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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Jan, N., Zedam, L., Mahmood, T., Ullah, K., & Ali, Z. (2018) · Journal of Intelligent & Fuzzy Systems · doi:10.3233/jifs-181253 · Cited by 20
“The term of linguistic variable was introduced by Zadeh [45, 46, 49] whose values are words or a sentence in natural or artiﬁcial language.”
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Gong, Z.-T., & Hai, S. (2016) · Fuzzy Sets Syst. · doi:10.1016/j.fss.2015.10.010 · Cited by 20
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“The main element of this structure is known as Computational Perception (CP), which is based on the concept of linguistic variable developed by Zadeh [20, 21, 22].”
Background
A linguistic truth-valued reasoning approach in decision making with incomparable information
Li, Z., Ruan, D., Zheng, P., & Yang, X. (2008) · Journal of Intelligent & Fuzzy Systems · doi:10.3233/ifs-2008-00403 · Cited by 20
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Zhu, W., & Wang, F.-Y. (2007) · International Conference on Fuzzy Systems and Knowledge Discovery · doi:10.1109/fskd.2007.592 · Cited by 20
“To this end, researchers have proposed many methods other than classical logic, for example, fuzzy set theory [31], rough set theory [10], computing with words [18, 27, 28, 29, 30], granular computing [5, 25, 23], quotient space theory [33, 34], computational theory for linguistic dynamic systems [19].”
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Al-Araji, Z. J., Ahmad, S. S. S., Kausar, N., Farhani, A., Ozbılge, E., & Çağın, T. (2022) · IEEE Access · doi:10.1109/access.2022.3225462 · Cited by 27
“Experiments on fuzzy decision-making arose from research into the fuzzy sets [30], fuzzy environments [77], approximate reasoning [55], [56], [78], and fuzzy decision systems applications [79], being worked on by a signiﬁcant number of scientists from all over the world [80].”
Background
Copula extended power aggregation operators and MEREC method under linguistic q-rung orthopair fuzzy information: an application to plastic waste management solution selection
Ali, J. (2025) · Evolutionary Intelligence · doi:10.1007/s12065-025-01080-4 · Cited by 19
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García-Zamora, D., Cruz, A., Neres, F., Santiago, R., Roldán-López-de-Hierro, A.-F., Paiva, R., Dimuro, G., Martínez, L., Bedregal, B. R. C., & Bustince, H. (2024) · Fuzzy Sets Syst. · doi:10.1016/j.fss.2024.108863 · Cited by 19
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“Type-II Fuzzy Inference System is an extended concept of Type-I Fuzzy Inference System and was introduced by Zadeh (1975) which allows incorporation of uncertainty of the membership functions into fuzzy sets (Castillo and Melin 2008).”
Method
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“To reduce this study deficiency and express the opinion in natural language, the concept of linguistic variable was established by Zadeh [27], [28].”
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“Figure 4 shows that the TABLE 3 Fuzzy comparison pairwise of criteria with respect to the goal Criterion C1 C2 C3 C1 (1, 1, 1, 1) (1/7, 1/6, 1/6, 1/5) (1/3, 1/2, 1/2, 1) C2 (5, 6, 6, 7) (1, 1, 1, 1) (3, 3, 3, 3)”
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“The presence of linguistic hedges or modifiers has high impact on determination of semantic orientation of opinionated word [10, 39, 40].”
Background
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Verma, R. (2021) · Axioms · doi:10.3390/axioms10020113 · Cited by 17
“Firstly, Zadeh [46,47] developed the idea of the linguistic term set (LTS) in 1975.”
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“Differently, in decision-making problems, numerous attri butes are tough to give attribute values, but they can easy give linguistic assessment values, so for this Zadeh (1975) ﬁrstly give the concept of linguistic variable, which can estimate the evaluation of objects.”
