Cited by 2,555Multi-Criteria Decision MakingFuzzy and Soft Set TheoryRough Sets and Fuzzy Logic

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

Zadeh, L.A.·1975·Information Sciences

DOI 10.1016/0020-0255(75)90046-8

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“Since Zadeh (1975a, 1975b, 1975c) ﬁrst introduced linguistic variables to cope with qualitative information, linguistic variables have received considerable attention (Her-rera et al ., 1995, 2000; Herrera and Herrera-Viedma, 1997; Herrera and Martínez, 2000; Liu, 2009; Xu, 2009) and have been…”
On the weakness of linear programming to interpret the nature of solution of fully fuzzy linear system
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“Zadeh was the pioneer in the field of fuzzy sets and systems in [1,2].”
Background
Fuzzy weights estimation method based on the linguistic expression of criteria relevance
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“For this purpose, the concept of linguistic variables is applied (Zadeh, 1975a, b, c).”
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“2.2 A concise overview of fuzzy sets and fuzzy arithmetic Fuzzy set theory goes back to Zadeh (1965), who proposed fuzzy sets as means for dealing with non-probabilistic uncertainty.”
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“Zadeh (1975) gave the concept of linguistic variables which explored further uses of the FSs.”
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Background
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“Takagi and Sugeno [18] proposed a fuzzy IF-THEN rules system as the local input–output relations of a nonlinear system to scale the population of rules under a multi-dimensional fuzzy inference system, known as the T-S model [21].”
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“After, different fuzzy approaches, such as type-2 fuzzy sets (Zadeh 1975), intuitionistic fuzzy sets (IFSs) (Atanassov 1986), Pythagorean fuzzy sets (PFSs) (Yager 2013), and hesitant fuzzy set (HFSs) (Torra 2010) were proposed to handle ambiguity better by different researchers.”
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“Zadeh [63, 64] expressed the linguistic variables to overcome this complexity.”
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Background
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“…and linguistic-based approaches, as developed by Zadeh (1975a,b,c), is much suitable and straightforward to handle uncertainty and thus has been studied extensively (see Zadeh 1975a,b,c, 1976; Tong and Bonissone 1980; Del-gado et al. 1998, 1992; Bordogna et al. 1997; Herrera et al. 1995, 1996).”
Background
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Background
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“T2 FSs are extensions of T1 FSs was first introduced by Zadeh [38], [39].”
Background
An intelligent decision support system to prevent and control of dengue
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“, sg} a linguistic term set of granularity g [2, 3, 4].”
BackgroundMethod
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“To deal with cultural differences, doctors were found to need several core skills, such as empathic communication [28,38,39,53] and being respectful to the patient [1,31,35,42,64].”
Background
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“However, we will show that such proposition does not hold true for the well known supremum metric on the space of fuzzy numbers.”
Background
A fuzzy time series model based on N-th Quantile Discretization Approach for TAIEX forecasting
Chang, J.-R., & Liu, C.-C. (2013) · International Conference on Knowledge and Smart Technology · doi:10.1109/kst.2013.6512778 · Cited by 6
“FUZZY TIME SERIES Based on Zadeh’s works [9-12], Song and Chissom [6] first proposed a forecasting model called Fuzzy Time Series, which provided a theoretic framework to model a special dynamic process whose observations are linguistic values.”
Method
Fuzzy logic controlled landing of a Boeing 747
McLauchlan, L. (2009) · 2009 IEEE/RSJ International Conference on Intelligent Robots and Systems · doi:10.1109/iros.2009.5354295 · Cited by 6
Similarity Measure of Interval-Valued Fuzzy Sets and Application to Pattern Recognition
Zeng, W.-Y., & Yin, Q. (2008) · 2008 Fifth International Conference on Fuzzy Systems and Knowledge Discovery · doi:10.1109/fskd.2008.605 · Cited by 6
“Another well-known generalization of an ordinary fuzzy set is interval-valued fuzzy set, which was first introduced by Zadeh [18].”
Influential
Fuzziness in Covering Generalized Rough Sets
Xu, W., & Zhang, X.-Y. (2006) · Cybersecurity and Cyberforensics Conference · doi:10.1109/chicc.2006.4347200 · Cited by 6
“For example, fuzzy set theory [17] , rough sets [7] , computing with words [14] [18] [19] , linguistic dynamic systems [13] [14] , and many others, have been developed and applied to real-world problems.”
