Some operations on intuitionistic fuzzy sets

By S. K. De, R. Biswas, Akhil Ranjan Roy. Fuzzy Sets Syst., 2000

559 citations recorded by the source corpus.

Subfields: Artificial Intelligence, Management Science and Operations Research, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/5334efb9641b7dba2aa401a491a9afbeedf5b329

How researchers see this paper

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

In Artificial Intelligence

1. Peide Liu
2. Peng Wang
3. Zeshui Xu
4. Weize Wang
5. Xinwang Liu
6. Ronald R. Yager
7. Xindong Peng
8. Harish Garg

In Management Science and Operations Research

1. Peide Liu
2. Peng Wang
3. Weize Wang
4. Xinwang Liu
5. Harish Garg
6. Zeshui Xu
7. Ronald R. Yager
8. Meimei Xia

In Statistics and Probability

1. Peide Liu
2. Peng Wang
3. Weize Wang
4. Xinwang Liu
5. Ronald R. Yager
6. Zeshui Xu
7. Meimei Xia
8. Harish Garg

Citations in the corpus

• Intuitionistic Fuzzy Aggregation Operators (2007, methodology): “AN intuitionistic fuzzy set (A-IFS), developed by Atanassov [1], [2], is a powerful tool to deal with vagueness [3].”
• Choquet integrals of weighted intuitionistic fuzzy information (2010, background): “[6] further defined the concentration, dilation and normalization of IFSs, and proved some propositions in this context.”
• Some q‐Rung Orthopair Fuzzy Aggregation Operators and their Applications to Multiple‐Attribute Decision Making (2018, unknown): “Suppose α = 〈u, v〉, α1 = 〈u1, v1〉, and α2 = 〈u2, v2〉 are any three q-ROFNs, and n, n1, n2 > 0, then (1) α1 ⊕ α2 = α2 ⊕ α1, (8) (2) α1 ⊗ α2 = α2 ⊗ α1, (9) (3) n(α1 ⊕ α2) = nα1 ⊕ nα2, (10) (4) n1α ⊕ n2α = (n1 + n2)α, (11) (5) α1 ⊗ α2 = αn1+n2, (12) (6) α1 n ⊗ α2 = (α1 ⊗ α2).”
• Intuitionistic Fuzzy Information Aggregation Using Einstein Operations (2012, background): “[19] further defined the concentration, dilation, and normalization of AIFSs.”
• Some similarity measures of intuitionistic fuzzy sets and their applications to multiple attribute decision making (2007, unknown): “The IFS generalizes the fuzzy set introduced by Zadeh (1965), and has been found to be highly useful to deal with vagueness ( De et al., 2000 ).”
• Dynamic intuitionistic fuzzy multi-attribute decision making (2008, background): “[16] added some new operations such as concentration, dilation and normalization of IFSs.”
• Some q‐Rung Orthopai Fuzzy Bonferroni Mean Operators and Their Application to Multi‐Attribute Group Decision Making (2018, unknown): “(4) ã1 ⊗ ã2 = ( u1u2, ( v q 1 + v 2 − v 1 v 2 )1/q) (4) (5) λã1 = (( 1 − (1 − uq1) )1/q, v1λ) , λ > 0 (5)”
• Similarity measures of intuitionistic fuzzy sets based on Hausdorff distance (2004, unknown): “For any positive real number n, De et al. (2000) defined the IFS F n as follows: F n ¼ fðx; ½lF ðxÞ n ; 1 ½1 mF ðxÞ nÞjx 2 Xg: Using the above operation, they also defined the concentration and dilation of F as follows: concentration: CONðF Þ ¼ F 2; dilation: DILðF Þ ¼ F 1=2: Like fuzzy sets, CONðF…”
• NOTE ON FUZZY SETS (2014, unknown): “[3] investigated some”