Research Article
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Year 2020, Issue: 33, 15 - 25, 31.12.2020

Taha Öztürk , Adem Yolcu

Abstract

References

  • L. A. Zadeh, Fuzzy Sets, Information and Control 8 (1965) 338-353.
  • C. Chang, Fuzzy Topological Spaces, Journal of Mathematical analysis and Applications 24 (1968) 182-190.
  • R. Lowen, Fuzzy Topological Spaces and Fuzzy Compactness, Journal of Mathematical analysis and Applications 56(3) (1976) 621-633.
  • R. Lowen, Initial and Final Fuzzy Topologies and The Fuzzy Tycho no Theorem, Journal of Mathematical analysis and Applications 58(1) (1977) 11-21.
  • K. Atanassov, Intuitionistic fuzzy sets, Fuzzy Sets and Systems 20 (1986) 87-96.
  • D. Coker, An introduction of intuitionistic fuzzy topological spaces, Fuzzy Sets and Systems 88 (1997) 81-89.
  • I. M. Hanafy, Completely continuous functions in intuitionistic fuzzy topological spaces, Czechoslovak Mathematical Journal 53(4) (2003) 793-803.
  • K. Hur, J. H., Kim, J. H., Ryou, Intuitionistic Fuzzy Topological Spaces, The Pure and Applied Mathematics 11(3) (2004) 243-265.
  • R. Saadati and J. H., Park, On the Intuitionistic Fuzzy Topological Spaces, Chaos, Solitons and Fractals 27(2) (2006) 331-344.
  • R. R. Yager, Pythagorean Fuzzy Subsets, Proceeding Joint IFSA World Congress NAFIPS Annual Meeting, 1, Edmonton, Canada, (2013) 57-61.
  • R. R. Yager, A. M., Abbasov, Pythagorean Membership Grades, Complex Numbers, and Decision Making, International Journal of Intelligent Systems 28(5) (2014) 436-452.
  • P. Ren, Z. Xu, X. Gou, Pythagorean Fuzzy TODIM Approach to Multi-criteria Decision Making, Applied Soft Computing, 42 (2016) 246-259.
  • S. Zeng, J. Chen, X. Li, A Hybrid Method for Pythagorean Fuzzy Multiple-Criteria Decision Making, International Journal of Information Technology and Decision Making 15(2) (2016) 403-422.
  • X. Zhang, Z. Xu, Extension of TOPSIS to multiple criteria decisions making with Pythagorean fuzzy sets, International Journal of Intelligent Systems 29(12) (2014) 1061-1078.
  • H. Garg, New Logarithmic Operational Laws and Their Aggregation Operators for Pythagorean Fuzzy Set and Their Applications, International Journal of Intelligent Systems 34(1) (2019) 82-106.
  • H. Garg, A New Generalized Pythagorean Fuzzy Information Aggregation Using Einstein Operations and Its Application to Decision Making. International Journal of Intelligent Systems 31(9) (2016) 886-920.
  • W. Liang, X. Zhang, M. Liu, The Maximizing Deviation Method Based on Interval-valued Pythagorean Fuzzy Weighted Aggregating Operator for Multiple Criteria Group Decision Analysis. Discrete Dynamics in Nature and Society, (2015) Article ID 746572.
  • Z. Ma, Z. Xu, Symmetric Pythagorean fuzzy weighted geometric/averaging operators and their application in multicriteria decision-making problems, International Journal of Intelligent Systems 31(12) (2016) 1198-1219.
  • H. Garg, A Novel Correlation Coefficients Between Pythagorean Fuzzy Sets and Its Applications to Decision-making Processes, International Journal of Intelligent Systems 31(12) (2016) 1234-1252.
  • X. Zhang, A Novel Approach Based on Similarity Measure for Pythagorean Fuzzy Multiple Criteria Group Decision Making. International Journal of Intelligent Systems 31(6) (2016) 593-611.
  • Y. Hou, F. Zafar, W. Yu, Q, Zhai Y., A Novel Method for Multi-attribute Decision Making with Interval-valued Pythagorean Fuzzy Linguistic Information, International Journal of Intelligent Systems 32(10) (2017) 1085-1112.
  • Z. Liu, P. Liu, W. Liu, J. Pang, Pythagorean Uncertain Linguistic Partitioned Bonferroni Mean Operators and Their Application in Multi-attribute Decision Making. Journal of Intelligent and Fuzzy Systems 32(3) (2017) 2779-2790.
  • X. Peng, New Operations for Interval-valued Pythagorean Fuzzy Set, Scientia Iranica E, 26(2) (2019), 1049-1076.
  • X. Peng, G., Selvachandran, Pythagorean Fuzzy Set: State of the Art and Future Directions, Artificial Intelligence Review 52 (2019) 1873-1927.
  • X. Gou, Z. Xu, P. Ren, The Properties of Continuous Pythagorean Fuzzy Information, International Journal of Intelligent Systems 31(5) (2016) 401-424.
  • X. Peng, Y. Yang, Some Results for Pythagorean Fuzzy Sets, International Journal of Intelligent Systems 30(11) (2015) 1133-1160.
  • M. Olgun, M. Unver, Ş. Yardımcı, Pythagorean Fuzzy Topological Spaces, Complex and Intelligent Systems 5(2) (2019) 177-183.
  • K. Naeem, M. Riaz, X. D. Peng, D. Afzal, Pythagorean m-polar Fuzzy Topology with TOPSIS Approach in Exploring Most Effectual Method for Curing from COVID-19, International Journal of Biomathematics (2020) DOI: 10.1142/S1793524520500758.

