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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“…K in X is mostly characterized by a membership function (characteristic) fK (K) or lK(K) which relates with each point in X, a real number in the interval [0,1] with the value of fK (K) or lK(K) representing the ‘strength of belongingness’ or grade of membership of K in K (Zadeh 1965, 1975).”
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“Subsequently, Zadeh built a language model using fuzzy set theory and the concept of linguistic variables, known as the fuzzy linguistic method (Zadeh 1975).”
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Background
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“Zadeh 26 introduced the fuzzy set theory.”
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“IT2FLC contains at least one interval type-2 fuzzy set (IT2FS), which is a special case of type-2 FSs. IT2FLC reduces the computational complexity of the general type-2 FLC [3], [57]–[60].”
Background
RETRACTED: Linguistic q-rung orthopair fuzzy multiple-attribute group decision making based on the grey similarity degree and PROMETHEE II method
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Sensory evaluation of customer satisfaction using type-2 fuzzy logic
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“It should be noted that using the behavior planning procedures proposed in [11, 13] to achieve this goal does not allow each separate AUFV to solve its sub-stask autonomously so that the composition of the solutions of all of the tasks distributed among the flying vehicles during collective…”
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Representing uncertainty about fuzzy membership grade
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Revisiting type-2 triangular norms on normal convex fuzzy truth values
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FUZZY MULTICRITERIA FOR DETERMINING REASONABLE ADJUSTMENT IN HOUSING
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“…quantitative aspects that can be treated by precise numerical values with the help of fuzzy logic theory, in order to obtain an appropriate solution (Guo & Zhao, 2017; Herrera & Herrera-Viedma, 2000; Herrera-Viedma, Martínez, Mata, & Chiclana, 2005; Xu, 2005, 2007; Zadeh, 1975a, 1975b, 1975c).”
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Liu, J., Wang, M., Xu, P., Zeng, S.-Z., & Liu, M. (2019) · Economic Research-Ekonomska Istraživanja · doi:10.1080/1331677x.2019.1646146 · Cited by 3
“To handle these problems, linguistic reasoning (Zadeh, 1975) along with intuitionistic fuzzy set (IFS) (Atanassov, 1986) can be applied when processing the data which are both vague and imprecise.”
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Development of some linguistic aggregation operators with conservation of interaction between criteria and their application in multiple attribute group decision problems
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“Thus, the use of the fuzzy linguistic approach (Zadeh 1975a,b,c) is the most widespread mean to tackle these problems.”
Method
A Fuzzy Trustworthiness System with Probability Presentation Based on Center-of-gravity Method
Zhong, Y.-B., Liu, Z.-L., & Yuan, X.-H. (2015) · Annals of Data Science · doi:10.1007/s40745-015-0062-8 · Cited by 3
“And fuzzy inference is CRI reasoning method [3,4] or triple I method [5].”
Method
Sistema inteligente para procesamiento de imágenes en control de calidad basado en el modelo difuso singleton tipo 1
Dorantes, P. N. M., González, J., Mendez, G. M., Praga-Alejo, R. J., & Cosio, K. (2014) · Research on computing science · doi:10.13053/rcs-74-1-10 · Cited by 3
A numerical two-scale model of multi-granularity linguistic variables and it's application to group decision making
Cai, M., Sang, X.-Z., & Liu, X. (2014) · IEEE International Conference on Fuzzy Systems · doi:10.1109/fuzz-ieee.2014.6891572 · Cited by 3
“Linguistic Variables The concept of linguistic variables [31-33] is defined as a quintuple ) , , ), ( , ( M S U L T L , in which L is the name of the variable, ) (L T is the term set of labels or words of L , U is the universe of discourse, S is the syntactic rule, and M is the semantic rule which associates with each…”
Background
The Structure of the Type-Reduced Set of a Continuous Type-2 Fuzzy Set
Greenfield, S., & Chiclana, F. (2013) · EUSFLAT Conf. · doi:10.2991/eusflat.2013.102 · Cited by 3
“A type-2 fuzzy set Ã in X is a fuzzy set whose membership grades are themselves fuzzy [1, 15, 16].”
Background
Hesitant Fuzzy Linguistic Term Set Based Document Classification
Sahu, S. K., Sahu, N., Thakur, R. S., & Thakur, G. (2013) · International Conference on Communication Systems and Network Technologies · doi:10.1109/csnt.2013.126 · Cited by 3
“Zadeh, “The concept of a linguistic variable and its applications to approximate reasoning—Part I[40], D.”
New Generalized Definitions of Rough Membership Relations and Functions from Topological Point of View
El-Bably, M. K., Kozae, A. M., & El-Monsef, M. A. (2012) · JOURNAL OF ADVANCES IN MATHEMATICS · doi:10.24297/jam.v8i3.2575 · Cited by 3
“These include fuzzy set theory [16], rough set theory [35, 36], computing with words [17-19] and computational theory for linguistic dynamic systems [12].”
