Research Article
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Year 2022, , 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, , 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

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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