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Algebraic operations of virtual fuzzy parameterized soft sets and their application in decision-making

Year 2021, Volume: 42 Issue: 4, 878 - 889, 29.12.2021

Orhan Dalkılıç , Naime Demirtaş

Abstract

It is a difficult task for decision-makers to accurately state a membership degree in the range [0,1]. The virtual fuzzy parameterized soft sets (VFPSSs) proposed to overcome this problem is an effective mathematical tool constructed, including the abilities of fuzzy sets and soft sets. In this paper, algebraic operations of VFPSSs are defined and examined these operations' properties. Then, a decision-making algorithm is proposed by the aforesaid operations. Finally, the proposed algorithm is succesfully applied to a decision-making problem.

Keywords

Fuzzy set Soft set Virtual fuzzy parameterized soft set Algebraic operations Decision-making.

References

  • [1] Zadeh L.A., Fuzzy sets, Information and Control, 8 (1965) 338-353.
  • [2] Pawlak Z., Rough sets, International Journal of Computing and Information Sciences, 11 (1982) 341-356.
  • [3] Molodtsov D., Soft set theory-first results, Computers and Mathematics with Applications, 37 (1999) 19-31.
  • [4] Zou Y. and Xiao Z., Data analysis approaches of soft sets under incomplete information, Knowledge-Based Systems, 21 (2008) 941–945.
  • [5] Selvakumari K., Solving Game Problem Using Weighted Soft Sets, Journal of Computer and Mathematical Sciences, 9(10) (2018) 1307-1311.
  • [6] Deli I. and Çağman N., Application of soft sets in decision-making based on game theory, Ann Fuzzy Math Inform, 11(3) (2016) 425-438.
  • [7] Kamacı, H., A novel approach to similarity of soft sets, Adıyaman University Journal of Science, 9(1) (2019), 23-35.
  • [8] Aygün, E. and Kamacı, H., Some new algebraic structures of soft sets. Soft Computing, 25 (2021) 8609-8626.
  • [9] Kamacı, H., Interval-valued fuzzy parameterized intuitionistic fuzzy soft sets and their applications, Cumhuriyet Sci. J., 40(2) (2019) 317-331.
  • [10] Kamacı, H., On Hybrid Structures of Hypersoft Sets and Rough Sets, International Journal of Modern Science and Technology, 6(4) (2021) 69-82.
  • [11] Maji P.K., Roy A.R. and Biswas R., Fuzzy soft sets, Journal of Fuzzy Mathematics, 9(3) (2001) 589-602.
  • [12] Çağman N., Enginoğlu S. and Çıtak F., Fuzzy soft set theory and its applications, Iranian Journal of Fuzzy Systems, 8(3) (2011) 137-147.
  • [13] Demirtaş N. and Dalkılıç O., An application in the diagnosis of prostate cancer with the help of bipolar soft rough sets, on Mathematics and Mathematics Education (ICMME 2019), KONYA, 283, (2019).
  • [14] Demirtaş N., Hussaın S. and Dalkılıç O., New approaches of inverse soft rough sets and their applications in a decision-making problem, Journal of Applied Mathematics and Informatics, 38(3-4) (2020) 335-349.
  • [15] Dalkılıç O., An Application of VFPFSS’s in Decision-Making Problems, Journal of Polytechnic,758474 (2020).
  • [16] Kamal N.L.A.M., Abdullah L., Abdullah I., Alkhazaleh S. and Karaaslan F., Multi-valued interval neutrosophic soft set: Formulation and Theory, Neutrosophic Sets and Systems, 30(1) (2019) 12.
  • [17] Hooda D.S., Kumari R. and Sharma D.K., Intuitionistic Fuzzy Soft Set Theory and Its Application in Medical Diagnosis, International Journal of Statistics in Medical Research, 7(3) (2018) 70-76.
  • [18] Smarandache F, A Unifying Field in Logics: Neutrosophic Logic. Neutrosophy, Neutrosophic Set, Neutrosophic Probability, American Research Press, Rehoboth, NM, (1999).
  • [19] Çağman N., Çıtak F. and Enginoğlu S., FP-soft Set Theory and Its Applications, Annals of Fuzzy Mathematics and Informatics, 2 (2011) 219-226.
  • [20] Dalkılıç O. and Demirtas N., VFP-Soft Sets and Its Application on Decision-Making Problems, Journal of Polytechnic, 685634 (2020).
  • [21] Zimmermann, H., J. Fuzzy Set Theory and Its Applications. 2nd Edition. Dordrecht: Kluwer Academic Publishers, (1991).
  • [22] Çağman, N. and İrfan, D., Products of FP-soft sets and their applications, Hacettepe Journal of Mathematics and Statistics, 41(3) (2012) 365-374.

