The Concept of a Linguistic Variable and Its Application to Approximate Reasoning—I
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As a generalization of classical set theory, the primary objective of fuzzy sets is to enable a mathematical representation of linguistic variables, allowing decision-makers to model systems characterized by partially known or incomplete information.
“As a generalization of classical (crisp) set theory, the primary objective of fuzzy sets is to enable a mathematical representation of linguistic variables, allowing decision-makers to model systems characterized by partially known or incomplete information [48].”
From An Integrated AHP–Fuzzy AHP Evaluation Framework for Large Language Models in Software Engineering Education (2026) · cites this paper as [48]
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Is There a Need for Fuzzy Logic?
Zadeh, L. A. (2008) · Information Sciences · doi:10.1016/j.ins.2008.02.012 · Cited by 1,352 · see citing works
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“variables whose values are propositions and words drawn from a natural language [30], [31], [32].”
BackgroundZhang, X., Wang, H., Stojanovic, V., Cheng, P., He, S.-P., Luan, X., & Liu, F. (2021) · IEEE transactions on fuzzy systems · doi:10.1109/tfuzz.2021.3086224 · Cited by 194 · see citing works
“It is of great significance to introduce the type-2 fuzzy set [10], which can be seen as a generalization of the concept of type-1 fuzzy set.”
BackgroundMahmood, T., & Rehman, U. U. (2021) · International Journal of Intelligent Systems · doi:10.1002/int.22639 · Cited by 185
“15 – 17 To handle such kind of information a decision analyst needs a complex fuzzy set (CFS) which was given by Ramot et al. 18 where they wide the range of MD to the unit circle in the complex plane.”
MethodAli, Z., Mahmood, T., Ullah, K., & Khan, Q. (2021) · Reports in Mechanical Engineering · doi:10.31181/rme2001020105t · Cited by 178 · see citing works
“For example, interval-valued FS was explored by Zadeh (1975), Torra (2010) elaborated the principle of hesitant FS (HFS), Karnik and Mendel (2001) utilized certain operational laws based on type-2 FS (T-2FS), Mendel and John (2002) developed T2FS made simple, and Mahmood (2020) developed the theory…”
BackgroundThe applications of MCDM methods in COVID-19 pandemic: A state of the art review
Sotoudeh-Anvari, A. (2022) · Applied Soft Computing · doi:10.1016/j.asoc.2022.109238 · Cited by 163 · see citing works
“[39] L.A. Zadeh, Information and control, Fuzzy Sets 8 (3) (1965) 338–353.”
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“In response to these challenges, Fuzzy Logic (FL), introduced by Lotfi Zadeh in 1975, represents a paradigm shift from the binary precision of traditional logic systems (Zadeh, 1975).”
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Pythagorean Fuzzy TOPSIS Method for Green Supplier Selection in the Food Industry
Hajiaghaei-Keshteli, M., Cenk, Z., Erdebilli, B., Özdemir, Y., & Gholian-Jouybari, F. (2023) · Expert systems with applications · doi:10.1016/j.eswa.2023.120036 · Cited by 151
Linguistic Pythagorean fuzzy CRITIC-EDAS method for multiple-attribute group decision analysis
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An interval valued neutrosophic decision-making structure for sustainable supplier selection
Yazdani, M., Torkayesh, A., Stević, Ž., Chatterjee, P., Ahari, S. A., & Hernandez, V. D. (2021) · Expert systems with applications · doi:10.1016/j.eswa.2021.115354 · Cited by 144 · see citing works
Customer-oriented product design using an integrated neutrosophic AHP & DEMATEL & QFD methodology
Karaşan, A., Ilbahar, E., Çebi, S., & Kahraman, C. (2022) · Applied Soft Computing · doi:10.1016/j.asoc.2022.108445 · Cited by 136
Alkan, N., & Kahraman, C. (2021) · Applied Soft Computing · doi:10.1016/j.asoc.2021.107653 · Cited by 134 · see citing works
“After were introduced type-2 uzzy sets by Zadeh [22] in 1975, Atanassov [23] extended the uzzy sets into the intuitionistic fuzzy sets (IFSs) represented with membership and non-membership degrees including the hesitancy of decision-makers [24].”
