Pythagorean Membership Grades in Multicriteria Decision Making
By Ronald R. Yager. IEEE transactions on fuzzy systems, 2014
2,389 citations recorded by the source corpus.
Subfields: Artificial Intelligence, Education, Management Science and Operations Research
View Paper: https://www.semanticscholar.org/paper/ed5a63cd83a23edc2938386cddbb1a0dfc2c3259
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Citations in the corpus
- Pythagorean Fuzzy Choquet Integral Based MABAC Method for Multiple Attribute Group Decision Making (2016, methodology): “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.”
- Fundamental Properties of Interval‐Valued Pythagorean Fuzzy Aggregation Operators (2016, background): “16,18 Let X be a universe of discourse.”
- Pythagorean fuzzy subsets (2013, methodology): “More generally a complement C operator is a mapping C: [0, 1] → [0, 1] that satisfies 1) Boundary Conditions: C(0) = 1 and C(1) = 0 2) Monotonicity: If a ≤ b then C(a) ≥ C(b) 3) Continuity 4) Involution: C(C(a)) = a In [8] Yager introduced a family of complement operators defined by C(a) = (1 - aP)1”
- Generalized Pythagorean Fuzzy Geometric Aggregation Operators Using Einstein t‐Norm and t‐Conorm for Multicriteria Decision‐Making Process (2017, background): “Yager 17 proposed some new fuzzy weighted average and geometric-aggregated operators using the different PFNs for solving MCDM problems.”
- Extension of TOPSIS to Multiple Criteria Decision Making with Pythagorean Fuzzy Sets (2014, methodology): “3–7 Recently, Yager 8,9 introduced Pythagorean fuzzy set (PFS) characterized by a membership degree and a nonmembership degree satisfying the condition that the square sum of its membership degree and nonmembership degree is equal to or less than 1, which is a generalization of IFS.”
- TOPSIS Method Based on Correlation Coefficient under Pythagorean Fuzzy Soft Environment and Its Application towards Green Supply Chain Management (2021, methodology): “Yager [29,30] PFS accommodates more uncertainty comparative to IFS, but it cannot deal with parametrization.”
- Pythagorean fuzzy set: state of the art and future directions (2017, background): “Definition 4.5 (Yager 2014) Let pi = (μi , νi )(i = 1, 2, . . . , n) be a collection of PFNs and w = (w1, w2, . . . , wn)T be the associated weight vector of O-PFOWA operator, with ∑n i=1 wi = 1, then an original Pythagorean fuzzy ordered weighted averaging (O-PFOWA) operator is a mapping O-PFOWA:…”
- Some q‐Rung Orthopai Fuzzy Bonferroni Mean Operators and Their Application to Multi‐Attribute Group Decision Making (2018, methodology): “, ãm) = ( 1 m (m − 1) m ⊕ i,j=1 i =j ã i ⊗Dã j ) 1 s+t (11)”
- 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.”
- Multiple-Attribute Decision-Making Based on Archimedean Bonferroni Operators of q-Rung Orthopair Fuzzy Numbers (2019, background): “[42] R. R. Yager, “Pythagorean membership grades in multicriteria decision making,” IEEE Trans.”
- A Historical Account of Types of Fuzzy Sets and Their Relationships (2016, methodology): “former are used currently in decision making [158].”