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

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.

Keywords:

Pythagorean neutrosophic Sets with T and F are dependent neutrosophic components, clustering algorithm distance measure, similarity measure,

PDF

___

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.

Yayın Aralığı: Yılda 4 Sayı
Başlangıç: 2014
Yayıncı: Naim Çağman

Arşiv