MethodInfluentialBhattacharjee, P., Dey, V., & Mandal, U. (2020) · doi:10.1016/j.ssci.2020.104967 · Cited by 130
Zhang, H., & Wei, G. (2023) · Computational and Applied Mathematics · doi:10.1007/s40314-022-02183-9 · Cited by 129 · see citing works
“In the past decades, FSs have facilitated the advancement of various branches and derived many new versions (Frini 2017; Salah and Moselhi 2016; Chen et al. 2014; Zadeh 1975; Abdullah et al. 2014; Tao et al. 2015).”
BackgroundÇelik, E., & Gul, M. (2021) · Automation in Construction · doi:10.1016/j.autcon.2021.103699 · Cited by 126 · see citing works
Fuzzy Machine Learning: A Comprehensive Framework and Systematic Review
Lu, J., Ma, G., & Zhang, G.-Q. (2024) · IEEE transactions on fuzzy systems · doi:10.1109/tfuzz.2024.3387429 · Cited by 121 · see citing works
“2) Regression: Fuzzy regression models [50] perform a type of regression analysis that incorporates both possibility theory and fuzzy set theory [51].”
BackgroundMethodWu, Y., Deng, Z., Tao, Y., Wang, L., Liu, F., & Zhou, J. (2021) · Journal of Cleaner Production · doi:10.1016/j.jclepro.2021.129233 · Cited by 136 · see citing works
Spherical Linear Diophantine Fuzzy Sets with Modeling Uncertainties in MCDM
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Wei, G., Wei, C., & Guo, Y.-F. (2021) · Soft Computing - A Fusion of Foundations, Methodologies and Applications · doi:10.1007/s00500-021-05842-x · Cited by 110
“Especially, the hesitant fuzzy linguistic term sets (HFLTSs) are came up with by Rodriguez et al. (2012) on the foundation of HFSs (Torra 2010) and LTSs (Zadeh 1975) used to allow DMs to give a couple of possible linguistic variable.”
MethodGhoushchi, S. J., Haghshenas, S. S., Ghiaci, A. M., Guido, G., & Vitale, A. (2022) · Neural computing & applications (Print) · doi:10.1007/s00521-022-07929-4 · Cited by 107
“Zadeh [62] introduced Type-2 fuzzy sets; compared to the membership function of type-1 fuzzy sets, which are two-dimensional and fixed, type-2 fuzzy sets have a fuzzy three-dimensional membership function that provides more freedom to the decision-making process [63].”
MethodHosseini, S. M., Paydar, M., & Hajiaghaei-Keshteli, M. (2021) · Expert systems with applications · doi:10.1016/j.eswa.2021.115594 · Cited by 102
“Zadeh (1975) firstly introduced the main idea of this theory.”
Wan, S., Yan, J., & Dong, J.-Y. (2021) · Expert systems with applications · doi:10.1016/j.eswa.2021.116328 · Cited by 101
Jin, F.-F., Liu, J.-P., Zhou, L.-G., & Martínez, L. (2021) · Group Decision and Negotiation · doi:10.1007/s10726-021-09736-z · Cited by 101 · see citing works
Chen, Z.-S., Zhang, X., Rodríguez, R. M., Pedrycz, W., Martínez, L., & Skibniewski, M. (2022) · IEEE transactions on fuzzy systems · doi:10.1109/tfuzz.2022.3179594 · Cited by 100
“The notion of linguistic variables introduced by [42] is a mathematical semantic representation and used to approximately characterize a qualitative description.”
BackgroundMethodZhu, X., Meng, X., & Zhang, M. (2021) · Journal of Civil Engineering and Management · doi:10.3846/jcem.2021.15260 · Cited by 118 · see citing works
“As a special case of Type-2 fuzzy set, intervalvalued fuzzy set (IVFS) proposed by Zadeh (1975) and other researchers has attracted great attention because the membership function of interval arithmetic is much simpler than the general Type-2 fuzzy set.”
