Bulanık ikili esnek küme yardımıyla karar verme problemine matematiksel bir yaklaşım

Öz

Bulanık küme teorisi ve esnek küme teorisi hem teorik çalışmalar anlamında hem de çeşitli uygulamaların araştırılması anlamında sıklıkla kullanılan iki teori olarak karşımıza çıkmaktadır. Bulanık küme teorisinin tek başına yeterli olmadığı durumlarda, parametre eksikliğine bağlı olarak esnek küme teorisine de gerek duyulmuştur. Daha sonra bu iki kavram bir arada kullanılarak, bulanık esnek kavramı literatüre kazandırılmış ve bulanık esnek küme kavramı ile hem teorik hem de uygulama bazlı çalışmalar elde edilmiştir. Uygulama alanlarından en çok karşımıza çıkan ise karar verme problemi üzerine yapılan çalışmalardır. Bu çalışmada, bulanık ikili esnek küme kavramı kullanılarak, ihtiyaç duyulduğu takdirde, araçlarda uygun boya seçme karar verme problemine yer verilecektir. Bu amaç için, uygun evrensel kümeler ve parametre kümesi altında üyelik fonksiyonları ve karar verme matrisi ile hangi araca hangi marka boyanın daha uygun olduğunun tespiti için çalışmalar yapılacaktır.

Anahtar Kelimeler

• Bulanık ikili esnek küme
• karar verme problemi
• oto boyası

A mathematical approach to decision making problem with the fuzzy binary soft set

Öz

Fuzzy set theory and soft set theory are two theories that are frequently used both in theoretical studies and in the research of various applications. In cases where fuzzy set theory alone is not sufficient, soft set theory is also needed due to the lack of parameters. Later, by using these two concepts together, the fuzzy soft concept was introduced to the literature and both theoretical and application-based studies were obtained with the fuzzy soft set concept. One of the most common application areas is the studies on decision making problems. In this study, by using the concept of fuzzy binary soft set, the problem of deciding on the appropriate paint selection for vehicles, if needed, will be included. For this purpose, it will be tried to determine which brand of paint is more suitable for which vehicle with membership functions and decision making matrix under appropriate universal sets and parameter set.

Anahtar Kelimeler

• Fuzzy binary soft set
• decision making problem
• auto paint

Kaynakça

1. Zadeh, L. A., Fuzzy sets, Information and Control, 8, 3, 338-353, (1965).
2. Pawlak, Z., Rough sets, International Journal of Information and Computer Sciences, 11, 5, 341-356, (1982).
3. Molodtsov, D., Soft set theory-first results, Computers and Mathematics with Applications, 37, 19-31, (1999).
4. Maji, P. K., Biswas, R. ve Roy, A. R., Fuzzy soft sets, The Journal of Fuzzy Mathematics, 9, 589-602, (2001).
5. Açıkgöz, A. ve Taş, N., Binary soft set theory, European Journal of Pure and Applied Mathematics, 9, 4, 452-463, (2016).
6. Gino Metilda, P. ve Subhashini, Dr. J., Remarks on fuzzy binary soft set and its characters, International Conference on Materials and Mathematical Sciences, (2020).
7. Çağman, N. ve Enginoğlu, S., Soft matrix theory and its decision making, Computers and Mathematics with Applications, 59, 10, 3308-3314, (2010).
8. Kalaichelvi, Dr. A. ve Malini, P. H., Application of fuzzy soft sets to investment decision making problem, International Journal of Mathematical Sciences and Applications, 1, 3, 1583-1586, (2011).

9. Özgür, N. Y. ve Taş, N., A note on “application of fuzzy soft sets to investment decision making problem”, Journal of New Theory, 7, 1-10, (2015).
10. Taş, N., Özgür, N. Y. ve Demir, P., An application of soft set and fuzzy soft set theories to stock management, Süleyman Demirel University Journal of Natural and Applied Sciences, 21, 3, 791-796, (2017).
11. Karaca, F. ve Taş, N., Decision making problem for life and non-life insurances, Journal of the Institute of Science and Technology of Balıkesir University, 20, 1, 572-588, (2018).
12. İrkin, R., Özgür, N. Y. ve Taş, N., 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, (2018).
13. İrkin, R., Özgür, N. ve Taş, N., Using optimization method for determining lactic acid bacteria counts in white cheese with different salt concentrations, Journal of Food Processing and Preservation, 46, 4, 1-10, (2022).
14. Gino Metilda, P. ve Subhashini, Dr. J., An application of fuzzy binary soft set in decision making problems, Webology, 18, 6, 3672-3680, (2021).
15. Kaplan, E., New fixed-circle results on fuzzy metric spaces with an application to dynamic market equilibrium, Mathematica Moravica, 27, 1, 73-83, (2023).
16. Taş, N. ve Kaplan, E., Unmanned aerial vehicle application to fuzzy soft set based decision-making, Soft Computing Engineering Applications, CRC Press Taylor and Francis Group, (2025).
17. Maji, P. K., Biswas, R. ve Roy, A. R., Soft set theory, Computers and Mathematics with Applications, 45, 555-562, (2003).