions on Industrial Informatics · doi:10.1109/tii.2020.3024071 · Cited by 65
“In contrast, an interval type-2 (IT2) FLS provides better results for more complex system due to its additional freedom in the degree of membership by the footprint of uncertainty in their fuzzy sets (FSs) [20].”
Background
Hybridizations of generalized Dombi operators and Bonferroni mean operators under dual probabilistic linguistic environment for group decision‐making
Saha, A., Senapati, T., & Yager, R. (2021) · International Journal of Intelligent Systems · doi:10.1002/int.22563 · Cited by 48
Interval-Valued Spherical Fuzzy Analytic Hierarchy Process Method to Evaluate Public Transportation Development
Duleba, S., Gündoǧdu, F. K., & Moslem, S. (2021) · Informatica · doi:10.15388/21-infor451 · Cited by 48
Derivation and stability analysis of the analytical structures of the interval type-2 fuzzy PID controller
El-Nagar, A. M., & El-Bardini, M. (2014) · Applied Soft Computing · doi:10.1016/j.asoc.2014.08.040 · Cited by 48
A risk analysis study for chemical cargo tank cleaning process using Fuzzy Bayesian Network
Şenol, Y. E., & Yaşlı, F. (2021) · doi:10.1016/j.oceaneng.2021.109360 · Cited by 47
VIKOR method for Pythagorean hesitant fuzzy multi-attribute decision-making based on regret theory
Zhang, N., Zhou, Y., Liu, J., & Wei, G. (2023) · Engineering applications of artificial intelligence · doi:10.1016/j.engappai.2023.106857 · Cited by 46
An integrated qualitative group decision-making method for assessing health-care waste treatment technologies based on linguistic terms with weakened hedges
Wang, L., & Wang, H. (2022) · Applied Soft Computing · doi:10.1016/j.asoc.2022.108435 · Cited by 46
Evaluation of startup companies using multicriteria decision making based on hesitant fuzzy linguistic information envelopment analysis models
Lin, M.-W., Chen, Z.-Y., Chen, R., & Fujita, H. (2021) · International Journal of Intelligent Systems · doi:10.1002/int.22379 · Cited by 46
“The fuzzy linguistic approach proposed by Zadeh 21 can help experts to express their real opinions in terms of linguistic terms, such as "great" and "excellent."”
Method
A group consensus model with prospect theory under probabilistic linguistic term sets
Wang, Y., Zhan, J., Zhang, C., & Xu, Z. (2023) · Information Sciences · doi:10.1016/j.ins.2023.119800 · Cited by 49
An interaction and feedback mechanism-based group decision-making for emergency medical supplies supplier selection using T-spherical fuzzy information
Gurmani, S. H., Zhang, Z., Zulqarnain, R. M., & Askar, S. (2023) · Scientific Reports · doi:10.1038/s41598-023-35909-8 · Cited by 48
Ranking products through online reviews: A novel data-driven method based on interval type-2 fuzzy sets and sentiment analysis
Qin, J., Zeng, M., Wei, X. L., & Witold Pedrycz, C. (2023) · Journal of the Operational Research Society · doi:10.1080/01605682.2023.2215823 · Cited by 48
“Therefore, Zadeh (1975) proposed the concept of type-2 fuzzy sets (T2FSs).”
Background
Literature review on type-2 fuzzy set theory
De, A. K., Chakraborty, D., & Biswas, A. (2022) · Soft Computing - A Fusion of Foundations, Methodologies and Applications · doi:10.1007/s00500-022-07304-4 · Cited by 45
“Although the concept of type-2 fuzzy set theory was introduced in the literature by Zadeh (1975), but due to its computational bottleneck, it has not been used so much.”
BackgroundMethodInfluential
The application of probabilistic linguistic CODAS method based on new score function in multi-criteria decision-making
Chen, L.-X., & Gou, X. (2021) · Computational and Applied Mathematics · doi:10.1007/s40314-021-01568-6 · Cited by 45
“To describe this evaluation, Rodriguez et al. (2012) put forward the concept of hesitant fuzzy linguistic term set (HFLTS), which is a combination of hesitant fuzzy sets (HFS) (Torra 2010) and fuzzy linguistic approach (FLA) (Zadeh 1975).”
BackgroundMethod
Type-2 intuitionistic fuzzy matrix games based on a new distance measure: Application to biogas-plant implementation problem
Karmakar, S., Seikh, M. R., & Castillo, O. (2021) · Applied Soft Computing · doi:10.1016/j.asoc.2021.107357 · Cited by 45
An intuitionistic fuzzy entropy approach for supplier selection
Rahimi, M., Kumar, P., Moomivand, B., & Yari, G. (2021) · Complex & Intelligent Systems · doi:10.1007/s40747-020-00224-6 · Cited by 45
An overview of fuzzy multi-criteria decision-making methods in hospitality and tourism industries: bibliometrics, methodologies, applications and future directions
Liao, H.-C., Yang, S.-S., Zavadskas, E. K., & Škare, M. (2022) · Economic Research-Ekonomska Istraživanja · doi:10.1080/1331677x.2022.2150871 · Cited by 44
“Zadeh (1975) introduced the concept of linguistic variables and advocated using natural language instead of exact values to express qualitative information.”