BackgroundMethodXing, Y., Cao, M., Liu, Y., Zhou, M., & Wu, J. (2022) · Computers & industrial engineering · doi:10.1016/j.cie.2022.107935 · Cited by 99
Gao, Y.-B., Liu, J., Wang, Z.-H., & Wu, L.-G. (2021) · IEEE Transactions on Systems, Man, and Cybernetics: Systems · doi:10.1109/tsmc.2019.2911726 · Cited by 98
“Particularly, type-2 FLSs, which are described based on type-2 fuzzy sets [21], are extended from type-1 ones in order to comprehensively represent the uncertainties embed in fuzzy rule base [22].”
BackgroundTürk, S., Deveci, M., Özcan, E., Canıtez, F., & John, R. (2021) · Information Sciences · doi:10.1016/j.ins.2020.08.076 · Cited by 98 · see citing works
An integrated ELECTRE-I approach for risk evaluation with hesitant Pythagorean fuzzy information
Akram, M., Luqman, A., & Alcantud, J. (2022) · Expert systems with applications · doi:10.1016/j.eswa.2022.116945 · Cited by 97
A survey of quantum-like approaches to decision making and cognition
Ashtiani, M., & Azgomi, M. A. (2015) · Mathematical Social Sciences · doi:10.1016/j.mathsocsci.2015.02.004 · Cited by 96 · see citing works
Chen, Z.-S., Yang, L.-L., Chin, K., Yang, Y., Pedrycz, W., Chang, J.-P., Martínez, L., & Skibniewski, M. (2021) · Applied Soft Computing · doi:10.1016/j.asoc.2021.107903 · Cited by 96
Ayyıldız, E., & Gumus, A. T. (2021) · Environmental science and pollution research international · doi:10.1007/s11356-021-13223-y · Cited by 94
“Then, Zadeh extends Type-1 fuzzy sets with an interval of membership function and develops Type-2 fuzzy sets (Zadeh 1975).”
BackgroundAn extended MARCOS method for MCGDM under 2-tuple linguistic q-rung picture fuzzy environment
Akram, M., Khan, A., Luqman, A., Senapati, T., & Pamucar, D. (2023) · Engineering applications of artificial intelligence · doi:10.1016/j.engappai.2023.105892 · Cited by 93 · see citing works
Liu, S., He, X.-J., Chan, F., & Wang, Z.-Y. (2022) · Expert systems with applications · doi:10.1016/j.eswa.2022.117414 · Cited by 93 · see citing works
“Hence, Zadeh (1975) proposed the type-2 fuzzy sets, extending the conventional type-1 fuzzy set.”
BackgroundDouble hierarchy hesitant fuzzy linguistic entropy-based TODIM approach using evidential theory
Liu, P.-D., Shen, M., Teng, F., Zhu, B.-Y., Rong, L.-L., & Geng, Y. (2021) · Information Sciences · doi:10.1016/j.ins.2020.07.062 · Cited by 90 · see citing works
Ghoushchi, S. J., Garg, H., Bonab, S. R., & Rahimi, A. (2023) · Expert systems with applications · doi:10.1016/j.eswa.2023.119884 · Cited by 89
Deveci, M., Gokasar, I., Castillo, O., & Daim, T. (2022) · Computers & industrial engineering · doi:10.1016/j.cie.2022.108773 · Cited by 89
Çelik, E., Yücesan, M., & Gül, M. (2021) · Environmental Science and Pollution Research · doi:10.1007/s11356-021-13832-7 · Cited by 100 · see citing works
“Interval type-2 fuzzy sets Zadeh (1975) developed type-2 fuzzy sets as an extended version of classical fuzzy sets (Karnik and Mendel, 2001; Mendel, 2007).”
