Research Article

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

Volume: 42 Number: 4 December 29, 2021
EN

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

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. [1] Zadeh L.A., Fuzzy sets, Information and Control, 8 (1965) 338-353.
  2. [2] Pawlak Z., Rough sets, International Journal of Computing and Information Sciences, 11 (1982) 341-356.
  3. [3] Molodtsov D., Soft set theory-first results, Computers and Mathematics with Applications, 37 (1999) 19-31.
  4. [4] Zou Y. and Xiao Z., Data analysis approaches of soft sets under incomplete information, Knowledge-Based Systems, 21 (2008) 941–945.
  5. [5] Selvakumari K., Solving Game Problem Using Weighted Soft Sets, Journal of Computer and Mathematical Sciences, 9(10) (2018) 1307-1311.
  6. [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. [7] Kamacı, H., A novel approach to similarity of soft sets, Adıyaman University Journal of Science, 9(1) (2019), 23-35.
  8. [8] Aygün, E. and Kamacı, H., Some new algebraic structures of soft sets. Soft Computing, 25 (2021) 8609-8626.
  9. [9] Kamacı, H., Interval-valued fuzzy parameterized intuitionistic fuzzy soft sets and their applications, Cumhuriyet Sci. J., 40(2) (2019) 317-331.
  10. [10] Kamacı, H., On Hybrid Structures of Hypersoft Sets and Rough Sets, International Journal of Modern Science and Technology, 6(4) (2021) 69-82.
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. https://izlik.org/JA52HE49ES
AMA
1.Dalkılıç O, Demirtaş N. Algebraic operations of virtual fuzzy parameterized soft sets and their application in decision-making. CSJ. 2021;42(4):878-889. https://izlik.org/JA52HE49ES
Chicago
Dalkılıç, Orhan, and Naime Demirtaş. 2021. “Algebraic Operations of Virtual Fuzzy Parameterized Soft Sets and Their Application in Decision-Making”. Cumhuriyet Science Journal 42 (4): 878-89. https://izlik.org/JA52HE49ES.
EndNote
Dalkılıç O, Demirtaş N (December 1, 2021) Algebraic operations of virtual fuzzy parameterized soft sets and their application in decision-making. Cumhuriyet Science Journal 42 4 878–889.
IEEE
[1]O. Dalkılıç and N. Demirtaş, “Algebraic operations of virtual fuzzy parameterized soft sets and their application in decision-making”, CSJ, vol. 42, no. 4, pp. 878–889, Dec. 2021, [Online]. Available: https://izlik.org/JA52HE49ES
ISNAD
Dalkılıç, Orhan - Demirtaş, Naime. “Algebraic Operations of Virtual Fuzzy Parameterized Soft Sets and Their Application in Decision-Making”. Cumhuriyet Science Journal 42/4 (December 1, 2021): 878-889. https://izlik.org/JA52HE49ES.
JAMA
1.Dalkılıç O, Demirtaş N. Algebraic operations of virtual fuzzy parameterized soft sets and their application in decision-making. CSJ. 2021;42:878–889.
MLA
Dalkılıç, Orhan, and Naime Demirtaş. “Algebraic Operations of Virtual Fuzzy Parameterized Soft Sets and Their Application in Decision-Making”. Cumhuriyet Science Journal, vol. 42, no. 4, Dec. 2021, pp. 878-89, https://izlik.org/JA52HE49ES.
Vancouver
1.Orhan Dalkılıç, Naime Demirtaş. Algebraic operations of virtual fuzzy parameterized soft sets and their application in decision-making. CSJ [Internet]. 2021 Dec. 1;42(4):878-89. Available from: https://izlik.org/JA52HE49ES