Background
Modeling uncertainties associated with multi-attribute decision-making based evaluation of cooling system using interval-valued complex intuitionistic fuzzy hypersoft settings
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“Zadeh [49], [50], [51] proposed a linguistic variable (LV) that is able to precisely capturing qualitative data then the LV-based decision theories and methodologies have made tremendous progress [52], [53], [54].”
Background
Traffic and Transportation Analysis Techniques
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An attribute ranking method based on rough sets and interval-valued fuzzy sets
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Advanced linguistic intuitionistic fuzzy Maclaurin symmetric means for MAGDM
Li, J.-J., & Chen, M. (2024) · Applied intelligence (Boston) · doi:10.1007/s10489-023-05225-9 · Cited by 5
“LIFSs [16, 17], which are a combination of linguistic term sets [18] and intuitionistic fuzzy sets [19], are effective tools for characterizing fuzzy and uncertain phenomena.”
Multi-criteria group decision-making based on 2-tuple linguistic q-rung picture fuzzy sets
Khan, A., & Ahmad, U. (2023) · Granular Computing · doi:10.1007/s41066-023-00441-7 · Cited by 5
“The idea of a linguistic variable (LV), which is made up of a group of linguistic terms (LTs), was ﬁrst suggested by Zadeh (1975).”
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“…main approaches to define the syntactic rule G : (1) approach based on a context-free grammar (Bonissone 1980; Bordogna and Pasi 1993; Zadeh 1975b; 1975c; 1975d) and (2) approach based on primary terms with an ordered structure (Yager 1995; Bordogna, Fedrizzi, and Pasi 1997; Herrera and…”
Influential
Approximations of Fuzzy Numbers by Using r-s Piecewise Linear Fuzzy Numbers Based on Weighted Metric
Lv, H., & Wang, G.-X. (2022) · Mathematics · doi:10.3390/math10010145 · Cited by 5
Matrix games with proportional linguistic payoffs
Chauhan, P., & Gupta, A. (2021) · Soft Computing - A Fusion of Foundations, Methodologies and Applications · doi:10.1007/s00500-021-06363-3 · Cited by 5
An integrated approach for service quality evaluation of online health communities based on q-rung orthopair fuzzy linguistic aggregation operators
Hao, D., Zhang, R.-T., & Bai, K.-Y. (2021) · Journal of Intelligent & Fuzzy Systems · doi:10.3233/jifs-211257 · Cited by 5
Soft Computing Techniques and Their Applications in Intel-ligent Industrial Control Systems: A Survey
Wu, Z., Liao, H.-C., Lu, K.-Y., & Zavadskas, E. (2021) · International Journal of Computers Communications & Control · doi:10.15837/ijccc.2021.1.4142 · Cited by 5
RETRACTED: Hesitant fuzzy C-means algorithm and its application in image segmentation
Zeng, W.-Y., Ma, R., Yin, Q., Zheng, X., & Xu, Z.-S. (2020) · Journal of Intelligent & Fuzzy Systems · doi:10.3233/jifs-191973 · Cited by 5
Retracted
An extension to fuzzy ELECTRE
Chu, T.-C., & Le, H. (2019) · Soft Computing - A Fusion of Foundations, Methodologies and Applications · doi:10.1007/s00500-019-04381-w · Cited by 5
“Hatami-Marbini et al. (2013) indicated that the importance weights and performance ratings cannot be measured precisely as some DMs may express their judgments using linguistic terms such as low, medium or high in many real-world problems (Zadeh 1975; Tsaur et al. 2002).”
Background
An Estimation of a Hybrid Log-Poisson Regression Using a Quadratic Optimization Program for Optimal Loss Reserving in Insurance
Woundjiagué, A., Bidima, M. L. D. M., & Mwangi, R. (2019) · Advances in Fuzzy Systems · doi:10.1155/2019/1393946 · Cited by 5
Reliability-Based Design of Human Performance Conditions Using Fuzzy Perfection
Rotshtein, A. (2019) · Cybernetics and Systems Analysis · doi:10.1007/s10559-019-00128-5 · Cited by 5
A group decision support model based on incomplete hesitant fuzzy linguistic preference relations for mine disaster rescue
Song, Y., & Hu, J.-H. (2018) · Progress in Artificial Intelligence · doi:10.1007/s13748-018-0145-9 · Cited by 5
Continuity of Fuzzified Functions Using the Generalized Extension Principle
Wu, H.-C. (2017) · Symmetry · doi:10.3390/sym9120299 · Cited by 5
Fuzzy Robust Design of Dynamic Vibration Absorbers
Silva, A. D. G., Cavalini, A. A., & Steffen, V. (2016) · doi:10.1155/2016/2081518 · Cited by 5
“The extension principle [23] is a widely known method for mapping fuzzy inputs, in which the mapping process is made through the evaluation of an associated mathematical function.”
Blackwell’s theorem for fuzzy variables
Hong, D. (2013) · Fuzzy Optimization and Decision Making · doi:10.1007/s10700-013-9173-x · Cited by 5
Transitive Closure of Interval-valued Fuzzy Relations
González-del-Campo, R., Garmendia, L., & Recasens, J. (2013) · International Journal of Computational Intelligence Systems · doi:10.1080/18756891.2013.802117 · Cited by 5
“One of these generalizations are type-2 fuzzy sets, FS 2, 21 , 22 , 23 were introduced by Zadeh.”
