Karar vericilere odaklanan yeni bir matematiksel model: Sanal sezgisel bulanık parametreli esnek küme

Year 2021, Volume: 8 Issue: 3, 1565 - 1575, 30.09.2021

Orhan Dalkılıç

https://doi.org/10.31202/ecjse.940871

Abstract

Belirsizlik problemlerine yönelik [0,1] aralığında bir değeri doğru bir şekilde seçmek oldukça zor bir iştir. Ancak, karar vericiler tarafından ifade edilen veri kümeleri çoğu zaman [0,1] aralığındadır. Bu aralıkta ifade edilen verilere güvenerek bir karar verme sürecini yapılandırabilmek birçok hataya sebebiyet verebilir. Son zamanlarda bu duruma dikkat edebilen farklı matematiksel modeller geliştirilmiştir. Bu çalışmada bu amaca yönelik yeni bir matematiksel model olan sanal sezgisel bulanık parametreli esnek küme teorisi tanıtılmıştır. Dahası alt küme, tümleyen, birleşim, kesişim gibi bazı temel küme işlemleri de verilmiştir. Ayrıca önerilen küme teorisi için bir karar verme algoritması önerilerek bir belirsizlik problemi üzerinde nasıl uygulanabileceği örneklendirilmiştir. Son olarak karar vericiler tarafından ifade edilen değerlerin önemini vurgulayan bir karşılaştırmalı analiz verilmiştir.

Keywords

Sezgisel bulanık parametreli esnek küme, Sanal sezgisel bulanık parametreli esnek küme, Karar verme

A novel mathematical model focusing on decision makers: Virtual intuitionistic fuzzy parameterized soft set

Abstract

Choosing a value in the range [0,1] correctly for uncertainty problems is a very difficult task. However, the data sets expressed by decision makers are often in the range [0,1]. Structuring a decision-making process by relying on the data expressed in this range can cause many errors. Recently, different mathematical models have been developed that can pay attention to this situation. In this study, virtual intuitionistic fuzzy parameterized soft set theory, which is a new mathematical model for this purpose, is introduced. Moreover, some basic set operations such as subset, complement, union, intersection are also given. In addition, a decision making algorithm is proposed for the proposed set theory and how it can be applied on an uncertainty problem is exemplified. Finally, a comparative analysis emphasizing the importance of values expressed by decision makers is given.

Keywords

Intuitionistic fuzzy parameterized soft set, Virtual intuitionistic fuzzy parameterized soft set, Decision making

References

• Cağman, N., Cıtak, F., Enginoğlu, S., Fuzzy Parameterized Fuzzy Soft Set Theory and Its Applications. Turkish Journal of Fuzzy Systems, 2010, 1(1), 21–35.
• Dalkılıç, O., An Application of VFPFSS’s in Decision Making Problems. Journal of Polytechnic, 2021, https://doi.org/10.2339/politeknik.758474.
• Cağman, N., Cıtak, F., Enginoğlu, S., FP-Soft Set Theory and Its Applications. Annals of Fuzzy Mathematics and Informatics, 2011, 2(2), 219–226.
• Dalkılıç, O., Demirtas, N., VFP-Soft Sets and Its Application on Decision Making Problems, Journal of Polytechnic, 2021, https://doi.org/10.2339/politeknik.685634.
• Sulukan, E., Çağman, N., Aydın, T., Fuzzy parameterized intuitionistic fuzzy soft sets and their application to a performance-based value assignment problem. Journal of New Theory, 2019, (29), 79-88.
• Selvakumari, K., Solving Game Problem Using Weighted Soft Sets. Journal of Computer and Mathematical Sciences, 2018, 9(10), 1307-1311.
• Saeed, M., Ahmad, M.R., Saqlain, M., Riaz, M., Rudiments N-framed soft sets, Punjab University Journal of Mathematics, 2020, 52(5), 15-30.
• Demirtaş, N., 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.
• Deli, I., Çağman, N., Application of soft sets in decision making based on game theory, Ann Fuzzy Math Inform, 2016, 11(3), 425-438.
• Demirtaş, N., Hussaın, S., Dalkılıç, O., New approaches of inverse soft rough sets and their applications in a decision making problem. Journal of applied mathematics and informatics, 2020, 38(3-4), 335-349.
• Atanassov, K.T., Intuitionistic Fuzzy Sets. Fuzzy Sets and Systems, 1986, 20(1), 87–96.
• Molodtsov, D.A., Soft Set Theory–First Results. Computers and Mathematics with Applications, 1999, 37(4–5), 19–31.
• Zou, Y., Xiao, Z., Data analysis approaches of soft sets under incomplete information. Knowl. Base. Sys., 2008, 21, 941–945.
• El-Yagubi, E., Salleh, A.R., Intuitionistic fuzzy parameterised fuzzy soft set. Journal of Quality Measurement and Analysis, 2013, 9(2), 73-81.
• Maji, P.K., Biswas, R., Roy, A.R., Fuzzy Soft Sets. Journal of Fuzzy Mathematics, 2001, 9(3), 589–602.
• Maji, P.K., Biswas, R., Roy, A.R., Intuitionistic Fuzzy Soft Sets. The Journal of Fuzzy Mathematics, 2001, 9(3), 677–692.
• Zadeh, L.A., Fuzzy sets. Information and Control, 1965, 8, 338-353.
• Dalkılıç, O., Relations on neutrosophic soft set and their application in decision making. Journal of Applied Mathematics and Computing, 2021, 1-17.
• Dalkılıç, O., A novel approach to soft set theory in decision-making under uncertainty. International Journal of Computer Mathematics, 2021, 1-11. https://doi.org/10.1080/00207160.2020.1868445.
• Enginoğlu, S., Memiş, S., Çağman, N., A Generalization of Fuzzy Soft Max-Min Decision-Making Method and Its Application to a Performance-Based Value Assignment in Image Denoising. El-Cezerî Journal of Science and Engineering, 2019, 6(3), 466-481.
• Enginoğlu, S., Çağman, N., Karataş, S., Aydın, T., On soft topology. El-Cezerî Journal of Science and Engineering, 2015, 2(3), 23-38.
• Deli, I., Çağman, N., Intuitionistic fuzzy parameterized soft set theory and its decision making. Applied Soft Computing, 2015, 28, 109-113.