BackgroundA spherical fuzzy methodology integrating maximizing deviation and TOPSIS methods
Farrokhizadeh, E., Seyfi-Shishavan, S. A., Gündoğdu, F., Donyatalab, Y., Kahraman, C., & Seifi, S. H. (2021) · Engineering applications of artificial intelligence · doi:10.1016/j.engappai.2021.104212 · Cited by 89 · see citing works
A comprehensive bibliometric analysis of uncertain group decision making from 1980 to 2019
Wang, X.-X., Xu, Z.-S., Su, S., & Zhou, W. (2021) · Information Sciences · doi:10.1016/j.ins.2020.08.036 · Cited by 89 · see citing works
Tanim, A. H., Goharian, E., & Moradkhani, H. (2022) · Scientific Reports · doi:10.1038/s41598-022-15237-z · Cited by 88 · see citing works
Literature Review of the Recent Trends and Applications in Various Fuzzy Rule-Based Systems
Varshney, A. K., & Torra, V. (2023) · International Journal of Fuzzy Systems · doi:10.1007/s40815-023-01534-w · Cited by 100 · see citing works
“They use Linguistic Variables [5] to represent features in antecedents, whose values are context dependent on the membership function of the feature.”
MethodXing, Y., Wu, J., Chiclana, F., Yu, G.-F., Cao, M., & Herrera-Viedma, E. (2023) · Information Fusion · doi:10.1016/j.inffus.2023.01.004 · Cited by 84
“In the actual SN-GDM, individual experts may prefer to use linguistic terms to express their evaluation information [29–31]: assumed that there is an odd number of labels, with the middle one being s r 2 , and the following negator operator as neg ( s a ) = s r − a [32].”
Jin, F.-F., Cao, M., Liu, J.-P., Martínez-López, L., & Chen, H. (2021) · Applied Soft Computing · doi:10.1016/j.asoc.2021.107170 · Cited by 82
Türk, S., Koç, A., & Sahin, G. (2021) · Scientific Reports · doi:10.1038/s41598-021-84257-y · Cited by 82 · see citing works
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Kumar, K., & Chen, S.-M. (2021) · Information Sciences · doi:10.1016/j.ins.2021.11.014 · Cited by 81
A novel picture fuzzy CRITIC & REGIME methodology: Wearable health technology application
Haktanır, E., & Kahraman, C. (2022) · Engineering applications of artificial intelligence · doi:10.1016/j.engappai.2022.104942 · Cited by 80 · see citing works
Interpersonal comparison of subjective probabilities: Toward translating linguistic probabilities
Dhami, M. K., & Wallsten, T. S. (2005) · Memory & Cognition · doi:10.3758/bf03193213 · Cited by 75 · see citing works
Tan, X., Zhu, J., Palomares, I., & Liu, X. (2022) · Information Fusion · doi:10.1016/j.inffus.2021.09.006 · Cited by 78
Mishra, A. R., Rani, P., Krishankumar, R., Ravichandran, K. S., & Kar, S. (2021) · Applied Soft Computing · doi:10.1016/j.asoc.2021.107155 · Cited by 97 · see citing works
“Recently, it is revealing that the HFSs have powerfully associated with the existing FSs, namely, Intuitionistic Fuzzy Sets (IFSs) [62], Type-2 Fuzzy Sets (T2FSs) [63], and Fuzzy Multi Sets (FMSs) [64].”