Some Structures on Pythagorean Fuzzy Topological Spaces

Year 2020, Issue: 33, 15 - 25, 31.12.2020

Taha Öztürk , Adem Yolcu

Abstract

In this paper, we introduced some operations such as Pythagorean fuzzy interior, Pythagorean fuzzy closure, Pythagorean fuzzy boundary, Pythagorean fuzzy basic on Pythagorean fuzzy topological spaces. Also, the notions of Pythagorean fuzzy open (closed) functions and Pythagorean fuzzy homeomorphism are introduced, and their basic properties are investigated.

, , , , , .

Keywords

Pythagorean fuzzy interior Pythagorean fuzzy closure Pythagorean fuzzy boundary Pythagorean fuzzy topological spaces Pythagorean fuzzy open (closed) functions Pythagorean fuzzy homeomorphism

References

  • L. A. Zadeh, Fuzzy Sets, Information and Control 8 (1965) 338-353.
  • C. Chang, Fuzzy Topological Spaces, Journal of Mathematical analysis and Applications 24 (1968) 182-190.
  • R. Lowen, Fuzzy Topological Spaces and Fuzzy Compactness, Journal of Mathematical analysis and Applications 56(3) (1976) 621-633.
  • R. Lowen, Initial and Final Fuzzy Topologies and The Fuzzy Tycho no Theorem, Journal of Mathematical analysis and Applications 58(1) (1977) 11-21.
  • K. Atanassov, Intuitionistic fuzzy sets, Fuzzy Sets and Systems 20 (1986) 87-96.
  • D. Coker, An introduction of intuitionistic fuzzy topological spaces, Fuzzy Sets and Systems 88 (1997) 81-89.
  • I. M. Hanafy, Completely continuous functions in intuitionistic fuzzy topological spaces, Czechoslovak Mathematical Journal 53(4) (2003) 793-803.
  • K. Hur, J. H., Kim, J. H., Ryou, Intuitionistic Fuzzy Topological Spaces, The Pure and Applied Mathematics 11(3) (2004) 243-265.
  • R. Saadati and J. H., Park, On the Intuitionistic Fuzzy Topological Spaces, Chaos, Solitons and Fractals 27(2) (2006) 331-344.
  • R. R. Yager, Pythagorean Fuzzy Subsets, Proceeding Joint IFSA World Congress NAFIPS Annual Meeting, 1, Edmonton, Canada, (2013) 57-61.
  • R. R. Yager, A. M., Abbasov, Pythagorean Membership Grades, Complex Numbers, and Decision Making, International Journal of Intelligent Systems 28(5) (2014) 436-452.
  • P. Ren, Z. Xu, X. Gou, Pythagorean Fuzzy TODIM Approach to Multi-criteria Decision Making, Applied Soft Computing, 42 (2016) 246-259.
  • S. Zeng, J. Chen, X. Li, A Hybrid Method for Pythagorean Fuzzy Multiple-Criteria Decision Making, International Journal of Information Technology and Decision Making 15(2) (2016) 403-422.
  • X. Zhang, Z. Xu, Extension of TOPSIS to multiple criteria decisions making with Pythagorean fuzzy sets, International Journal of Intelligent Systems 29(12) (2014) 1061-1078.
  • H. Garg, New Logarithmic Operational Laws and Their Aggregation Operators for Pythagorean Fuzzy Set and Their Applications, International Journal of Intelligent Systems 34(1) (2019) 82-106.
  • H. Garg, A New Generalized Pythagorean Fuzzy Information Aggregation Using Einstein Operations and Its Application to Decision Making. International Journal of Intelligent Systems 31(9) (2016) 886-920.
  • W. Liang, X. Zhang, M. Liu, The Maximizing Deviation Method Based on Interval-valued Pythagorean Fuzzy Weighted Aggregating Operator for Multiple Criteria Group Decision Analysis. Discrete Dynamics in Nature and Society, (2015) Article ID 746572.
  • Z. Ma, Z. Xu, Symmetric Pythagorean fuzzy weighted geometric/averaging operators and their application in multicriteria decision-making problems, International Journal of Intelligent Systems 31(12) (2016) 1198-1219.
  • H. Garg, A Novel Correlation Coefficients Between Pythagorean Fuzzy Sets and Its Applications to Decision-making Processes, International Journal of Intelligent Systems 31(12) (2016) 1234-1252.
  • X. Zhang, A Novel Approach Based on Similarity Measure for Pythagorean Fuzzy Multiple Criteria Group Decision Making. International Journal of Intelligent Systems 31(6) (2016) 593-611.
  • Y. Hou, F. Zafar, W. Yu, Q, Zhai Y., A Novel Method for Multi-attribute Decision Making with Interval-valued Pythagorean Fuzzy Linguistic Information, International Journal of Intelligent Systems 32(10) (2017) 1085-1112.
  • Z. Liu, P. Liu, W. Liu, J. Pang, Pythagorean Uncertain Linguistic Partitioned Bonferroni Mean Operators and Their Application in Multi-attribute Decision Making. Journal of Intelligent and Fuzzy Systems 32(3) (2017) 2779-2790.
  • X. Peng, New Operations for Interval-valued Pythagorean Fuzzy Set, Scientia Iranica E, 26(2) (2019), 1049-1076.
  • X. Peng, G., Selvachandran, Pythagorean Fuzzy Set: State of the Art and Future Directions, Artificial Intelligence Review 52 (2019) 1873-1927.
  • X. Gou, Z. Xu, P. Ren, The Properties of Continuous Pythagorean Fuzzy Information, International Journal of Intelligent Systems 31(5) (2016) 401-424.
  • X. Peng, Y. Yang, Some Results for Pythagorean Fuzzy Sets, International Journal of Intelligent Systems 30(11) (2015) 1133-1160.
  • M. Olgun, M. Unver, Ş. Yardımcı, Pythagorean Fuzzy Topological Spaces, Complex and Intelligent Systems 5(2) (2019) 177-183.
  • K. Naeem, M. Riaz, X. D. Peng, D. Afzal, Pythagorean m-polar Fuzzy Topology with TOPSIS Approach in Exploring Most Effectual Method for Curing from COVID-19, International Journal of Biomathematics (2020) DOI: 10.1142/S1793524520500758.
There are 28 citations in total.

