Çoklu Üyelik Değerlerinin İşlendiği Belirsizlik Ortamlarına Yönelik Sanal Bulanık Parametreli Esnek Kümeler Üzerine Dayanan Yeni Bir Yaklaşım

Abstract

İnsanların ihtiyaçlarının artmaya ve çeşitlenmeye başladığı günümüzde birçok yeni belirsizlik ortamında veri işlemeye yönelik ihtiyaçlarda meydana gelmiştir. Bu belirsizlik ortamlarından biri de birden fazla üyelik değerinin işlenmesi gerektiği karar verme süreçleridir. Bu amaca yönelik yapılandırılan sanal bulanık parametreli esnek kümelere odaklanan bu çalışmada yeni bir karar verme algoritması önerilmiştir. Bu algoritmada karmaşık veri analizinde oluşabilecek olası hataların önüne geçmek için bazı yalın temsiller verilmiştir. Ardından, parametre önem ağırlıkları da dikkate alınarak daha iyi bir yaklaşım inşa edilmeye çalışılmıştır. Ayrıca, bu algoritmik yaklaşım sayesinde parametre önem ağırlıklarının nesneler üzerindeki etkisi farklı bulanık değerler için değerlendirilebilir. Bunlara ilaveten, inşa edilen algoritmanın en önemli avantajı karşılaşılan belirsizlik ortamı için en ideal sanal bulanık parametreli esnek kümenin tespitine yönelik adımların mevcudiyetidir. Son olarak önerilen algoritma için elde edilen sonuçlar irdelenerek bir tartışmaya yer verilmiştir.

Keywords

• Sanal bulanık parametreli esnek küme
• Parametre önem ağırlıkları
• Algoritma
• Karar verme.

A Novel Approach Based on Virtual Fuzzy Parameterized Soft Sets for Uncertainty Environments Where Multiple Membership Values are Processed

Abstract

Today, when people's needs have begun to increase and diversify, the need for data processing has occurred in many new uncertainties. One of these uncertain environments is the decision-making process where more than one membership value must be processed. In this paper, which focuses on virtual fuzzy parameterized soft sets structured for this purpose, a new decision-making algorithm is proposed. In this algorithm, some simple representations are given to avoid possible errors that may occur in complex data analysis. Then, a better approach has been tried to be built by taking into account the parameter importance weights. In addition, thanks to this algorithmic approach, the effect of parameter importance weights on objects can be evaluated for different fuzzy values. Moreover, the most important advantage of the constructed algorithm is the availability of steps to determine the most ideal virtual fuzzy parameterized soft set for the uncertainty environment encountered. Finally, the results obtained for the proposed algorithm are examined and a discussion is given.

Keywords

• Virtual fuzzy parameterized soft set
• Parameter importance weights
• Algorithm
• Decision making

References

1. [1] Zadeh, L. A. 1965. Fuzzy sets. Information and Control, 8, 338-353.
2. [2] Pawlak, Z. 1982. Rough sets. International Journal of Computational Intelligence Systems, 11, 341-356.
3. [3] Molodtsov, D. 1999. Soft set theory-first results. Computers and Mathematics with Applications, 37, 19-31.
4. [4] Çağman, N., Çıtak, F., Enginoğlu, S. 2011. FP-soft Set Theory and Its Applications. Annals of Fuzzy Mathematics and Informatics, 2, 219-226.
5. [5] Dalkılıç, O., Demirtaş, N. 2021. VFP-Soft Sets and Its Application on Decision Making Problems. Journal of Polytechnic, 24(4), 1391-1399.
6. [6] Maji, P. K., Roy, A. R., Biswas, R. 2003. Soft Set Theory. Computers and Mathematics with Applications, 45(4-5), 555–562.
7. [7] Irfan, A.M., Feng, F., Liu, X., Minc, W.K., Shabir, M. 2009. On some new operations in soft set Theory. Computers and Mathematics with Applications, 57, 1547-1553.
8. [8] Shabir, M., Naz, M. 2011. On soft topological spaces. Computers and Mathematics with Applications, 61, 1786-1799.

