Research Article
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Year 2022, Issue: 38, 1 - 13, 31.03.2022

Samet Memiş

https://doi.org/10.53570/jnt.1037280
Cited By: 1

Abstract

References

  • L. A. Zadeh, Fuzzy Sets, Information and Control 8 (1965) 338–353.
  • H. J. Zimmermann, Fuzzy Set Theory and Its Applications, Springer Science+Business Media, New York, 2011.
  • K. T. Atanassov, Intuitionistic Fuzzy Sets, Fuzzy Sets and Systems 20 (1) (1986) 87–96.
  • D. Molodtsov, Soft Set Theory-First Results, Computers and Mathematics with Applications 37 (4-5) (1999) 19–31.
  • H. Aktaş, N. Çağman, Soft Sets and Soft Groups, Information Sciences 177 (13) (2007) 2726–2735.
  • A. Sezgin, A New Approach to Semigroup Theory I: Soft Union Semigroups, Ideals and Bi-Ideals, Algebra Letters 2016 (2016) Article ID 3, 46 pages.
  • A. Sezgin, N. Çağman, F. Çıtak, α-Inclusions Applied to Group Theory via Soft Set and Logic, Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 68 (1) (2019) 334–352.
  • N. Çağman, S. Karataş, S. Enginoğlu, Soft Topology, Computers and Mathematics with Applications 62 (1) (2011) 351–358.
  • S. Enginoğlu, N. Çağman, S. Karataş, T. Aydın, On Soft Topology, El-Cezerî Journal of Science and Engineering 2 (3) (2015) 23–38.
  • T. Aydın, S. Enginoğlu, Some Results on Soft Topological Notions, Journal of New Results in Science 10 (1) (2021) 65–75.
  • P. K. Maji, R. Biswas, A. R. Roy, Soft Set Theory, Computers and Mathematics with Applications 45 (2003) 555–562.
  • P. K. Maji, A. R. Roy, R. Biswas, An Application of Soft Sets in a Decision Making Problem, Computers and Mathematics with Applications 44 (2002) 1077–1083.
  • N. Çağman, S. Enginoğlu, Soft Set Theory and Uni-Int Decision Making, European Journal of Operational Research 207 (2010) 848–855.
  • K. Hayat, M. I. Ali, F. Karaaslan, B. Y. Cao, M. H. Shah, Design Concept Evaluation Using Soft Sets Based on Acceptable and Satisfactory Levels: An Integrated TOPSIS and Shannon Entropy, Soft Computing 24 (2020) 2229–2263.
  • K. Hayat, Z. Tariq, E. Lughover, M. F. Aslam, New Aggregation Operators on Group-Based Generalized Intuitionistic Fuzzy Soft Sets, Soft Computing 25 (2021) 13353–13364.
  • M. M. Mushrif, S. Senqupta, A. K. Ray, Texture Classification Using a Novel, Soft-Set Theory Based Classification Algorithm, in: P. J. Narayanan, S. K. Nayar, H.-Y. Shum (Eds.), 7th Asian Conference on Computer Vision, Hyderabad, India, 2006, pp. 246–254.
  • B. Handaga, H. Onn, T. Herawan, FSSC: An Algorithm for Classifying Numerical Data Using Fuzzy Soft Set Theory, International Journal of Fuzzy System Applications 3 (4) (2012) 29–46.
  • I. T. R. Yanto, R. R. Seadudin, S. A. Lashari, Haviluddin, A Numerical Classification Technique Based on Fuzzy Soft Set Using Hamming Distance, in: R. Ghazali, M. M. Deris, N. M. Nawi, J. H. Abawajy (Eds.), Third International Conference on Soft Computing and Data Mining, Johor, Malaysia, 2018, pp. 252–260.
  • P. K. Maji, R. Biswas, A. R. Roy, Fuzzy Soft Sets, The Journal of Fuzzy Mathematics 9 (3) (2001) 589–602.
  • N. Çağman, S. Enginoğlu, F. Çıtak, Fuzzy Soft Set Theory and Its Applications, Iranian Journal of Fuzzy Systems 8 (3) (2011) 137–147.
  • N. Çağman, F. Çıtak, S. Enginoğlu, FP-Soft Set Theory and Its Applications, Annals of Fuzzy Mathematics and Informatics 2 (2) (2011) 219–226.
  • N. Çağman, F. Çıtak, S. Enginoğlu, Fuzzy Parameterized Fuzzy Soft Set Theory and Its Applications, Turkish Journal of Fuzzy Systems 1 (1) (2010) 21–35.
  • B. C. Cuong, Picture Fuzzy Sets, Journal of Computer Science and Cybernetics 30 (4) (2014) 409–420.
  • Y. Yang, C. Liang, S. Ji, T. Liu, Adjustable Soft Discernibility Matrix Based on Picture Fuzzy Soft Sets and Its Applications in Decision Making, Journal of Intelligent & Fuzzy Systems 29 (4) (2015) 1711–1722.
  • S. Memiş, A Study on Picture Fuzzy Sets, in: G. C¸ uvalcıo˘glu (Ed.), 7th IFS and Contemporary Mathematics Conference, Mersin, Turkey, 2021, pp. 125–132.
  • F. Herrera, E. Herrera-Viedma, L. Martnez, A Fusion Approach for Managing Multi-Granularity Linguistic Term Sets in Decision Making, Fuzzy Sets and Systems 114 (1) (2000) 43–58.
  • A. Arikrishnan, S. Sriram, Algebraic Operations on Picture Fuzzy Soft Matrices, Advances in Mathematics: Scientific Journal 9 (8) (2020) 6349–6358.
  • S. Memiş, S. Enginoğlu, An Application of Fuzzy Parameterized Fuzzy Soft Matrices in Data Classification, in: M. Kılıç, K. Özkan, M. Karaboyacı, K. Taşdelen, H. Kandemir, A. Beram (Eds.), International Conferences on Science and Technology; Natural Science and Technology ICONST-NST 2019, Prizren, Kosovo, 2019, pp. 68–77.
  • S. Memiş, S. Enginoğlu, U. Erkan, A Data Classification Method in Machine Learning Based on Normalised Hamming Pseudo-Similarity of Fuzzy Parameterized Fuzzy Soft Matrices, Bilge International Journal of Science and Technology Research 3 (Special Issue) (2019) 1–8.
  • S. Memiş, S. Enginoğlu, U. Erkan, Numerical Data Classification via Distance-Based Similarity Measures of Fuzzy Parameterized Fuzzy Soft Matrices, Journal of Applied Mathematics and Computing 9 (2021) 88583–88601.
  • S. Memiş S. Enginoğlu, U. Erkan, A Classification Method in Machine Learning Based on Soft Decision-Making via Fuzzy Parameterized Fuzzy Soft Matrices, Soft Computing 26 (3) (2022) 1165–1180.
  • S. Memiş, S. Enginoğlu, U. Erkan, A New Classification Method Using Soft Decision-Making Based on An Aggregation Operator of Fuzzy Parameterized Fuzzy Soft Matrices, Turkish Journal of Electrical Engineering & Computer Sciences 30 (3) (2022) 871–890.

