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Some Results for Pythagorean Fuzzy Sets
Open accessAbstract
Pythagorean fuzzy sets (PFSs), originally proposed by Yager (Yager, Abbasov. Int J Intell Syst 2013;28:436–452), are a new tool to deal with vagueness considering the membership grades are pairs satisfying the condition . As a generalized set, PFSs have close relationship with intuitionistic fuzzy sets (IFSs). PFSs can be reduced to IFSs satisfying the condition . However, the related operations of PFSs do not take different conditions into consideration. To better understand PFSs, we propose two operations: division and subtraction, and discuss their properties in detail. Then, based on Pythagorean fuzzy aggregation operators, their properties such as boundedness, idempotency, and monotonicity are investigated. Later, we develop a Pythagorean fuzzy superiority and inferiority ranking method to solve uncertainty multiple attribute group decision making problem. Finally, an illustrative example for evaluating the Internet stocks performance is given to verify the developed approach and to demonstrate its practicality and effectiveness.
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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
Mahmood, T., Ullah, K., Khan, Q., & Jan, N. (2019) · Neural Computing and Applications · doi:10.1007/s00521-018-3521-2 · Cited by 910
Fundamental Properties of Interval-Valued Pythagorean Fuzzy Aggregation Operators
Peng, X., & Yang, Y. (2016) · International Journal of Intelligent Systems · doi:10.1002/int.21790 · Cited by 537
Self-citationZhang, X. (2016) · Information Sciences · doi:10.1016/j.ins.2015.10.012 · Cited by 459
Senapati, T., & Yager, R. R. (2019) · Engineering Applications of Artificial Intelligence · doi:10.1016/j.engappai.2019.05.012 · Cited by 451
Linear Diophantine fuzzy set and its applications towards multi-attribute decision-making problems
Riaz, M., & Hashmi, M. R. (2019) · Journal of Intelligent & Fuzzy Systems · doi:10.3233/jifs-190550 · Cited by 377
Metadata
- Authors
- Peng, X., & Yang, Y.
- Venue
- International Journal of Intelligent Systems
- Publisher
- Hindawi Limited
- Published
- 2015-05-07
- Volume
- 30
- Issue
- 11
- Pages
- 1133-1160
- ISSN
- 0884-8173 (ISSN-L)
- OpenAlex
- W2104077967
- Cited by
- 862
- References
- 1
- FWCI
- 61.93
- Type
- journal article
- Language
- en
- Open access
- bronze
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