An Extended LibQUAL+ Model Based on Fuzzy Linguistic Information
Cabrerizo, F., Pérez, I. J., López-Gijón, J., & Herrera-Viedma, E. (2012) · Modeling Decisions for Artificial Intelligence · doi:10.1007/978-3-642-34620-0_10 · Cited by 3
Fuzzy Knowledge Representation Using Probability Measures of Fuzzy Events
Walaszek-Babiszewska, A. (2008) · doi:10.5772/6113 · Cited by 3
“…of the variable, L(X) is a set of linguistic values (words) which X takes, U is an universe of discourse, and M is a www.intechopen.com Automation and Robotics 330 semantic function, that assigns the fuzzy meaning (fuzzy subsets Ai, i=1,…,I in U) to each linguistic value from L(X) (Zadeh, 1975).”
Design Exploration With Imprecise Latency and Register Constraints
Chantrapornchai, C., Surakampontorn, W., & Sha, E. (2006) · IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems · doi:10.1109/tcad.2006.882591 · Cited by 3
Quality Makes the Information Market
van Gils, B., Proper, H., van Bommel, P., & van der Weide, T. P. (2006) · OTM Conferences · doi:10.1007/11914853_21 · Cited by 3
“In our quality framework, the concept of a linguistic variable is used to describe the fuzzy assessments made by actors [22, 23, 24, 21].”
Method
A comparative investigation of the impact of digitalisation and work-from-home policy on firm performance: MNEs vs international SMEs
Hajiagha, S. H. R., Mahdiraji, H. A., Behnam, M., & Garza-Reyes, J. (2026) · Technology and Society · doi:10.1016/j.techsoc.2025.103169 · Cited by 3
A Systematic Analysis of EDAS Method and Power Aggregation Operators Based on Bipolar Complex Fuzzy Linguistic for Rural Energy Infrastructure Decision
Fan, Y.-F., Ali, Z., & Yin, S. (2024) · IEEE Access · doi:10.1109/access.2024.3369917 · Cited by 3
“…CFSs (BCFSs) with two same grades in different directions, called positive truth grade and negative truth grade, such as In 1975, Zadeh [23], [24], [25] initiated the linguistic term set (LTS), which is very flexible and very effective in coping with uncertain and vague information, where to…”
Synthesizing fuzzy tree automata
Moghari, S. (2022) · RAIRO - Theoretical Informatics and Applications · doi:10.1051/ita/2022005 · Cited by 3
“Fuzzy linguistic variables are powerful tools for the approximate characterization of concepts that are not well-defined to be described in quantitative terms [22, 49, 50].”
BackgroundMethod
Model for ore deposits selection by using the fuzzy TOPSIS method
Popović, G., Stanujkić, D., Karabašević, D., & Štirbanović, Z. (2020) · doi:10.5937/jmma2001059p · Cited by 3
“According to Zadeh, the linguistic variables are defined as variables whose values are words or sentences in a natural or artificial language.”
BackgroundInfluential
Interval Type-2 Intuitionistic Fuzzy Logic System for Forecasting the Electricity Load
Eyoh, I., Eyoh, J., & Umoeka, I. J. (2020) · International Journal of Advances in Scientific Research and Engineering · doi:10.31695/ijasre.2020.33903 · Cited by 3
“This deficiency in type-1 FS led to the introduction of type-2 FS in [23], which is an extension of the type-1 FS.”
Background
Multiagent Approach to Fuzzy-Linguistic Knowledge Integration
Modliński, Ł., & Popek, G. (2018) · Computational Methods in Science and Technology · doi:10.12921/cmst.2018.0000047 · Cited by 3
“That is, it employs the Zadehian linguistic variable [20], [21], [22] as a base for a semantic model under-”
Method
Measurement of Level-of-Satisfaction of Decision Maker in Intelligent Fuzzy-MCDM Theory: A Generalized Approach
Vasant, P., Bhattacharya, A., & Abraham, A. (2008) · doi:10.1007/978-0-387-76813-7_9 · Cited by 3
“(11) was indicated as an S-curve MF by Zadeh (1971; 1975).”