Enhanced CRITIC-REGIME method for decision making based on Pythagorean fuzzy rough number
Akram, M., Zahid, S., & Deveci, M. (2023) · Expert systems with applications · doi:10.1016/j.eswa.2023.122014 · Cited by 76
Bonab, S. R., Ghoushchi, S. J., Deveci, M., & Haseli, G. (2022) · Expert systems with applications · doi:10.1016/j.eswa.2022.119205 · Cited by 76
A novel alpha-level sets based fuzzy DEMATEL method considering experts' hesitant information
Zhang, Z., Wang, L., Wang, Y.-M., & Martínez-López, L. (2022) · Expert systems with applications · doi:10.1016/j.eswa.2022.118925 · Cited by 76
Critical Thinking About Explainable AI (XAI) for Rule-Based Fuzzy Systems
Mendel, J. M., & Bonissone, P. P. (2021) · IEEE Transactions on Fuzzy Systems · doi:10.1109/tfuzz.2021.3079503 · Cited by 95 · see citing works
“One branch of fuzzy logic research and applications uses these fuzzy implication MFs to perform approximate reasoning (e.g., [28]–[31]), but this is not the branch followed by most engineering and computer science advocates of fuzzy systems, due to the inherent bias in those MFs, which is due to…”
Pirbalouti, R. G., Dehkordi, M. K., Mohammadpour, J., Zarei, E., & Yazdi, M. (2023) · International journal of hydrogen energy · doi:10.1016/j.ijhydene.2023.03.028 · Cited by 74 · see citing works
“Zadeh [70] Type-2 fuzzy sets Sambuc [71] Interval-Value Spherical Fuzzy Sets Atanassov [72] Intuitionistic fuzzy sets Yager [73] Fuzzy bags Garibaldi and Ozen [74] Nonstationary fuzzy system Smarandache [75] Neutrosophic fuzzy sets Torra [76] Hesitant fuzzy set Yager [77] Pythagorean fuzzy subsets…”
BackgroundHabib, A., Akram, M., & Kahraman, C. (2022) · Expert systems with applications · doi:10.1016/j.eswa.2022.117016 · Cited by 74
Hashjin, N. M., Amiri, M. H., Mohammadzadeh, A., Mirjalili, S., & Khodadadi, N. (2024) · Cluster Computing · doi:10.1007/s10586-024-04475-7 · Cited by 73
Pamucar, D., Deveci, M., Gokasar, I., Delen, D., Köppen, M., & Pedrycz, W. (2023) · Decision Support Systems · doi:10.1016/j.dss.2023.113944 · Cited by 73
Lei, F., Wei, G., & Chen, X.-D. (2021) · International Journal of Intelligent Systems · doi:10.1002/int.22514 · Cited by 73
“Then, Equations (15) and (16) calculate the normalized probabilistic double hierarchy linguistic prospect weights.”
BackgroundZhu, J.-X., Ma, X.-L., Martínez, L., & Zhan, J.-M. (2023) · IEEE transactions on fuzzy systems · doi:10.1109/tfuzz.2023.3236386 · Cited by 72 · see citing works
“Facedwiththisscenario,Zadeh[12]initiatedtheconceptof linguisticvariables,whichismorerelevanttopeople’sthinking habits.”
Senapati, T., Chen, G.-Y., Mesiar, R., Yager, R., & Saha, A. (2022) · International Journal of General Systems · doi:10.1080/03081079.2022.2036140 · Cited by 71
“As a result, some new methodologies and hypotheses have been considered to be extensions of the FS hypothesis, for example, interval-valued FS (Zadeh 1975), intuitionistic FS (Atanassov 1986), fuzzy multiset (Yager 1986), and Type-2 FS (Dubois and Prade 1980).”
BackgroundWu, T., Liu, X.-W., Qin, J., & Herrera, F. (2021) · Applied Soft Computing · doi:10.1016/j.asoc.2021.107665 · Cited by 71 · see citing works
Mondal, A., & Roy, S. (2021) · International Journal of Intelligent Systems · doi:10.1002/int.22623 · Cited by 71 · see citing works
“Steps 3 and 4: The normalized decision matrix is obtained using Equations (31) (for E1, E3 and G2) and (32) (for E2, G1, S1 and S2).”
MethodInfluentialKahraman, C., & Alkan, N. (2021) · Notes on Intuitionistic Fuzzy Sets · doi:10.7546/nifs.2021.27.1.24-52 · Cited by 70 · see citing works
“Type-2 fuzzy sets have been introduced by Zadeh [43] to handle the vagueness in membership functions as an extension of ordinary fuzzy sets.”