Background
Enhanced ELECTRE II method with 2-tuple linguistic m-polar fuzzy sets for multi-criteria group decision making
Akram, M., Noreen, U., & Deveci, M. (2022) · Expert systems with applications · doi:10.1016/j.eswa.2022.119237 · Cited by 44
Identification of key influencing factors to Chinese coal power enterprises transition in the context of carbon neutrality: A modified fuzzy DEMATEL approach
Li, Y., Zhao, K., & Zhang, F. (2022) · Energy · doi:10.1016/j.energy.2022.125427 · Cited by 44
Novel measures for linguistic hesitant Pythagorean fuzzy sets and improved TOPSIS method with application to contributions of system-of-systems
Han, Q., Li, W., Xu, Q., Song, Y., Fan, C.-L., & Zhao, M.-R. (2022) · Expert systems with applications · doi:10.1016/j.eswa.2022.117088 · Cited by 44
Comparative Assessment of Multiple Linear Regression and Fuzzy Linear Regression Models
Pandit, P., Dey, P., & Krishnamurthy, K. (2021) · SN Computer Science · doi:10.1007/s42979-021-00473-3 · Cited by 44
“SN Computer Science analysis, when the relationships between variables are too vague or complex [63, 64].”
A Novel Method for a COVID-19 Classification of Countries Based on an Intelligent Fuzzy Fractal Approach
Castillo, O., & Melin, P. (2021) · Healthcare · doi:10.3390/healthcare9020196 · Cited by 44
“The fuzzy system can be established in the form of the Mamdani reasoning method, and centroid as the defuzzification approach [4].”
Method
RETRACTED ARTICLE: Optimization using the firefly algorithm of ensemble neural networks with type-2 fuzzy integration for COVID-19 time series prediction
Melín, P., Sánchez, D., Monica, J. C., & Castillo, O. (2021) · Soft Computing · doi:10.1007/s00500-020-05549-5 · Cited by 48
“It can be represented as a set of ordered pairs of elements x, and its membership value is given as: L.A. Zadeh also proposes the concept of a type-2 fuzzy set in 1975 (Zadeh 1975).”
Background
Retracted
Predicting Energy Consumption of Residential Buildings Using Metaheuristic-optimized Artificial Neural Network Technique in Early Design Stage
Kaloop, M. R., Ahmad, F., Samui, P., Elbeltagi, E., Hu, J. W., & Wefki, H. (2025) · Building and Environment · doi:10.1016/j.buildenv.2025.112749 · Cited by 43
Evaluating lecturer performance in Vietnam: An application of fuzzy AHP and fuzzy TOPSIS methods
Do, Q. H., Tran, V., & Tran, T. (2024) · Heliyon · doi:10.1016/j.heliyon.2024.e30772 · Cited by 43
“The concept of fuzzy set theory [20] emerged to address uncertainties stemming from imprecision or vagueness.”
Background
An opinions-updating model for large-scale group decision-making driven by autonomous learning
Cheng, X., Zhang, K., Wu, T., Xu, Z.-S., & Gou, X.-J. (2024) · Information Sciences · doi:10.1016/j.ins.2024.120238 · Cited by 43
An integrated FMEA framework considering expert reliability for classification and its application in aircraft power supply system
Liu, Z.-M., Zhao, Y., & Liu, P.-D. (2023) · Engineering applications of artificial intelligence · doi:10.1016/j.engappai.2023.106319 · Cited by 43
An integrated interval type-2 fuzzy BWM-MARCOS model for location selection of e-scooter sharing stations: The case of a university campus
Altay, B., Çelik, E., Okumuş, A., Balin, A., & Gul, M. (2023) · Engineering applications of artificial intelligence · doi:10.1016/j.engappai.2023.106095 · Cited by 43
Forecasting the COVID-19 with Interval Type-3 Fuzzy Logic and the Fractal Dimension
Castillo, O., Castro, J. R., & Melin, P. (2022) · International Journal of Fuzzy Systems · doi:10.1007/s40815-022-01351-7 · Cited by 43
“The fuzzy rules can be established with the Mamdani reasoning method, and the centroid as defuzzification approach [4].”
BackgroundMethod
Group decision making based on weighted distance measure of linguistic intuitionistic fuzzy sets and the TOPSIS method
Kumar, K., & Chen, S.-M. (2022) · Information Sciences · doi:10.1016/j.ins.2022.07.184 · Cited by 43
Effect of short-term frozen storage on taste of gonads of female Eriocheir sinensis and the classification of taste quality combined with sensory evaluation and fuzzy logic model.
