Research Article
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Year 2020, Issue: 33, 85 - 94, 31.12.2020

Abstract

References

  • L. A. Zadeh, Fuzzy Sets, Information and Control, 8(1965), 338- 353.
  • K. Atanassov, Intuitionistic Fuzzy Sets, Fuzzy Sets and Systems 20 (1986) 87-96.
  • R.R. Yager, A.M. Abbasov, Pythagorean Membership Grades, Complex Numbers and Decision Making, International Journal of Intelligent Systems 28 (2013) 436-452.
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  • F. Smarandache, Degree of Dependence and Independence of The (sub)components of Fuzzy Set and Neutrosophic set, Neutrosophic Sets and Systems 11 (2016) 95-97.
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  • J. Ye, Multicriteria Decision-making Method Using The Correlation Coefficient under Single-valued Neutrosophic Environment, International Journal of General Systems 42(4) (2013) 386-394.
  • J. Ye, Similarity Measure Between Interval Neutrosophic Sets and Their Applications in Multicriteria Decision making, Journal of Intelligent and Fuzzy Systems 26 (2014) 165-172.
  • Z.S. Xu, J. Chen, J.J. Wu, Clustering Algorithm for Intuitionistic Fuzzy Sets, Information Science 19 (2008) 3775-3790.
  • H.M. Zhang, Z.S. Xu, Q. Chen, Clustering Method of Intuitionistic Fuzzy Sets, Control Decision 22 (2007) 882-888.
  • J. Ye, Clustering Methods Using Distance-Based Similarity Measures of Single-valued Neutrosophic Sets, Journal Intelligent Systems 23 (2014) 379-389.
  • X. Peng, Y. Yang, Some Results for Pythagorean Fuzzy Sets, International Journal of Intelligent Systems 30 (2015) 1133-1160.
  • R.R. Yager, Pythagorean Fuzzy Subsets, in: Proc Joint IFSA World Congress and NAFIPS Annual Meeting, Edmonton, Canada, (2013) 57-61.

Similarity Measures of Pythagorean Neutrosophic Sets with Dependent Neutrosophic Components Between T and F

Year 2020, Issue: 33, 85 - 94, 31.12.2020

Abstract

Clustering plays an important role in data mining, pattern recognition and machine learning. This paper proposes Pythagorean neutrosophic clustering methods based on similarity measures between Pythagorean neutrosophic sets with T and F are dependent neutrosophic components [PN-Set]. First, we define a generalized distance measure between PN-Sets and propose two distance-based similarity measures of PN-Sets. Then, we present a clustering algorithm based on the similarity measures of PN-Sets to cluster Pythagorean neutrosophic data. Finally, an illustrative example is given to demonstrate the application and effectiveness of the developed clustering methods.

References

  • L. A. Zadeh, Fuzzy Sets, Information and Control, 8(1965), 338- 353.
  • K. Atanassov, Intuitionistic Fuzzy Sets, Fuzzy Sets and Systems 20 (1986) 87-96.
  • R.R. Yager, A.M. Abbasov, Pythagorean Membership Grades, Complex Numbers and Decision Making, International Journal of Intelligent Systems 28 (2013) 436-452.
  • F. Smarandache, A Unifying Field in Logics: Neutrosophic Logic, Neutrosophy, Neutrosophic Set, Neutrosophic Probability; American Research Press: Rehoboth, DE, USA, 1999.
  • F. Smarandache, Degree of Dependence and Independence of The (sub)components of Fuzzy Set and Neutrosophic set, Neutrosophic Sets and Systems 11 (2016) 95-97.
  • J. Ye, Single-valued Neutrosophic Cross-entropy for Multicriteria Decision-making Problems, Applied Mathematical Modelling 38 (2014) 1170-1175.
  • J. Ye, Multicriteria Decision-making Method Using The Correlation Coefficient under Single-valued Neutrosophic Environment, International Journal of General Systems 42(4) (2013) 386-394.
  • J. Ye, Similarity Measure Between Interval Neutrosophic Sets and Their Applications in Multicriteria Decision making, Journal of Intelligent and Fuzzy Systems 26 (2014) 165-172.
  • Z.S. Xu, J. Chen, J.J. Wu, Clustering Algorithm for Intuitionistic Fuzzy Sets, Information Science 19 (2008) 3775-3790.
  • H.M. Zhang, Z.S. Xu, Q. Chen, Clustering Method of Intuitionistic Fuzzy Sets, Control Decision 22 (2007) 882-888.
  • J. Ye, Clustering Methods Using Distance-Based Similarity Measures of Single-valued Neutrosophic Sets, Journal Intelligent Systems 23 (2014) 379-389.
  • X. Peng, Y. Yang, Some Results for Pythagorean Fuzzy Sets, International Journal of Intelligent Systems 30 (2015) 1133-1160.
  • R.R. Yager, Pythagorean Fuzzy Subsets, in: Proc Joint IFSA World Congress and NAFIPS Annual Meeting, Edmonton, Canada, (2013) 57-61.
There are 13 citations in total.

Details

Primary Language English
Subjects Mathematical Sciences
Journal Section Research Article
Authors

Jansi Rajan This is me 0000-0003-0588-9067

Mohana Krıshnaswamy This is me 0000-0002-0640-575X

Publication Date December 31, 2020
Submission Date January 8, 2019
Published in Issue Year 2020 Issue: 33

Cite

APA Rajan, J., & Krıshnaswamy, M. (2020). Similarity Measures of Pythagorean Neutrosophic Sets with Dependent Neutrosophic Components Between T and F. Journal of New Theory(33), 85-94.
AMA Rajan J, Krıshnaswamy M. Similarity Measures of Pythagorean Neutrosophic Sets with Dependent Neutrosophic Components Between T and F. JNT. December 2020;(33):85-94.
Chicago Rajan, Jansi, and Mohana Krıshnaswamy. “Similarity Measures of Pythagorean Neutrosophic Sets With Dependent Neutrosophic Components Between T and F”. Journal of New Theory, no. 33 (December 2020): 85-94.
EndNote Rajan J, Krıshnaswamy M (December 1, 2020) Similarity Measures of Pythagorean Neutrosophic Sets with Dependent Neutrosophic Components Between T and F. Journal of New Theory 33 85–94.
IEEE J. Rajan and M. Krıshnaswamy, “Similarity Measures of Pythagorean Neutrosophic Sets with Dependent Neutrosophic Components Between T and F”, JNT, no. 33, pp. 85–94, December 2020.
ISNAD Rajan, Jansi - Krıshnaswamy, Mohana. “Similarity Measures of Pythagorean Neutrosophic Sets With Dependent Neutrosophic Components Between T and F”. Journal of New Theory 33 (December 2020), 85-94.
JAMA Rajan J, Krıshnaswamy M. Similarity Measures of Pythagorean Neutrosophic Sets with Dependent Neutrosophic Components Between T and F. JNT. 2020;:85–94.
MLA Rajan, Jansi and Mohana Krıshnaswamy. “Similarity Measures of Pythagorean Neutrosophic Sets With Dependent Neutrosophic Components Between T and F”. Journal of New Theory, no. 33, 2020, pp. 85-94.
Vancouver Rajan J, Krıshnaswamy M. Similarity Measures of Pythagorean Neutrosophic Sets with Dependent Neutrosophic Components Between T and F. JNT. 2020(33):85-94.


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