A novel mathematical approach to uncertainty problems: VFPIFS-set

Year 2022, Volume: 12 Issue: 2, 614 - 623, 15.04.2022

Orhan Dalkılıç

https://doi.org/10.17714/gumusfenbil.870783

Abstract

In this paper, fuzzy parametrized intuitionistic fuzzy soft (briefly FPIFS-) set theory, which is a generalization of virtual fuzzy parametrized intuitionistic fuzzy soft (briefly VFPIFS-) sets proposed for uncertainty problems, is given and some important properties of it are examined. In addition, an uncertainty problem was exemplified and the best object was selected by giving a decision-making approach for VFPIFS-sets. Finally, a comparative analysis was done for both mathematical models.

Keywords

FPIFS-set, Decision making, VFPIFS-set

Belirsizlik problemlerine yönelik yeni bir matematiksel yaklaşım: VFPIFS-küme

Abstract

Bu çalışma da belirsizlik problemlerine yönelik önerilen bulanık parametreli sezgisel bulanık esnek (kısaca FPIFS-) kümelerin bir genellemesi olan sanal bulanık parametreli sezgisel bulanık esnek (kısaca VFPIFS-) küme teorisi verilmiştir ve bazı önemli özellikleri incelenmiştir. Ayrıca bir belirsizlik problemi örneklendirilerek VFPIFS-kümeler için bir karar verme yaklaşımı verilerek en iyi nesnenin seçimi yapılmıştır. Son olarak her iki matematiksel model için bir karşılaştırmalı analiz yapılmıştır.

Keywords

FPIFS-küme, Karar verme, VFPIFS-küme

References

• Atanassov, K. T. (1986). Intuitionistic fuzzy sets. Fuzzy Sets and Systems 20(1), 87–96.
• Çağman, N., Cıtak, F., & Enginoğlu, S. (2010). Fuzzy parameterized fuzzy soft set theory and ıts applications. Turkish Journal of Fuzzy Systems 1(1), 21–35.
• Çağman, N., Cıtak, F., & Enginoğlu, S. (2011). FP-soft set theory and ıts applications. Annals of Fuzzy Mathematics and Informatics 2(2), 219–226.
• Dalkılıç, O. (2020). An application of VFPFSS’s in decision making problems. Journal of Polytechnic, https://doi.org/10.2339/politeknik.758474.
• Dalkılıç, O., & Demirtas, N. (2020). VFP-soft sets and ıts application on decision making problems. Journal of Polytechnic, https://doi.org/10.2339/politeknik.685634.
• Deli, I., & Çağman, N. (2016). Application of soft sets in decision making based on game theory. Annuals of Fuzzy Mathematics and Informatics, 11(3), 425-438.
• Demirtaş, N., & Dalkılıç O. (2019). 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.
• Demirtaş N., Hussaın, S., & Dalkılıç, O. (2020). New approaches of inverse soft rough sets and their applications in a decision making problem. Journal of Applied Mathematics and Informatics, 38(3-4) 335-349.
• Irkin, R., Ozgur, N.Y., & Tas, N. (2018). Optimization of lactic acid bacteria viability using fuzzy soft set modelling. An International Journal of Optimization and Control: Theories and Applications, 8(2) 266-275.
• Kalaichelvi, A., & Malini, P.H. (2011). Application of fuzzy soft sets to investment decision making problem. International Journal of Mathematical Sciences and Applications, 1(3) 1583-1586.
• Karaca, F. & Taş, N. (2018). Decision making problem for life and non-life insurances. Journal of Balıkesir University Institute of Science and Technology, 20(1) 572-588.
• Maji, P. K., Biswas, R., & Roy, A. R. (2001a). Fuzzy soft sets. Journal of Fuzzy Mathematics 9(3), 589–602.
• Maji, P. K., Biswas, R., & Roy, A. R. (2001b). Intuitionistic fuzzy soft sets. The Journal of Fuzzy Mathematics 9(3), 677–692.
• Molodtsov, D. A. (1999). Soft Set Theory–First Results. Computers and Mathematics with Applications 37(4–5), 19–31.
• Nihal, T., Özgür, N.Y., & Demir, P. (2017). An application of soft set and fuzzy soft set theories to stock management. Süleyman Demirel Üniversitesi Fen Bilimleri Enstitüsü Dergisi, 21(3) 791-796.
• Özgür, N.Y., & Nihal, T. (2015). A note on application of fuzzy soft sets to investment decision making problem. Journal of New Theory, (7) 1-10.
• Saeed M., Ahmad M.R., Saqlain M., & Riaz, M. (2020). Rudiments N-framed soft sets. Punjab University Journal of Mathematics, 52(5) 15-30.
• Selvakumari, K. (2018). Solving game problem using weighted soft sets. Journal of Computer and Mathematical Sciences, 9(10) 1307-1311.
• Sulukan, E., Çağman, N., & Aydın, T. (2019). Fuzzy parameterized intuitionistic fuzzy soft sets and their application to a performance-based value assignment problem. Journal of New Theory, (29), 79-88.
• Zadeh, L. A. (1965). Fuzzy sets. Information and Control, 8, 338-353.
• Zou, Y., & Xiao, Z. (2008). Data analysis approaches of soft sets under incomplete information. Knowledge-Based Systems, 21, 941–945. https://doi.org/10.1016/j.knosys.2008.04.004