MethodInfluentialWang, C.-N., Nguyen, N.-A.-T., & Dang, T.-T. (2022) · Scientific Reports · doi:10.1038/s41598-022-08257-2 · Cited by 69
Fuzzy Deep Learning for the Diagnosis of Alzheimer's Disease: Approaches and Challenges
Tanveer, M., Sajid, M., Akhtar, M., Quadir, A., Goel, T., Aimen, A., Mitra, S., Zhang, Y., Lin, C., & Ser, J. D. (2024) · IEEE Transactions on Fuzzy Systems · doi:10.1109/tfuzz.2024.3409412 · Cited by 81 · see citing works
“The focal points in fuzzy systems research involve three primary fuzzy techniques: the fuzzy set (referred to as type-1 fuzzy set) [28], the type-2 fuzzy set [34], and the linguistic variable [35].”
BackgroundCircular Intuitionistic Fuzzy Decision Making and Its Application
Çakır, E., & Taş, M. (2023) · Expert systems with applications · doi:10.1016/j.eswa.2023.120076 · Cited by 68 · see citing works
Akram, M., Niaz, Z., & Feng, F. (2022) · Granular Computing · doi:10.1007/s41066-022-00332-3 · Cited by 68
“To present the verbal preference, Zadeh (1975) introduced the concept of linguistic variables (LVs).”
Brenjkar, E., & Delijani, E. B. (2021) · Journal of Petroleum Science and Engineering · doi:10.1016/j.petrol.2021.110033 · Cited by 68
Song, Y., Li, G.-X., Ergu, D., & Liu, N. (2021) · Journal of the Operational Research Society · doi:10.1080/01605682.2021.1873079 · Cited by 68
“The use of linguistic terms or fuzzy numbers to evaluate qualitative variables is an intuitive and flexible approach, because they conform to people’s cognitive process and reasoning (Li, Kou, Lin et al., 2015; Li, Kou & Peng, 2015; Zadeh, 1975; Zhao et al., 2018).”
MethodAn Incentive Mechanism-Based Minimum Adjustment Consensus Model Under Dynamic Trust Relationship
Xing, Y., Wu, J., Chiclana, F., Liang, C., & Yager, R. R. (2024) · IEEE Transactions on Cybernetics · doi:10.1109/tcyb.2023.3349257 · Cited by 67
“…pair ξ = In GDM, experts may express their preferences using terms from a set of ordinal linguistic terms: S = { s 0 , s 1 , . . . , s r } ( r even) such that s 0 s 1 · · · s r , s ( r / 2 ) represents indifference of preference, and negator operator neg ( s a ) = s r − a [57], [58], [59].”
MethodJin, F.-F., Cai, Y., Pedrycz, W., & Liu, J.-P. (2022) · Computers & industrial engineering · doi:10.1016/j.cie.2022.108281 · Cited by 67 · see citing works
Analysis of evolutionary process in intuitionistic fuzzy set theory: A dynamic perspective
Yu, D., Sheng, L.-B., & Xu, Z.-S. (2022) · Information Sciences · doi:10.1016/j.ins.2022.04.019 · Cited by 67 · see citing works
Circular intuitionistic fuzzy TOPSIS method: pandemic hospital location selection
Alkan, N., & Kahraman, C. (2021) · Journal of Intelligent & Fuzzy Systems · doi:10.3233/jifs-219193 · Cited by 67 · see citing works
“Later, q-rung orthopair fuzzy sets (Q-ROFSs) have been proposed as a general class of IFSs and PFSs by Yager [52].”
RetractedPeng, X.-D., Krishankumar, R., & Ravichandran, K. (2021) · Soft Computing - A Fusion of Foundations, Methodologies and Applications · doi:10.1007/s00500-020-05437-y · Cited by 67
“Definition 1 (Zadeh 1975) An interval-valued fuzzy set (IVFS) I in U is given by I = {< χ, [I−(χ), I+(χ)] >| χ ∈ U }, (1) where 0 ≤ I−(χ) ≤ I+(χ) ≤ 1.”