9. [9] İç, Y., Yurdakul, M. 2019. Analysis of the effect of the number of criteria and alternatives on the ranking results in applications of the multi-criteria decision-making approaches in machining center selection problems. Journal of the Faculty of Engineering and Architecture of Gazi University, 35, 991-1002.
10. [10] Dağdeviren, M., Dönmez, N., Kurt, M. 2013. Developing a new model for supplier evaluation process for a company and its application. Journal of the Faculty of Engineering and Architecture of Gazi University, 21, 247-255.
11. [11] Dağdeviren, M., Eren, T. 2013. Analytical hierarchy process and use of 0-1 goal programming methods in selecting supplier firm. Journal of the Faculty of Engineering and Architecture of Gazi University, 16, 41-52.
12. [12] Chen, C. T., Lin, C. T., Huang, S. F. 2006. A fuzzy approach for supplier evaluation and selection in supply chain management. International Journal of Production Economics, 102(2), 289-301.
13. [13] Fatimah, F., Rosadi, D., Hakim, R. F., Alcantud, J.C.R. 2018. N-soft sets and their decision making algorithms. Soft Computing, 22(12), 3829-3842.
14. [14] Çağman, N., Enginoğlu, S. 2010. Soft set theory and uni–int decision making. European Journal of Operational Research, 207(2), 848-855.
15. [15] Roy, A. R., Maji, P.K. 2007. A fuzzy soft set theoretic approach to decision making problems. Journal of Computational and Applied Mathematics, 203(2), 412-418.
16. [16] 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.
17. [17] Maji, P. K., Roy, A. R., Biswas, R. 2001. Fuzzy soft sets. Journal of Fuzzy Mathematics, 9(3), 589-602.
18. [18] Çağman, N., Çıtak, F., Enginoğlu, S. 2010. Fuzzy parameterized fuzzy soft set theory and its applications. Turkish Journal of Fuzzy Systems, 1(1), 21-35.
19. [19] Meng, D., Zhang, X., Qin, K. 2011. Soft rough fuzzy sets and soft fuzzy rough sets. Computers and Mathematics with Applications, 62(12), 4635-4645.
20. [20] Fujita, T., Smarandache, F. 2025. An introduction to advanced soft set variants: Superhypersoft sets, indetermsuperhypersoft sets, indetermtreesoft sets, bihypersoft sets, graphicsoft sets, and beyond. Neutrosophic Sets and Systems, 82, 817-843.
21. [21] Demirtaş, N., Dalkılıç, O. 2020. Decompositions of Soft α-continuity and Soft A-continuity. Journal of New Theory, (31), 86-94.
22. [22] Baser, Z., Ulucay, V. 2025. Energy of a neutrosophic soft set and its applications to multi-criteria decision-making problems. Neutrosophic Sets and Systems, 79(1), 28.
23. [23] Ashraf, S., Jana, C., Sohail, M., Choudhary, R., Ahmad, S., Deveci, M. 2025. Multi-criteria decision-making model based on picture hesitant fuzzy soft set approach: An application of sustainable solar energy management. Information Sciences, 686, 121334.
24. [24] Dalkılıç, O. 2022. Generalization of neutrosophic parametrized soft set theory and its applications. Journal of Polytechnic, 25(2), 675-684.
25. [25] Xu, K., Pedrycz, W., Li, Z., Nie, W. 2018. Constructing a virtual space for enhancing the classification performance of fuzzy clustering. IEEE Transactions on Fuzzy Systems, 27(9), 1779-1792.
26. [26] Dalkılıç, O. 2022. On topological structures of virtual fuzzy parametrized fuzzy soft sets. Complex and Intelligent Systems, 8, 337–348.
27. [27] Mohaghegh, S. 2000. Virtual-intelligence applications in petroleum engineering: part 3-fuzzy logic. Journal of petroleum technology, 52(11), 82-87.
28. [28] Aydın, T., Enginoğlu, S. 2021. Interval-valued intuitionistic fuzzy parameterized interval-valued intuitionistic fuzzy soft sets and their application in decision-making. Journal of Ambient Intelligence and Humanized Computing, 12(1), 1541-1558.