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Pythagorean Membership Grades, Complex Numbers, and Decision Making: PYTHAGOREAN MEMBERSHIP GRADES AND FUZZY SUBSETS
Abstract
We describe the idea of Pythagorean membership grades and the related idea of Pythagorean fuzzy subsets. We focus on the negation and its relationship to the Pythagorean theorem. We look at the basic set operations for the case of Pythagorean fuzzy subsets. A relationship is shown between Pythagorean membership grades and complex numbers. We specifically show that Pythagorean membership grades are a subclass of complex numbers called Π-i numbers. We investigate operations that are closed under Π-i numbers. We consider the problem of multicriteria decision making with satisfactions expressed as Pythagorean membership grades, Π-i numbers. We look at the use of the geometric mean and ordered weighted geometric operator for aggregating criteria satisfaction.
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Cites
Atanassov, K. T. (1986) · Fuzzy Sets and Systems · doi:10.1016/s0165-0114(86)80034-3 · Cited by 16,465
Cited by
Yager, R. R. (2013) · 2013 Joint IFSA World Congress and NAFIPS Annual Meeting (IFSA/NAFIPS) · doi:10.1109/ifsa-nafips.2013.6608375 · Cited by 2,703
Self-citationGeneralized Orthopair Fuzzy Sets
Yager, R. R. (2017) · IEEE Transactions on Fuzzy Systems · doi:10.1109/tfuzz.2016.2604005 · Cited by 2,251
Self-citationMahmood, T., Ullah, K., Khan, Q., & Jan, N. (2019) · Neural Computing and Applications · doi:10.1007/s00521-018-3521-2 · Cited by 910
Zhang, X. (2016) · Information Sciences · doi:10.1016/j.ins.2015.10.012 · Cited by 459
Spherical fuzzy sets and their applications in multi-attribute decision making problems
Ashraf, S., Abdullah, S., Mahmood, T., Ghani, F., & Mahmood, T. (2019) · Journal of Intelligent & Fuzzy Systems · doi:10.3233/jifs-172009 · Cited by 407
Metadata
- Authors
- Yager, R. R., & Abbasov, A. M.
- Venue
- International Journal of Intelligent Systems
- Publisher
- Hindawi Limited
- Published
- 2013-03-04
- Volume
- 28
- Issue
- 5
- Pages
- 436-452
- ISSN
- 0884-8173 (ISSN-L)
- OpenAlex
- W1668569279
- Cited by
- 1,430
- References
- 1
- FWCI
- 14.05
- Type
- journal article
- Language
- en
- Open access
- closed
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- Yager, R. R., & Abbasov, A. M. (2013). Pythagorean Membership Grades, Complex Numbers, and Decision Making: PYTHAGOREAN MEMBERSHIP GRADES AND FUZZY SUBSETS. International Journal of Intelligent Systems. https://doi.org/10.1002/int.21584
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