Characterizing Buzz and Sentiment in Internet Sources: Linguistic Summaries and Predictive Behaviors
Tong, R. M., & Yager, R. (2006) · Computing Attitude and Affect in Text · doi:10.1007/1-4020-4102-0_21 · Cited by 3
Toward resilient and adaptive warehousing with fuzzy-based selection of automated storage systems for industry 5.0
Ayyildiz, E., Kesici, B., & Erdoğan, M. (2026) · Applied Soft Computing · doi:10.1016/j.asoc.2026.115202 · Cited by 2
A Novel Method to Investigate the Effect of Normalization Techniques on Fuzzy Multi-Criteria Decision-Making in Web Service Quality Assessments
Kalibatienė, D., & Simanavičienė, R. (2026) · Applied Sciences · doi:10.3390/app16062940 · Cited by 2
A programming framework for solving multi-objective multi-item solid transportation problem considering pollution and danger factors under uncertain environment
Zhu, J., Qiu, X., Zhao, Y., Liu, X., & Liu, L. (2025) · Soft Computing - A Fusion of Foundations, Methodologies and Applications · doi:10.1007/s00500-025-10921-4 · Cited by 2
Mathematical Model of the Software Development Process with Hybrid Management Elements
Semenov, S., Tsukur, V., Molokanova, V., Muchacki, M., Litawa, G., Mozhaiev, M., & Petrovska, I. (2025) · Applied Sciences · doi:10.3390/app152111667 · Cited by 2
Multi-attributive border approximation area comparison model based on Sugeno-Weber power fuzzy linguistic variables with Z-number information
Garg, H., Ali, Z., Pérez-Domínguez, L., & Hezam, I. H. (2025) · Alexandria Engineering Journal · doi:10.1016/j.aej.2025.09.043 · Cited by 2
Analysis of the challenges faced by Latin American banking sector in the context of Big Data
CARRIÓN-SALAZAR, J. P., Anholon, R., Minatogawa, V., Rojas-Córdova, C., Tapia-Ubeda, F. J., Sigahi, T. F. A. C., & Rampasso, I. S. (2025) · Journal of Modelling in Management · doi:10.1108/jm2-11-2023-0264 · Cited by 1
A New Approach to Near Approximation in Fuzzy Ideals of an MV-Algebras
Jokar, F., & Davvaz, B. (2025) · Foundations of Computing and Decision Sciences · doi:10.2478/fcds-2025-0003 · Cited by 2
Generalized harmonic fuzzy partition C-means clustering
Wu, C.-M., & Zhou, S. (2025) · Journal of Supercomputing · doi:10.1007/s11227-024-06723-4 · Cited by 2
“In 1975, Zadeh [31] proposed the theory of interval-valued fuzzy sets.”
Logical Formalisms for Ethics
Assadi, Z. (2024) · Conference on Information Technology for Social Good · doi:10.1145/3677525.3678691 · Cited by 2
Evaluation of Spare Parts Support Capacity of Civil Aircrafts Based on Type-2 Hesitant Pythagorean Fuzzy Sets and Improved Technique for Order Preference by Similarity to Ideal Solution
You, L., Wang, L.-L., Lv, X., Xiang, H.-C., & Wang, Z. (2024) · Applied Sciences · doi:10.3390/app14177475 · Cited by 2
Probabilistic multiplicative unbalanced linguistic game using linguistic cloud model
Chauhan, P., & Gupta, A. (2024) · Journal of Supercomputing · doi:10.1007/s11227-024-06240-4 · Cited by 2
Decision-Making Based on Fuzzy Linguistic Signatures
Ammar, N., & Kóczy, L. T. (2023) · 2023 4th International Conference on Communications, Information, Electronic and Energy Systems (CIEES) · doi:10.1109/ciees58940.2023.10378751 · Cited by 2
“Instead of a formal mapping, linguistic granulation of the universe may be much more flexible, and thus more particularly important role in the characterization of complex and/or ill-defined relations among variables [8].”
Background
Introduction to non-convex fuzzy geometry
Chakraborty, D., & Das, S. (2023) · Fuzzy Sets Syst. · doi:10.1016/j.fss.2023.108758 · Cited by 2
Evaluation of medical diagnosis of prostate cancer based on fuzzy TOPSIS–database interaction
Demirtaş, N., & Dalkılıç, O. (2023) · Computational and Applied Mathematics · doi:10.1007/s40314-023-02454-z · Cited by 2
“Deﬁnition 2.4 (Zadeh 1975) A linguistic variable is a variable whose values are linguistic terms.”
BackgroundMethodInfluential
System of linear fuzzy differential equations in the space of vector-valued linearly correlated fuzzy numbers
Shen, Y. (2023) · Fuzzy Sets Syst. · doi:10.1016/j.fss.2023.108672 · Cited by 2
T-Spherical 2-Tuple Linguistic Aggregation Operators and Their Applications in the Decision-Making Strategy
Mahmood, T., Ali, Z., & Awsar, A. (2023) · Mathematical Problems in Engineering · doi:10.1155/2023/6098162 · Cited by 2
RETRACTED: Methodology for teaching quality evaluation of college volleyball training with probabilistic double hierarchy linguistic information
Huang, B., & Chen, F. (2022) · Journal of Intelligent & Fuzzy Systems · doi:10.3233/jifs-222945 · Cited by 2
Retracted
Fuzzy Semantic Models of Fuzzy Concepts in Fuzzy Systems
Wang, Y.-X. (2022) · International journal of fuzzy systems and advanced applications · doi:10.46300/91017.2022.9.9 · Cited by 2
Modeling of Information Dissemination Processes Based on Diffusion Equations with Fuzzy Time Accounting
Ivohin, E., Voloshyn, O., & Makhno, M. F. (2021) · Cybernetics and Systems Analysis · doi:10.1007/s10559-021-00416-z · Cited by 2
Managing consistency and consensus measures and adjustment strategies in group decision making with probabilistic linguistic preference relations
Liang, P., Hu, J., & Chin, K. (2021) · Journal of Intelligent & Fuzzy Systems · doi:10.3233/jifs-211371 · Cited by 2
“It is usually the perception derived from a ﬁnite semantic scale with qualitative description such as linguistic terms sets (LTSs) rather than numerical values [5].”

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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