Fan, L., Xiao, T., Xian, C., Ding, W., & Wang, X.-C. (2022) · Food Chemistry · doi:10.1016/j.foodchem.2022.132105 · Cited by 43
A Robust Self-Adaptive Interval Type-2 TS Fuzzy Logic for Controlling Multi-Input–Multi-Output Nonlinear Uncertain Dynamical Systems
Al-Mahturi, A., Santoso, F., Garratt, M. A., & Anavatti, S. G. (2022) · IEEE Transactions on Systems, Man & Cybernetics. Systems · doi:10.1109/tsmc.2020.3030078 · Cited by 43
“Hence, to address the shortcomings of Type-1 FLS, an improved version of FLS was introduced, which is regarded as the Type-2 FLSs. Type-2 FLS were initiated by Zadeh in 1975 [16] to accommodate system uncertainties.”
Background
N-Dimensional Admissibly Ordered Interval-Valued Overlap Functions and Its Influence in Interval-Valued Fuzzy-Rule-Based Classification Systems
Asmus, T. D. C., Sanz, J., Dimuro, G., Bedregal, B., Fernández, J., & Bustince, H. (2021) · IEEE transactions on fuzzy systems · doi:10.1109/tfuzz.2021.3052342 · Cited by 43
“To deal with this problem, one may adopt interval-valued fuzzy sets (IVFSs) [32], [33], [34], since it is capable to model both vagueness (soft class boundaries) and uncertainty (with respect to the membership function), as discussed in [35], [36], [37].”
Background
A study of plithogenic graphs: applications in spreading coronavirus disease (COVID-19) globally
Sultana, F., Gulistan, M., Ali, M., Yaqoob, N., Khan, M., Rashid, T., & Ahmed, T. (2022) · Journal of Ambient Intelligence and Humanized Computing · doi:10.1007/s12652-022-03772-6 · Cited by 26
“Further, Zadeh (1975) extended fuzzy sets (FS) to interval- valued fuzzy sets in which values of membership are intervals instead of real numbers between 0 and 1.”
Background
An integrated interval type-2 fuzzy sets and multiplicative half quadratic programming-based MCDM framework for calculating aggregated risk ranking results of failure modes in FMECA
Boral, S., Chaturvedi, S., Howard, I., Naikan, V., & McKee, K. K. (2021) · Process Safety and Environmental Protection · doi:10.1016/j.psep.2021.04.006 · Cited by 42
Prioritizing the effective strategies for construction and demolition waste management using fuzzy IDOCRIW and WASPAS methods
Eghbali-Zarch, M., Tavakkoli-Moghaddam, R., Dehghan-Sanej, K., & Kaboli, A. (2021) · doi:10.1108/ecam-08-2020-0617 · Cited by 42
A universal approach to imprecise probabilities in possibility theory
Hose, D., & Hanss, M. (2021) · International Journal of Approximate Reasoning · doi:10.1016/j.ijar.2021.03.010 · Cited by 42
Ship Collision Risk Evaluation using AIS and weather data through fuzzy logic and deep learning
Korupoju, A. K., Kapadia, V., Vilwathilakam, A. S., & Samanta, A. (2024) · Ocean Engineering · doi:10.1016/j.oceaneng.2024.120116 · Cited by 41
Logic-oriented fuzzy neural networks: A survey
Alateeq, M., & Witold Pedrycz, C. (2024) · Expert Systems with Applications · doi:10.1016/j.eswa.2024.125120 · Cited by 49
An improvement to the interval type-2 fuzzy VIKOR method
Jana, C., Mohamadghasemi, A., Pal, M., & Martínez, L. (2023) · Knowledge-Based Systems · doi:10.1016/j.knosys.2023.111055 · Cited by 41
Using an Interval Type-2 Fuzzy AROMAN Decision-Making Method to Improve the Sustainability of the Postal Network in Rural Areas
Nikolić, I., Milutinović, J., Božanić, D., & Dobrodolac, M. (2023) · Mathematics · doi:10.3390/math11143105 · Cited by 41
Multi-criteria decision making based on vector similarity measures of picture type-2 hesitant fuzzy sets
Özlü, Ş. (2023) · Granular Computing · doi:10.1007/s41066-023-00382-1 · Cited by 41
“Therefore, the concept of type-2 fuzzy sets was produced by Zadeh (1975) but when this concept fails to meet the degree of hesitation, Picture fuzzy sets (PFSs) (Cuong and Kreinovich 2014) were introduced to model complexity information.”
An innovative picture fuzzy distance measure and novel multi-attribute decision-making method
Ganie, A. H., & Singh, S. (2021) · Complex & Intelligent Systems · doi:10.1007/s40747-020-00235-3 · Cited by 41
Type-2 fuzzy mixed-integer bi-level programming approach for multi-source multi-user water allocation under future climate change
Yue, Q., Wang, Y., Liu, L., Niu, J., Guo, P., & Li, P. (2020) · doi:10.1016/j.jhydrol.2020.125332 · Cited by 41
Alternative prioritization of freeway incident management using autonomous vehicles in mixed traffic using a type-2 neutrosophic number based decision support system
Gokasar, I., Simic, V., Deveci, M., & Senapati, T. (2023) · Engineering applications of artificial intelligence · doi:10.1016/j.engappai.2023.106183 · Cited by 40

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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