Another View on Picture Fuzzy Soft Sets and Their Product Operations with Soft Decision-Making

Year 2022, Issue: 38, 1 - 13, 31.03.2022

Samet Memiş

https://doi.org/10.53570/jnt.1037280
Cited By: 1

Abstract

Cuong [Picture Fuzzy Sets, Journal of Computer Science and Cybernetics 30 (4) (2014) 409–420] has introduced the concept of picture fuzzy soft sets (pfs-sets) relying on his definition and operations of picture fuzzy sets (pf -sets), in which there exist some inconsistencies. Yang et al. [Adjustable Soft Discernibility Matrix Based on Picture Fuzzy Soft Sets and Its Applications in Decision Making, Journal of Intelligent & Fuzzy Systems 29 (4) (2015) 1711–1722] have claimed that they have introduced the concept of pfs-sets with the inconsistencies in Cuong’s definition of pf -sets. Therefore, this study redefines the concept of pfs-sets to deal with the inconsistencies therein. Moreover, it investigates some of the properties of pfs-sets and their product operations and proposes a soft decision-making method via pfs-sets. Finally, pfs-sets, their product operations, and the proposed method are discussed for further research.

Keywords

Fuzzy Sets Picture Fuzzy Sets Soft Sets Picture Fuzzy Soft Sets Intuitionistic Fuzzy Sets

References

  • L. A. Zadeh, Fuzzy Sets, Information and Control 8 (1965) 338–353.
  • H. J. Zimmermann, Fuzzy Set Theory and Its Applications, Springer Science+Business Media, New York, 2011.
  • K. T. Atanassov, Intuitionistic Fuzzy Sets, Fuzzy Sets and Systems 20 (1) (1986) 87–96.
  • D. Molodtsov, Soft Set Theory-First Results, Computers and Mathematics with Applications 37 (4-5) (1999) 19–31.
  • H. Aktaş, N. Çağman, Soft Sets and Soft Groups, Information Sciences 177 (13) (2007) 2726–2735.
  • A. Sezgin, A New Approach to Semigroup Theory I: Soft Union Semigroups, Ideals and Bi-Ideals, Algebra Letters 2016 (2016) Article ID 3, 46 pages.
  • A. Sezgin, N. Çağman, F. Çıtak, α-Inclusions Applied to Group Theory via Soft Set and Logic, Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 68 (1) (2019) 334–352.
  • N. Çağman, S. Karataş, S. Enginoğlu, Soft Topology, Computers and Mathematics with Applications 62 (1) (2011) 351–358.
  • S. Enginoğlu, N. Çağman, S. Karataş, T. Aydın, On Soft Topology, El-Cezerî Journal of Science and Engineering 2 (3) (2015) 23–38.
  • T. Aydın, S. Enginoğlu, Some Results on Soft Topological Notions, Journal of New Results in Science 10 (1) (2021) 65–75.
  • P. K. Maji, R. Biswas, A. R. Roy, Soft Set Theory, Computers and Mathematics with Applications 45 (2003) 555–562.
  • P. K. Maji, A. R. Roy, R. Biswas, An Application of Soft Sets in a Decision Making Problem, Computers and Mathematics with Applications 44 (2002) 1077–1083.
  • N. Çağman, S. Enginoğlu, Soft Set Theory and Uni-Int Decision Making, European Journal of Operational Research 207 (2010) 848–855.
  • K. Hayat, M. I. Ali, F. Karaaslan, B. Y. Cao, M. H. Shah, Design Concept Evaluation Using Soft Sets Based on Acceptable and Satisfactory Levels: An Integrated TOPSIS and Shannon Entropy, Soft Computing 24 (2020) 2229–2263.
  • K. Hayat, Z. Tariq, E. Lughover, M. F. Aslam, New Aggregation Operators on Group-Based Generalized Intuitionistic Fuzzy Soft Sets, Soft Computing 25 (2021) 13353–13364.