Multiple Criteria Decision Making Based on Discrete Linguistic Stochastic Variables
Ren, J., Gao, Y., & Bian, C. (2013) · Mathematical Problems in Engineering · doi:10.1155/2013/546508 · Cited by 5
Pricing Currency Option Based on the Extension Principle and Defuzzification via Weighting Parameter Identification
Xu, J.-X., Tan, Y., Gao, J.-G., & Feng, E. (2013) · Journal of Applied Mathematics · doi:10.1155/2013/623945 · Cited by 5
Duality theorems in fuzzy optimization problems
Nehi, H. M., & Drayab, A. (2013) · doi:10.1007/s12543-013-0130-8 · Cited by 5
Type-2 fuzzy load regulation of a servomechanism with backlash using only motor position measurements
Cázarez-Castro, N., Aguilar, L., Castillo, O., & Castro, J. R. (2010) · International Conference on Fuzzy Systems · doi:10.1109/fuzzy.2010.5584046 · Cited by 5
“Type-2 fuzzy logic systems (T2FLSs) [7] are a generalization of T1FLSs [8],[9],[10], which allow us to deal with the uncertainty induced into a mechanical system by noise, frictions, backlash, etc.”
Background
Imperfect Information in Software Design Processes
Noppen, J. (2007) · doi:10.3990/1.9789036525114 · Cited by 5
Ranking alternatives via maximizing set and minimizing set based fuzzy MCDM approach
Chu, T.-C. (2004) · doi:10.1080/02533839.2004.9670858 · Cited by 5
“…set and minimizing set based fuzzy MCDM approach for selecting alternatives is suggested, where ratings of alternatives versus different criteria and the importance weights of criteria are assessed in fuzzy numbers or linguistic values (Zadeh, 1975a; 1975b; 1976) represented by fuzzy numbers.”
Background
Propositional fuzzy logics: Decidable for some (algebraic) operators; undecidable for more complicated ones
Gehrke, M., Kreinovich, V., & Bouchon-Meunier, B. (1999) · International Journal of Intelligent Systems · doi:10.1002/(sici)1098-111x(199909)14:9%3c935::aid-int6%3e3.0.co;2-e · Cited by 5
Adaptive, Fuzzy Boundary Observer for a Class of Euler-Bernoulli Beam Systems With Uncertainties
Wu, R., Xiao, Y., Luo, B., Xu, X.-D., Yang, C.-H., & Huang, T.-W. (2024) · IEEE Transactions on Instrumentation and Measurement · doi:10.1109/tim.2024.3451597 · Cited by 5
“Type-2 fuzzy sets (T2 FSs) were first introduced in [25], which can effectively represent the uncertainty of a system through primary and secondary membership functions (MFs).”
Background
Novel Aczel-Alsina Power Aggregation Operators for Circular Pythagorean Fuzzy Linguistics With Application to Waste Reduction and Recycling in Green Supply Chain Management
Ali, Z., Ali, M., Yin, S., & Yang, M.-S. (2024) · IEEE Access · doi:10.1109/access.2024.3474178 · Cited by 5
“Zadeh [26], [27], [28] derived the linguistic term set (LTS).”
Background
Optimization of Interval Type-2 Fuzzy Logic System Using Grasshopper Optimization Algorithm
Hassan, S., Khanesar, M. A., Hussein, N. K., Belhaouari, S. B., Amjad, U., & Mashwani, W. K. (2022) · Computers Materials & Continua · doi:10.32604/cmc.2022.022018 · Cited by 5
“The idea of Fuzzy Set Theory was given by Zadeh [27] to cater the ambiguities and uncertainties present in real world problems.”
Method
New Frontiers in Determining Criteria and Strategies in Rural Area Sustainable Development in Serbia: Fuzzy AHP Approach
Mladenović, M., Simjanović, D. J., Ranđelović, B. M., Dobričanin, S., Zdravković, N., & Đokić, D. (2025) · World · doi:10.3390/world6040141 · Cited by 4
“Initially developed for linguistic purposes, fuzzy set theory has proven indispensable in representing uncertainty and imprecision in decision-making processes [66,67].”
TOPSIS method for ability evaluation of industrial internet platform energizing digital transformation of manufacturing with DHHFLTSs
Liu, H.-L., & Wang, Y. (2025) · Int. J. Knowl. Based Intell. Eng. Syst. · doi:10.1177/13272314241295962 · Cited by 4
A New Fusion Method of Fuzzy Numbers and Linguistic Terms Based on Individual Semantics in Mixed Decision Making Problems
Ren, F., & Hao, F. (2024) · International Journal of Fuzzy Systems · doi:10.1007/s40815-024-01879-w · Cited by 4
Railway Transportation Scheme Selection Based a CODAS-COPRAS Method in Triangular Dense Fuzzy Linguistic Term Lock Environment
Fan, J., Yuan, Y., & Wu, M. (2024) · International Journal of Fuzzy Systems · doi:10.1007/s40815-024-01778-0 · Cited by 4
Short-Term Load Forecasting Using Application of Interval Type 2 Fuzzy Logic
Moyo, E. N., Sharma, G., Bokoro, P., Rameshar, V., & Muremi, L. (2024) · 2024 32nd Southern African Universities Power Engineering Conference (SAUPEC) · doi:10.1109/saupec60914.2024.10445101 · Cited by 4
Fuzzy quantitative attack tree analysis
Dang, T. K. N., Lopuhaä-Zwakenberg, M., & Stoelinga, M. (2024) · Fundamental Approaches to Software Engineering · doi:10.48550/arxiv.2401.12346 · Cited by 4
“5 } ∈ F ( Z ) is defined by Arithmetic operations on fuzzy elements are performed following Zadeh’s extension principle [12,4,38,40,39,37].”
Method