Background
RETRACTED: GRA method for waste incineration plants location problem with probabilistic linguistic multiple attribute group decision making
Lei, F., Lu, J., Wei, G., Wu, J., Wei, C., & Guo, Y.-F. (2020) · Journal of Intelligent & Fuzzy Systems · doi:10.3233/jifs-191443 · Cited by 17
Retracted
A bi-projection model based on linguistic terms with weakened hedges and its application in risk allocation
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Fan, Q.-F., Wang, T., Chen, Y., & Zhang, Z.-F. (2017) · International Journal of Fuzzy Systems · doi:10.1007/s40815-017-0357-3 · Cited by 17
“In 1975, Zadeh proposed the deﬁnition and operation of type-2 fuzzy sets [1].”
Background
Linguistic multi-attribute decision making with multiple priorities
Yan, H., Zhang, X., & Li, Y. (2017) · Computers & industrial engineering · doi:10.1016/j.cie.2017.03.032 · Cited by 17
“In any linguistic approach to solve a decision problem, the term set of a linguistic variable (Zadeh, 1975a,b,c) and its associated semantics must be defined first to supply the users with an instrument by which they can naturally express their opinions.”
Background
Concepts of solutions of uncertain equations with intervals, probabilities and fuzzy sets for applied tasks
Kovalerchuk, B., & Kreinovich, V. (2016) · Granular Computing · doi:10.1007/s41066-016-0031-4 · Cited by 17
“Most of the work in fuzzy equations has been concerned with algorithms and theorems for solving fuzzy linear equations, e.g., (Yager 1979; Sanchez 1984; Di Nola et al. 1985; Zhao and Govind 1991; Peeva 1991; Buckley and Feuring 2000; Horcik 2008; Skalna et al. 2008; Allahvi-ranloo et al. 2011;…”
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Malkaw, G., Ahmad, N., & Ibrahim, H. (2015) · Computational Mathematics and Modeling · doi:10.1007/s10598-015-9283-0 · Cited by 17
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Li, C.-C., & Dong, Y.-C. (2014) · International Journal of Computational Intelligence Systems · doi:10.1080/18756891.2014.960232 · Cited by 17
“The basic notations and operational laws of linguistic variables are introduced in 15,19,21,22,33,34,39,48”
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Rosado, A., Ribeiro, R., Zadrożny, S., & Kacprzyk, J. (2006) · doi:10.1007/3-540-33289-8_1 · Cited by 17
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Wang, F., Pan, Y.-X., Xu, G., & Wei, Q. (2024) · Expert systems with applications · doi:10.1016/j.eswa.2024.125899 · Cited by 16
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
A fuzzy-based framework for evaluation of website design quality index
Kaur, S., & Gupta, S. K. (2020) · International Journal on Digital Libraries · doi:10.1007/s00799-020-00292-6 · Cited by 16
Interval valued trapezoidal neutrosophic set: multi-attribute decision making for prioritization of non-functional requirements
Khatter, K. (2020) · Journal of Ambient Intelligence and Humanized Computing · doi:10.1007/s12652-020-02130-8 · Cited by 16
“Later, Zadeh (1975) proposed the interval valued fuzzy sets (IVFS) if grade of membership is uncertain and cannot be expressed in terms of a crisp value.”
A fuzzy social vulnerability evaluation from the perception of disaster bearers against meteorological disasters
Cai, M., & Wei, G. (2020) · Natural Hazards · doi:10.1007/s11069-020-04088-4 · Cited by 16
“Linguistic computational models are important techniques of computing with words which are first proposed by Zadeh (1996).”