  • M. M. Mushrif, S. Senqupta, A. K. Ray, Texture Classification Using a Novel, Soft-Set Theory Based Classification Algorithm, in: P. J. Narayanan, S. K. Nayar, H.-Y. Shum (Eds.), 7th Asian Conference on Computer Vision, Hyderabad, India, 2006, pp. 246–254.
  • B. Handaga, H. Onn, T. Herawan, FSSC: An Algorithm for Classifying Numerical Data Using Fuzzy Soft Set Theory, International Journal of Fuzzy System Applications 3 (4) (2012) 29–46.
  • I. T. R. Yanto, R. R. Seadudin, S. A. Lashari, Haviluddin, A Numerical Classification Technique Based on Fuzzy Soft Set Using Hamming Distance, in: R. Ghazali, M. M. Deris, N. M. Nawi, J. H. Abawajy (Eds.), Third International Conference on Soft Computing and Data Mining, Johor, Malaysia, 2018, pp. 252–260.
  • P. K. Maji, R. Biswas, A. R. Roy, Fuzzy Soft Sets, The Journal of Fuzzy Mathematics 9 (3) (2001) 589–602.
  • N. Çağman, S. Enginoğlu, F. Çıtak, Fuzzy Soft Set Theory and Its Applications, Iranian Journal of Fuzzy Systems 8 (3) (2011) 137–147.
  • N. Çağman, F. Çıtak, S. Enginoğlu, FP-Soft Set Theory and Its Applications, Annals of Fuzzy Mathematics and Informatics 2 (2) (2011) 219–226.
  • N. Çağman, F. Çıtak, S. Enginoğlu, Fuzzy Parameterized Fuzzy Soft Set Theory and Its Applications, Turkish Journal of Fuzzy Systems 1 (1) (2010) 21–35.
  • B. C. Cuong, Picture Fuzzy Sets, Journal of Computer Science and Cybernetics 30 (4) (2014) 409–420.
  • Y. Yang, C. Liang, S. Ji, T. Liu, Adjustable Soft Discernibility Matrix Based on Picture Fuzzy Soft Sets and Its Applications in Decision Making, Journal of Intelligent & Fuzzy Systems 29 (4) (2015) 1711–1722.
  • S. Memiş, A Study on Picture Fuzzy Sets, in: G. C¸ uvalcıo˘glu (Ed.), 7th IFS and Contemporary Mathematics Conference, Mersin, Turkey, 2021, pp. 125–132.
  • F. Herrera, E. Herrera-Viedma, L. Martnez, A Fusion Approach for Managing Multi-Granularity Linguistic Term Sets in Decision Making, Fuzzy Sets and Systems 114 (1) (2000) 43–58.
  • A. Arikrishnan, S. Sriram, Algebraic Operations on Picture Fuzzy Soft Matrices, Advances in Mathematics: Scientific Journal 9 (8) (2020) 6349–6358.
  • S. Memiş, S. Enginoğlu, An Application of Fuzzy Parameterized Fuzzy Soft Matrices in Data Classification, in: M. Kılıç, K. Özkan, M. Karaboyacı, K. Taşdelen, H. Kandemir, A. Beram (Eds.), International Conferences on Science and Technology; Natural Science and Technology ICONST-NST 2019, Prizren, Kosovo, 2019, pp. 68–77.
  • S. Memiş, S. Enginoğlu, U. Erkan, A Data Classification Method in Machine Learning Based on Normalised Hamming Pseudo-Similarity of Fuzzy Parameterized Fuzzy Soft Matrices, Bilge International Journal of Science and Technology Research 3 (Special Issue) (2019) 1–8.
  • S. Memiş, S. Enginoğlu, U. Erkan, Numerical Data Classification via Distance-Based Similarity Measures of Fuzzy Parameterized Fuzzy Soft Matrices, Journal of Applied Mathematics and Computing 9 (2021) 88583–88601.
  • S. Memiş S. Enginoğlu, U. Erkan, A Classification Method in Machine Learning Based on Soft Decision-Making via Fuzzy Parameterized Fuzzy Soft Matrices, Soft Computing 26 (3) (2022) 1165–1180.
  • S. Memiş, S. Enginoğlu, U. Erkan, A New Classification Method Using Soft Decision-Making Based on An Aggregation Operator of Fuzzy Parameterized Fuzzy Soft Matrices, Turkish Journal of Electrical Engineering & Computer Sciences 30 (3) (2022) 871–890.
There are 32 citations in total.

