Picture fuzzy sets
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In this paper, we introduce the concept of picture fuzzy sets (PFS), which are direct extensions of the fuzzy sets and the intuitonistic fuzzy sets. Then some operations on PFS with some properties are considered. The following sections are devoted to the Zadeh Extension Principle, picture fuzzy relations and picture fuzzy soft sets. Here, the basic preliminaries of PFS theory are presented.
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Cites
Molodtsov, D. A. (1999) · Computers & Mathematics with Applications · doi:10.1016/s0898-1221(99)00056-5 · Cited by 4,728 · see citing works
Interval valued intuitionistic fuzzy sets
Atanassov, K. T., & Gargov, G. (1989) · Fuzzy Sets and Systems · doi:10.1016/0165-0114(89)90205-4 · Cited by 2,933 · see citing works
Atanassov, K. T. (1999) · Studies in fuzziness and soft computing · doi:10.1007/978-3-7908-1870-3_1 · Cited by 2,224 · see citing works
Fuzzy Preference Modelling and Multicriteria Decision Support
Fodor, J. C., & Roubens, M. (1994) · Springer eBooks · doi:10.1007/978-94-017-1648-2 · Cited by 2,023 · see citing works
Interval-Valued Intuitionistic Fuzzy Sets
Atanassov, K. T. (2019) · Studies in fuzziness and soft computing · doi:10.1007/978-3-030-32090-4 · Cited by 1,828 · see citing works
Distances between intuitionistic fuzzy sets
Szmidt, E. J., & Kacprzyk, J. (2000) · Fuzzy Sets and Systems · doi:10.1016/s0165-0114(98)00244-9 · Cited by 1,637 · see citing works
On some new operations in soft set theory
Ali, M. İ., Feng, F., Liu, X., et al. (2009) · Computers & Mathematics with Applications · doi:10.1016/j.camwa.2008.11.009 · Cited by 1,458 · see citing works
Nguyen, H. T., Nguyen, H. T., & Walker, E. A. (2005) · Chapman & Hall/CRC eBooks · doi:10.1201/9781420057102 · Cited by 1,059 · see citing works
On Intuitionistic Fuzzy Sets Theory
Atanassov, K. T. (2012) · Studies in fuzziness and soft computing · doi:10.1007/978-3-642-29127-2 · Cited by 994 · see citing works
Picture fuzzy sets - A new concept for computational intelligence problems
Cường, B. C., & Крейнович, В. (2013) · World Congress on Information and Communication Technologies · doi:10.1109/wict.2013.7113099 · Cited by 690 · see citing works
Self-citationNguyen, H. T., Walker, C. A., & Walker, E. A. (2018) · Chapman & Hall/CRC eBooks · doi:10.1201/9780429505546 · Cited by 405 · see citing works
Construction of intuitionistic fuzzy relations with predetermined properties
Bustince, H. (2000) · Fuzzy Sets and Systems · doi:10.1016/s0165-0114(97)00381-3 · Cited by 101 · see citing works
Intuitionistic fuzzy relations (Part I)
López, P. B., & Sola, H. N. B. (1995) · RACO (Revistes Catalanes amb Accés Obert) (Consorci de Serveis Universitaris de Catalunya) · Cited by 89 · see citing works
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Research works printed but not linked: 6
- [7]7. B. C. Cuong, "Picture fuzzy sets first results. part 1," Seminar Neuro-Fuzzy Systems with Applications, Preprint 03/2013, Institute of Mathematics, Hanoi, May 2013.
- [8]8. --, "Picture fuzzy sets first results. part 2," Seminar Neuro-Fuzzy Systems with Applications, Preprint 04/2013, Institute of Mathematics, Hanoi, June 2013.
- [9]9. B. C. Cuong and V. Kreinovich, "An extended soft set model: picture fuzzy soft set," Seminar Neuro-Fuzzy Systems with Applications, Preprint 04/2014, Institute of Mathematics, Hanoi, June 2014.
- [12]12. P. Maji, R. Biswas, and A. R. Roy, "Soft set theory," Computers & Mathematics with Applica- tions, vol. 45, no. 4, pp. 555-562, 2003.
- [13]13. D. Molodtsov, "Soft set theoryfirst results," Computers & Mathematics with Applications, vol. 37, no. 4, pp. 19-31, 1999.
- [16]16. L. A. Zadeh, "Fuzzy sets," Information and control, vol. 8, no. 3, pp. 338-353, 1965. Received on September 26 -2014 Revised on October 07 -2014
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T-spherical linear Diophantine fuzzy aggregation operators for multiple attribute decision-making
Al-Quran, A. (2023) · AIMS Mathematics · doi:10.3934/math.2023618 · Cited by 28 · see citing works
Aleksić, A., Tadić, D., Komatina, N., & Nestić, S. (2025) · Mathematics · doi:10.3390/math13132216 · Cited by 11 · see citing works
- Authors
- Cường, B. C.
- Corresponding author
- Cường, Bùi Công
- Venue
- Journal of Computer Science and Cybernetics
- Published
- 2015-02-02
- Volume
- 30
- Issue
- 4
- ISSN
- 1813-9663 (ISSN-L)
- OpenAlex
- W1983286635
- Cited by
- 875
- References
- 13
- Citations by year
- 2026: 46 · 2025: 97 · 2024: 139 · 2023: 165 · 2022: 110 · 2021: 133 · 2020: 86 · 2019: 46 · 2018: 29 · 2017: 8 · 2016: 10 · 2015: 4
- FWCI
- 21.24
- Type
- journal article
- Language
- en
- Open access
- bronze
- doi.org
- Locations
- Journal of Computer Science and Cybernetics (publishedVersion)
- Funders
- National Foundation for Science and Technology Development (102.05)
- Topics
- Social Sciences › Decision Sciences › Management Science and Operations Research › Fuzzy and Soft Set Theory
- Social Sciences › Decision Sciences › Management Science and Operations Research › Multi-Criteria Decision Making
- Physical Sciences › Computer Science › Computational Theory and Mathematics › Rough Sets and Fuzzy Logic
- Keywords
- picture fuzzy sets, fuzzy sets, intuitionistic fuzzy sets, Zadeh extension principle
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