Yu, K., Wu, Q., Chen, X., Wang, W.-Z., & Mardani, A. (2023) · Annals of Operations Research · doi:10.1007/s10479-023-05616-8 · Cited by 66 · see citing works
“However, because the traditional type-1 fuzzy sets (T1FSs) have unavoidable limitations in dealingwithuncertaininformation,Zadeh(1975)proposedtype-2fuzzysets(T2FSs)tosolve theproblemofuncertainty.”
Foroozesh, N., Karimi, B., Mousavi, S., & Mojtahedi, M. (2023) · Journal of Industrial Information Integration · doi:10.1016/j.jii.2023.100440 · Cited by 66 · see citing works
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Sharaf, I. (2022) · Soft Computing - A Fusion of Foundations, Methodologies and Applications · doi:10.1007/s00500-022-07749-7 · Cited by 66 · see citing works
“Several researchers developed other types of fuzzy sets besides Zadeh’s type 1 (T1FSs) and type 2 (T2FSs) ordinary fuzzy sets (Zadeh 1965, 1975).”
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Possibilistic classification by support vector networks
Hao, P.-Y., Chiang, J.-H., & Chen, Y.-D. (2022) · Neural Networks · doi:10.1016/j.neunet.2022.02.007 · Cited by 65
Numerical approach in the Hilbert space to solve a fuzzy Atangana-Baleanu fractional hybrid system
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Alkan, N., & Kahraman, C. (2022) · Engineering applications of artificial intelligence · doi:10.1016/j.engappai.2022.104809 · Cited by 64
Dang, R., Li, X.-M., Li, C.-T., & Xu, C. (2021) · doi:10.1016/j.scs.2021.103230 · Cited by 64
Saraji, M. K., Mardani, A., Köppen, M., Mishra, A., & Rani, P. (2021) · Artificial Intelligence Review · doi:10.1007/s10462-021-10029-9 · Cited by 64 · see citing works
“Recently, it is worth mentioning that the HFSs have powerfully related to the existing FSs, namely, Intuitionistic Fuzzy Sets (IFSs) (Atanassov 1986), Type-2 Fuzzy Sets (T2FSs) (Zadeh 1975), Fuzzy Multi-Sets (FMSs) (Yager 1986).”
BackgroundMohammed, H. J. (2021) · Journal of Sustainable Finance & Investment · doi:10.1080/20430795.2021.1886551 · Cited by 64
“RE TR AC TE D compositional rule of inference (Zadeh 1975) to draw conclusions from the fuzzy rule sets.”
BackgroundInfluentialRetractedLiu, B., Pavlou, P. A., & Cheng, X. (2021) · Information Systems Research · doi:10.1287/isre.2021.1045 · Cited by 73 · see citing works
Deep learning in economics: a systematic and critical review
Zheng, Y., Xu, Z., & Xiao, A. (2023) · Artificial Intelligence Review · doi:10.1007/s10462-022-10272-8 · Cited by 62 · see citing works
“Meanwhile, the combination of linguistic variables and economics assists to collect much natural linguistic information and reveal some undiscovered laws of economic motion (Zadeh, 1975).”
BackgroundA framework of LR fuzzy AHP and fuzzy WASPAS for health care waste recycling technology
Chakraborty, S., & Saha, A. K. (2022) · Applied Soft Computing · doi:10.1016/j.asoc.2022.109388 · Cited by 62
Risk assessment of renewable energy-based island microgrid using the HFLTS-cloud model method
Wu, Y., Hu, M., Liao, M., Liu, F., & Xu, C. (2020) · Journal of Cleaner Production · doi:10.1016/j.jclepro.2020.125362 · Cited by 64 · see citing works
Mondal, A., Roy, S., & Zhan, J.-M. (2023) · Expert systems with applications · doi:10.1016/j.eswa.2023.120431 · Cited by 61 · see citing works
- 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)
- 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
- 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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