Details

Primary Language English
Subjects Mathematical Sciences
Journal Section Research Article
Authors

Samet Memiş 0000-0002-0958-5872

Publication Date March 31, 2022
Submission Date December 15, 2021
Published in Issue Year 2022 Issue: 38

Cite

APA Memiş, S. (2022). Another View on Picture Fuzzy Soft Sets and Their Product Operations with Soft Decision-Making. Journal of New Theory(38), 1-13. https://doi.org/10.53570/jnt.1037280
AMA Memiş S. Another View on Picture Fuzzy Soft Sets and Their Product Operations with Soft Decision-Making. JNT. March 2022;(38):1-13. doi:10.53570/jnt.1037280
Chicago Memiş, Samet. “Another View on Picture Fuzzy Soft Sets and Their Product Operations With Soft Decision-Making”. Journal of New Theory, no. 38 (March 2022): 1-13. https://doi.org/10.53570/jnt.1037280.
EndNote Memiş S (March 1, 2022) Another View on Picture Fuzzy Soft Sets and Their Product Operations with Soft Decision-Making. Journal of New Theory 38 1–13.
IEEE S. Memiş, “Another View on Picture Fuzzy Soft Sets and Their Product Operations with Soft Decision-Making”, JNT, no. 38, pp. 1–13, March 2022, doi: 10.53570/jnt.1037280.
ISNAD Memiş, Samet. “Another View on Picture Fuzzy Soft Sets and Their Product Operations With Soft Decision-Making”. Journal of New Theory 38 (March 2022), 1-13. https://doi.org/10.53570/jnt.1037280.
JAMA Memiş S. Another View on Picture Fuzzy Soft Sets and Their Product Operations with Soft Decision-Making. JNT. 2022;:1–13.
MLA Memiş, Samet. “Another View on Picture Fuzzy Soft Sets and Their Product Operations With Soft Decision-Making”. Journal of New Theory, no. 38, 2022, pp. 1-13, doi:10.53570/jnt.1037280.
Vancouver Memiş S. Another View on Picture Fuzzy Soft Sets and Their Product Operations with Soft Decision-Making. JNT. 2022(38):1-13.

Cited By

Picture fuzzy soft $$\sigma$$-algebra and picture fuzzy soft measure and their applications to multi-criteria decision-making
Granular Computing
https://doi.org/10.1007/s41066-022-00333-2
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