Pythagorean fuzzy subsets

By Ronald R. Yager. Joint IFSA World Congress and NAFIPS Annual Meeting, 2013

2,112 citations recorded by the source corpus.

Subfields: Computational Theory and Mathematics, Management Science and Operations Research

View Paper: https://www.semanticscholar.org/paper/7d615595bed34e5499ef0b5f017548eadd16dfd7

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Computational Theory and Mathematics

1. Xindong Peng
2. Harish Garg
3. Zeshui Xu
4. Yong Yang
5. Ronald R. Yager
6. Francisco Herrera
7. Xiaolu Zhang
8. Ganeshsree Selvachandran

In Management Science and Operations Research

1. Xindong Peng
2. Harish Garg
3. Yong Yang
4. Zeshui Xu
5. Ganeshsree Selvachandran
6. Peide Liu
7. Huiyong Yuan
8. Xiaolu Zhang

Citations in the corpus

• Pythagorean Fuzzy Choquet Integral Based MABAC Method for Multiple Attribute Group Decision Making (2016, background): “3,13 Recently, Yager 14 proposed Pythagorean fuzzy set (PFS) characterized by a membership degree and a nonmembership degree which satisfies the condition that the square sum of its membership degree and nonmembership degree is less than or equal to 1.”
• An approach toward decision-making and medical diagnosis problems using the concept of spherical fuzzy sets (2019, background): “Definition 2 [26] For any universal set X, a Pythagorean FS is defined as S 1⁄4 x; s x ð Þ; d x ð Þ for all x 2 X f g Here s; d : X ! 0; 1 1⁄2 represents the degree of membership and degree of non-membership, respectively, provided that 0 s(2) x ð Þ þ d(2) x ð Þ 1 and h x ð Þ 1⁄4 ffiffiffiffiffiffif”
• A novel accuracy function under interval-valued Pythagorean fuzzy environment for solving multicriteria decision making problem (2016, methodology): “As for the PFNs, Yager [15, 17] defined the operations for three PFNs α = 〈μ, ν〉, α1 = 〈μ1, ν1〉 and α2 = 〈μ2, ν2〉, λ > 0, as follows – α1 ⊕ α2 = 〈√ μ1 + μ2 − μ1μ2, ν1ν2 〉 – α1 ⊗ α2 = 〈 μ1μ2, √ ν2 1 + ν2 2 − ν2 1ν 2 〉 – λ · α = 〈√1 − (1 − μ2)λ, νλ〉 – α = 〈μλ,√1 − (1 − ν2)λ〉”
• Linguistic Pythagorean fuzzy sets and its applications in multiattribute decision‐making process (2018, background): “So, Yager 26,27 introduced a nonstandard fuzzy set called Pythagorean fuzzy (PF) set (PFS), which is an extension of IFS theory, and meet the conditions that the square sum of its membership degree and nonmembership degree is less than or equal to one.”
• A Novel Approach Based on Similarity Measure for Pythagorean Fuzzy Multiple Criteria Group Decision Making (2016, methodology): “10,11 Obviously, based on the definitions of the Pythagorean fuzzy distance measure and the complement operation of PFNs, the sm ( β 1 , β 2 ) can be further written as P ROPOSITION 3.1.”
• Pythagorean Fuzzy Information Measures and Their Applications (2017, background): “(9) E9(M) = 1 (√2−1)×|X| ∑ x∈X(sin 1+μ(2)M (x)−ν2 M (x) 4 π + sin 1−μ(2)M (x)+ν2 M (x) 4 π − 1); (10) E10(M) = 1 (√2−1)×|X| ∑ x∈X(cos 1+μ(2)M (x)−ν2 M (x) 4 π + cos 1−μ(2)M (x)+ν2 M (x) 4 π − 1); (11) E11(M) = 1 |X| ∑ x∈X cot( 1 4 π + |μ(2)M (x)−ν2 M (x)| 4(1+π2 M (x)) π );”
• Application of Exponential Jensen Picture Fuzzy Divergence Measure in Multi-Criteria Group Decision Making (2019, methodology): “The quantitative fuzzy information can be expressed by fuzzy set (FS) [1], intuitionistic fuzzy set (IFS) [2], Pythagorean fuzzy set (PyFS) [3,4], picture fuzzy set (PFS) [5] and so on.”
• Fundamental Properties of Interval‐Valued Pythagorean Fuzzy Aggregation Operators (2016, neutral): “(2) The interval-valued Pythagorean fuzzy medium concordance set U ′ kl : U ′ kl = {j | s(p̃kj ) > s(p̃lj ) and a(p̃kj ) ≤ a(p̃lj )} (17)”
• A New Generalized Pythagorean Fuzzy Information Aggregation Using Einstein Operations and Its Application to Decision Making (2016, methodology): “Given three PFNs α = P ( μ, ν ), α 1 = (cid:4) μ 1 , ν 1 (cid:5) , and α 2 = (cid:4) μ 2 , ν 2 (cid:5) , Yager and Yager and Abbasov 12,14 defined the basic operations, which can be defined as follows: For PFNs, Yager and Abbasov 14 introduced a score function S as follows: .”
• Some Results for Pythagorean Fuzzy Sets (2015, methodology): “The relative closeness coefficient is obtained as follows: ξk = d(Wk, W −) d(Wk, W−) + d(Wk, W+) , (11)”
• Pythagorean fuzzy set: state of the art and future directions (2017, background): “Yager (2013) initially proposed serval basic operations to handle PFNs. Zhang andXu (2014) replenished some new operations such as ⊕ and ⊗.”
• Fermatean fuzzy sets (2019, background): “For such instances, Yager (2013) launched a new notion of Pythagorean fuzzy set to manage this condition.”