BackgroundMethodInfluential
L-Fuzzy Sets and Isomorphic Lattices: Are All the “New” Results Really New? †
Klement, E., & Mesiar, R. (2018) · Mathematics · doi:10.3390/math6090146 · Cited by 16
“…∗ , ≤ L ∗ ) according to Propositions 1 and 2 were used in the literature: in the mid-seventies I ( I ) -fuzzy sets were called interval-valued in [4,12–14], in the eighties ﬁrst the name “intuitionistic” fuzzy sets was used for L ∗ -fuzzy sets in [6,7] (compare also [84–86]) and then grey sets…”
Influential
A bibliometric analysis of fuzzy decision making research
Blanco-Mesa, F., MerigóLindahl, J. M., & Gil-Lafuente, A. (2016) · Annual Conference on the North American Fuzzy Information Processing Society · doi:10.1109/nafips.2016.7851585 · Cited by 16
Fuzzy random regression based multi-attribute evaluation and its application to oil palm fruit grading
Nureize, A., Watada, J., & Wang, S. (2014) · Annals of Operations Research · doi:10.1007/s10479-011-0979-z · Cited by 16
“Fuzzy arithmetic and fuzzy operations for fuzzy numbers have been studied through the use of the extension principle which involved the concept of possibility (Nguyen 1978; Zadeh 1975a, 1975b, 1975c).”
Method
Effects of Diabetic Neuropathy on Body Sway and Slip Perturbation Detection in Older Population
Kim, B., & Robinson, C. (2006) · International Journal of Occupational Safety and Ergonomics · doi:10.1080/10803548.2006.11076686 · Cited by 16
Fuzzy Space Monitoring and Fault Detection Applications
Ribeiro, R. A. (2006) · Journal of Decision Systems · doi:10.3166/jds.15.267-286 · Cited by 16
“Another important concept for fuzzy logic, particularly for fuzzy inference systems, is the concept of linguistic variable (Zadeh, 1987b).”
Background
Fuzzy sets approaches to statistical parametric and nonparametric tests
Kahraman, C., Bozdag, C., Ruan, D., & Özok, A. (2004) · International Journal of Intelligent Systems · doi:10.1002/int.20037 · Cited by 16
“m np n 1 2 because p 1 2 if H0 is true (23)”
SISO Intuitionistic Fuzzy Systems: IF- ${t}$ -Norm, IF- ${R}$ -Implication, and Universal Approximators
Li, J., & Gong, Z.-T. (2019) · IEEE Access · doi:10.1109/access.2019.2918169 · Cited by 16
An outranking method for optimizing anti-aircraft missile system with 2-tuple linguistic m-polar fuzzy data
Akram, M., Noreen, U., & Deveci, M. (2024) · Engineering applications of artificial intelligence · doi:10.1016/j.engappai.2024.107923 · Cited by 15
Analyzing the Shelter Site Selection Criteria for Disaster Preparedness Using Best–Worst Method under Interval Type-2 Fuzzy Sets
Çelik, E. (2024) · Sustainability · doi:10.3390/su16052127 · Cited by 15
“Consequently, in 1975, Zadeh expanded the classical fuzzy sets to type-2 fuzzy sets [40–42].”
Background
A New Fuzzy Extension of the Simple WISP Method
Karabašević, D., Ulutaş, A., Stanujkić, D., Saracevic, M., & Popović, G. (2022) · Axioms · doi:10.3390/axioms11070332 · Cited by 15
Rank aggregation based multi-attribute decision making with hybrid Z-information and its application
Tao, Z., Liu, X., Zhou, L.-G., & Chen, H. (2019) · Journal of Intelligent & Fuzzy Systems · doi:10.3233/jifs-190344 · Cited by 15
Trapezoidal Pythagorean fuzzy linguistic entropic combined ordered weighted Minkowski distance operator based on preference relations
Xian, S.-D., Xiao, Y., Li, L., & Yu, D.-X. (2019) · International Journal of Intelligent Systems · doi:10.1002/int.22139 · Cited by 15
Comparison Between Numerical Solutions of Fuzzy Initial-Value Problems via Interactive and Standard Arithmetics