Year 2021, Volume: 42 Issue: 4, 878 - 889, 29.12.2021

Orhan Dalkılıç , Naime Demirtaş

Abstract

References

  • [1] Zadeh L.A., Fuzzy sets, Information and Control, 8 (1965) 338-353.
  • [2] Pawlak Z., Rough sets, International Journal of Computing and Information Sciences, 11 (1982) 341-356.
  • [3] Molodtsov D., Soft set theory-first results, Computers and Mathematics with Applications, 37 (1999) 19-31.
  • [4] Zou Y. and Xiao Z., Data analysis approaches of soft sets under incomplete information, Knowledge-Based Systems, 21 (2008) 941–945.
  • [5] Selvakumari K., Solving Game Problem Using Weighted Soft Sets, Journal of Computer and Mathematical Sciences, 9(10) (2018) 1307-1311.
  • [6] Deli I. and Çağman N., Application of soft sets in decision-making based on game theory, Ann Fuzzy Math Inform, 11(3) (2016) 425-438.
  • [7] Kamacı, H., A novel approach to similarity of soft sets, Adıyaman University Journal of Science, 9(1) (2019), 23-35.
  • [8] Aygün, E. and Kamacı, H., Some new algebraic structures of soft sets. Soft Computing, 25 (2021) 8609-8626.
  • [9] Kamacı, H., Interval-valued fuzzy parameterized intuitionistic fuzzy soft sets and their applications, Cumhuriyet Sci. J., 40(2) (2019) 317-331.
  • [10] Kamacı, H., On Hybrid Structures of Hypersoft Sets and Rough Sets, International Journal of Modern Science and Technology, 6(4) (2021) 69-82.
  • [11] Maji P.K., Roy A.R. and Biswas R., Fuzzy soft sets, Journal of Fuzzy Mathematics, 9(3) (2001) 589-602.
  • [12] Çağman N., Enginoğlu S. and Çıtak F., Fuzzy soft set theory and its applications, Iranian Journal of Fuzzy Systems, 8(3) (2011) 137-147.
  • [13] Demirtaş N. and Dalkılıç O., An application in the diagnosis of prostate cancer with the help of bipolar soft rough sets, on Mathematics and Mathematics Education (ICMME 2019), KONYA, 283, (2019).
  • [14] Demirtaş N., Hussaın S. and Dalkılıç O., New approaches of inverse soft rough sets and their applications in a decision-making problem, Journal of Applied Mathematics and Informatics, 38(3-4) (2020) 335-349.
  • [15] Dalkılıç O., An Application of VFPFSS’s in Decision-Making Problems, Journal of Polytechnic,758474 (2020).
  • [16] Kamal N.L.A.M., Abdullah L., Abdullah I., Alkhazaleh S. and Karaaslan F., Multi-valued interval neutrosophic soft set: Formulation and Theory, Neutrosophic Sets and Systems, 30(1) (2019) 12.
  • [17] Hooda D.S., Kumari R. and Sharma D.K., Intuitionistic Fuzzy Soft Set Theory and Its Application in Medical Diagnosis, International Journal of Statistics in Medical Research, 7(3) (2018) 70-76.
  • [18] Smarandache F, A Unifying Field in Logics: Neutrosophic Logic. Neutrosophy, Neutrosophic Set, Neutrosophic Probability, American Research Press, Rehoboth, NM, (1999).
  • [19] Çağman N., Çıtak F. and Enginoğlu S., FP-soft Set Theory and Its Applications, Annals of Fuzzy Mathematics and Informatics, 2 (2011) 219-226.
  • [20] Dalkılıç O. and Demirtas N., VFP-Soft Sets and Its Application on Decision-Making Problems, Journal of Polytechnic, 685634 (2020).
  • [21] Zimmermann, H., J. Fuzzy Set Theory and Its Applications. 2nd Edition. Dordrecht: Kluwer Academic Publishers, (1991).
  • [22] Çağman, N. and İrfan, D., Products of FP-soft sets and their applications, Hacettepe Journal of Mathematics and Statistics, 41(3) (2012) 365-374.
There are 22 citations in total.

Details

Primary Language English
Subjects Mathematical Sciences
Journal Section Natural Sciences
Authors

Orhan Dalkılıç 0000-0003-3875-1398

Naime Demirtaş 0000-0003-4137-4810

Publication Date December 29, 2021
Submission Date April 16, 2021
Acceptance Date October 27, 2021
Published in Issue Year 2021Volume: 42 Issue: 4

Cite

APA Dalkılıç, O., & Demirtaş, N. (2021). Algebraic operations of virtual fuzzy parameterized soft sets and their application in decision-making. Cumhuriyet Science Journal, 42(4), 878-889.