Authors: Zadeh, L. A.
Affiliations: University of California, Berkeley (US)
Corresponding author: Zadeh, L.A.
Venue: Information Sciences
Publisher: Elsevier BV
Published: 1975-01
Volume: 8
Issue: 4
Pages: 301-357
ISSN: 0020-0255 (ISSN-L)
DOI: 10.1016/0020-0255(75)90046-8
OpenAlex: W4240278385
Cited by: 2,555
References: 0
Citations by year: 2026: 42 · 2025: 72 · 2024: 83 · 2023: 106 · 2022: 135 · 2021: 130 · 2020: 134 · 2019: 133 · 2018: 122 · 2017: 100 · 2016: 115 · 2015: 136 · 2014: 95 · 2013: 83 · 2012: 69
FWCI: 13.96
Type: journal article
Language: en
Open access: closed
Licence: www.elsevier.com/tdm/userlicense/1.0/ (tdm)
Locations: Information Sciences (publishedVersion)
Topics: Social Sciences › Decision Sciences › Management Science and Operations Research › Multi-Criteria Decision Making
Social Sciences › Decision Sciences › Management Science and Operations Research › Fuzzy and Soft Set Theory
Physical Sciences › Computer Science › Computational Theory and Mathematics › Rough Sets and Fuzzy Logic
Keywords: ELECTRE II, multi-criteria group decision-making, outranking relations, fuzzy ELECTRE, linguistic variables, approximate reasoning

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

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