Wasques, V., Esmi, E., Barros, L., & Bede, B. (2019) · Joint IFSA World Congress and NAFIPS Annual Meeting · doi:10.1007/978-3-030-21920-8_62 · Cited by 15
Large Group Decision Making
Carrascosa, I. P. (2018) · SpringerBriefs in Computer Science · doi:10.1007/978-3-030-01027-0 · Cited by 15
Selection of Human Working Conditions Based on Fuzzy Perfection
Rotshtein, A. (2018) · Journal of computer & systems sciences international · doi:10.1134/s1064230718060096 · Cited by 15
Portfolio Selection Using Z-Number Theory: Two Solution Methodologies
Jirofti, A., & Najafi, A. (2018) · International Journal of Fuzzy Systems · doi:10.1007/s40815-018-0513-4 · Cited by 15
Computational Intelligence Assisted Design
Chen, Y., & Li, Y. (2018) · doi:10.1201/9781315153179 · Cited by 15
Scaled Prioritized Operators Based on the Linguistic Intuitionistic Fuzzy Numbers and Their Applications to Multi-Attribute Decision Making
Liu, P.-D., & Liu, W. (2018) · International Journal of Fuzzy Systems · doi:10.1007/s40815-018-0459-6 · Cited by 15
A Method for Unbalanced Linguistic Term Sets and its Application in Group Decision Making
Cai, M., Gong, Z., & Yu, X.-B. (2016) · International Journal of Fuzzy Systems · doi:10.1007/s40815-016-0209-6 · Cited by 15
“Zadeh [1, 4, 5] ﬁrst introduced the concept of a linguistic variable as a model of words or labels that can represent vague concepts in natural language.”
Background
Correlation coefficient of interval-valued intuitionistic fuzzy sets
Zeng, W.-Y., & Wang, J.-Y. (2011) · International Conference on Fuzzy Systems and Knowledge Discovery · doi:10.1109/fskd.2011.6019507 · Cited by 15
“After Zadeh [17], [18], [19] introduced interval-valued fuzzy set, Attanassov and Gargov [2] pioneered the concept of interval-valued intuitionistic fuzzy set, which is characterized by a membership function and a non-membership function whose values are interval-numbers rather than exact real numbers.”
Background
Evolutionary optimization of interval type-2 membership functions using the Human Evolutionary Model
Sepúlveda, R., Castillo, O., Melin, P., Montiel, O., & Aguilar, L. (2007) · 2007 IEEE International Fuzzy Systems Conference · doi:10.1109/fuzzy.2007.4295401 · Cited by 15
A Solution for Systems of Linear Fuzzy Equations in Spite of the Non-existence of a Field of Fuzzy Numbers
Vroman, A., Deschrijver, G., & Kerre, E. (2005) · Int. J. Uncertain. Fuzziness Knowl. Based Syst. · doi:10.1142/s0218488505003485 · Cited by 15
Linguistic Pythagorean fuzzy Aczel-Alsina aggregation operators and their application in multi-attribute group decision-making: An approach for smart city development
Gurmani, S. H., Rasool, Z., Ali, R., Bano, S., Chen, H., Feng, Y., & Zulqarnain, R. M. (2025) · Engineering applications of artificial intelligence · doi:10.1016/j.engappai.2025.111215 · Cited by 14
Improving disturbance rejection and tracking performance of interval type-2 T-S fuzzy systems with time-varying delay
Zhao, J.-Y., & Zhao, T. (2025) · Applied Mathematics and Computation · doi:10.1016/j.amc.2024.129150 · Cited by 14
Multi-criteria decision-making for the selection of best airport ground access mode with a new fuzzy rough-entropy based method
Akram, Z., Ahmad, U., & Alcantud, J. (2024) · Engineering applications of artificial intelligence · doi:10.1016/j.engappai.2024.108843 · Cited by 14
RETRACTED ARTICLE: Dispatching and rebalancing for ride-sharing autonomous mobility-on-demand systems based on a fuzzy multi-criteria approach
Khemiri, R., Naija, M., & Expósito, E. (2022) · Soft Computing · doi:10.1007/s00500-022-07377-1 · Cited by 14
“E It is more desirable to specify these preferences using natural language (Zadeh 1975).”