Details

Primary Language English
Subjects Mathematical Sciences
Journal Section Research Article
Authors

Taha Öztürk 0000-0003-2402-6507

Adem Yolcu 0000-0002-4317-652X

Publication Date December 31, 2020
Submission Date June 16, 2020
Published in Issue Year 2020 Issue: 33

Cite

APA Öztürk, T., & Yolcu, A. (2020). Some Structures on Pythagorean Fuzzy Topological Spaces. Journal of New Theory(33), 15-25.
AMA Öztürk T, Yolcu A. Some Structures on Pythagorean Fuzzy Topological Spaces. JNT. December 2020;(33):15-25.
Chicago Öztürk, Taha, and Adem Yolcu. “Some Structures on Pythagorean Fuzzy Topological Spaces”. Journal of New Theory, no. 33 (December 2020): 15-25.
EndNote Öztürk T, Yolcu A (December 1, 2020) Some Structures on Pythagorean Fuzzy Topological Spaces. Journal of New Theory 33 15–25.
IEEE T. Öztürk and A. Yolcu, “Some Structures on Pythagorean Fuzzy Topological Spaces”, JNT, no. 33, pp. 15–25, December 2020.
ISNAD Öztürk, Taha - Yolcu, Adem. “Some Structures on Pythagorean Fuzzy Topological Spaces”. Journal of New Theory 33 (December 2020), 15-25.
JAMA Öztürk T, Yolcu A. Some Structures on Pythagorean Fuzzy Topological Spaces. JNT. 2020;:15–25.
MLA Öztürk, Taha and Adem Yolcu. “Some Structures on Pythagorean Fuzzy Topological Spaces”. Journal of New Theory, no. 33, 2020, pp. 15-25.
Vancouver Öztürk T, Yolcu A. Some Structures on Pythagorean Fuzzy Topological Spaces. JNT. 2020(33):15-2.
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