Retracted
Neutrosophic Riemann integration and its properties
Biswas, S., Moi, S., & Sarkar, S. P. (2021) · Soft Computing - A Fusion of Foundations, Methodologies and Applications · doi:10.1007/s00500-021-06200-7 · Cited by 14
“It is the generalization of classical set Type 2 fuzzy sets (Zadeh 1975) Its membership function is a fuzzy function It is one kind of generalization of fuzzy sets Intuitionistic fuzzy sets (Atanassov 1999) Every element of this set has a membership value as well as a non-membership value It is…”
Background
On General Framework of Type-1 Membership Function Construction: Case Study in QoS Planning
Miliauskaitė, J., & Kalibatienė, D. (2019) · International Journal of Fuzzy Systems · doi:10.1007/s40815-019-00753-4 · Cited by 14
Model-based hearing diagnostics based on wideband tympanometry measurements utilizing fuzzy arithmetic.
Sackmann, B., Dalhoff, E., & Lauxmann, M. (2019) · Hearing Research · doi:10.1016/j.heares.2019.02.011 · Cited by 14
New approach for estimation of criteria weights based on a linguistic evaluation
Borovička, A. (2019) · Expert systems with applications · doi:10.1016/j.eswa.2019.01.069 · Cited by 14
A survey of type-2 fuzzy aggregation and application for multiple criteria decision making
Qin, J. (2019) · Journal of Data, Information and Management · doi:10.1007/s42488-019-00002-1 · Cited by 14
“In order to handle the high complex uncertain problem, the type-2 fuzzy sets (T2FSs) was developed as an extension of type-1 fuzzy sets (T1FSs) (Zadeh 1975a; Zadeh 1975b; Zadeh 1975c).”
Method
A Programming-Based Algorithm for Probabilistic Uncertain Linguistic Intuitionistic Fuzzy Group Decision-Making
Gong, K., & Chen, C. (2019) · Symmetry · doi:10.3390/sym11020234 · Cited by 17
Type-2 Multi-Fuzzy Sets and Their Applications in Decision Making
Kar, M. B., Roy, B., Kar, S., Majumder, S., & Pamucar, D. (2019) · Symmetry · doi:10.3390/sym11020170 · Cited by 14
“The concept of T2FS was introduced by Zadeh [6–8].”
Background
A Hesitant Fuzzy Linguistic Multi-criteria Decision-Making Approach Based on Regret Theory
Xia, M. (2018) · International Journal of Fuzzy Systems · doi:10.1007/s40815-018-0502-7 · Cited by 16
INVENTORY MODEL WITH DEMAND AS TYPE-2 FUZZY NUMBER: A FUZZY DIFFERENTIAL EQUATION APPROACH
Debnath, B., Majumder, P., Bera, U., & Maiti, M. (2018) · doi:10.22111/ijfs.2018.3576 · Cited by 14
“Type-2 fuzzy sets (T2 FSs) are extensions of type-1 fuzzy sets was first introduced by Zadeh [41, 42].”
Background
Characterization and prediction of the backscattered form function of an immersed cylindrical shell using hybrid fuzzy clustering and bio‐inspired algorithms
Agounad, S., Aassif, E., Khandouch, Y., Maze, G., & Décultot, D. (2018) · Ultrasonics · doi:10.1016/j.ultras.2017.06.015 · Cited by 14
Multiple Attribute Decision-Making Methods with Unbalanced Linguistic Variables Based on Maclaurin Symmetric Mean Operators
Teng, F., Liu, P.-D., Zhang, L., & Zhao, J. (2018) · International Journal of Information Technology and Decision Making · doi:10.1142/s0219622018500013 · Cited by 14
Multi-criteria shortest path for rough graph
Majumder, S., & Kar, S. (2017) · Journal of Ambient Intelligence and Humanized Computing · doi:10.1007/s12652-017-0601-6 · Cited by 14
“In order to process and represent the useful data hidden within these imprecise or ill-defined information, many researchers have proposed several improved theories like fuzzy set (Zadeh 1965), type-2 fuzzy set (Zadeh 1975a, b), rough set (Pawlak 1982), uncertainty theory (Liu 2007), etc.”
Background
Fuzzy measure identification for criteria coalitions using linguistic information
Bernal, R., Karanik, M., & Peláez, J. I. (2015) · Soft Computing - A Fusion of Foundations, Methodologies and Applications · doi:10.1007/s00500-015-1589-5 · Cited by 14
“Linguistic labels (Zadeh 1975a,b,c) and preference relations to establish the importance (weight) of each criterion and groups of them are used.”
Parameterizing the Semantics of Fuzzy Attribute Implications by Systems of Isotone Galois Connections
Vychodil, V. (2014) · IEEE transactions on fuzzy systems · doi:10.1109/tfuzz.2015.2470530 · Cited by 14
Approximate case-based reasoning on neural networks
Shen, Z., Lui, H., & Ding, L. (1994) · International Journal of Approximate Reasoning · doi:10.1016/0888-613x(94)90010-8 · Cited by 14
“This is so-called approximate reasoning [2, 3].”
Background
A Review on Interval Type-2 Fuzzy-Model-Based Control Systems: Membership-Function-Dependent Perspectives
Lam, H.-K., Xiao, B., & Chen, M. (2025) · IEEE transactions on fuzzy systems · doi:10.1109/tfuzz.2025.3609627 · Cited by 13
“Extending the grade of membership in (type-1) fuzzy set themselves as another fuzzy set to incorporate uncertainties, the type-2 fuzzy set theory was presented along with the concept “footprint of uncertainty” (FOU) in 1975 [2], [3], [4].”
An interval type-2 fuzzy MARCOS modelling to assess performance effectiveness of survival craft on cargo ship
Aydin, M., Camliyurt, G., Gul, M., Sezer, S., Çelik, E., & Akyuz, E. (2025) · Ocean Engineering · doi:10.1016/j.oceaneng.2025.120899 · Cited by 13
Cosine similarity measures between q-rung orthopair linguistic sets and their application to group decision making problems
Ali, J., & Naeem, M. (2022) · Scientific Reports · doi:10.1038/s41598-022-18694-8 · Cited by 13
“Step 9 Ranking: (24) Q̌ij = q− ROLWA � Q(1)ij ,Q 2 ij , .”
BackgroundInfluential
A Review of Various Controller Techniques Designed for the Operational Control of DC and Servo Motors
Harshitha, S., Shamanth, S., & Chari, A. K. (2022) · Journal of Physics, Conference Series · doi:10.1088/1742-6596/2273/1/012001 · Cited by 13
Consistency and Consensus Driven for Hesitant Fuzzy Linguistic Decision Making with Pairwise Comparisons
Ren, P., Liu, Z.-X., Zhang, W.-G., & Wu, X.-L. (2021) · Expert systems with applications · doi:10.1016/j.eswa.2022.117307 · Cited by 13
“Considering that people are familiar with language messages, Zadeh (1975) introduced the linguistic term set (LTS), and noted its basic form as”
Influential
Accessing electronic health records in critical incidents using context-aware attribute-based access control
Psarra, E., Verginadis, Y., Patiniotakis, I., Apostolou, D., & Mentzas, G. N. (2021) · Intelligent Decision Technologies · doi:10.3233/idt-210214 · Cited by 14
“Fuzzy logic is intended to model logical reasoning with vague or imprecise statements and emerged in the context of the theory of fuzzy sets, introduced by Zadeh [32,33].”
Matrix games with linguistic intuitionistic fuzzy Payoffs : Basic results and solution methods
Verma, R., & Aggarwal, A. (2021) · Artificial Intelligence Review · doi:10.1007/s10462-021-10014-2 · Cited by 13
“The theory of fuzzy sets (FSs), proposed by Zadeh (1975), provides an efficient tool to deal with uncertainty and fuzziness occurred in many organizational decision making and game-related problems.”
Background

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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