VFP-Esnek Kümelerle Yenilikçi Karar Verme: Karşılaştırmalı Bir Analiz

Year 2025, Volume: 20 Issue: 1, 109 - 119, 27.03.2025

Orhan Dalkılıç

https://doi.org/10.55525/tjst.1375167

Abstract

Bu çalışma sanal bulanık parametreli (VFP-)yumuşak küme teorisi çerçevesinde temel küme özelliklerini incelemektedir. Bu özelliklerin kapsamlı bir incelemesini sağlayarak temel içgörüleri ve değerlendirmeleri sunar. Çalışma aynı zamanda veri analizini kolaylaştırmak için VFP-soft kümelerinin tanımını basitleştirerek onu daha erişilebilir ve daha az karmaşık hale getiriyor. Ayrıca makale, VFP-soft kümelerinde parametre ağırlıklandırmaya yönelik iki farklı yaklaşımın entegrasyonunu araştırıyor. Özellikle araştırma, VFP-soft kümelerine dayanan yeni bir karar verme algoritması sunmakta ve bunun etkinliğini değerlendirmek için karşılaştırmalı bir analiz gerçekleştirmektedir. Bu çalışma, VFP-soft kümelerinin ve uygulamalarının anlaşılmasını geliştirerek alana katkıda bulunurken, aynı zamanda gerçek dünya senaryoları için pratik bir karar verme aracı da sağlıyor.

Keywords

Bulanık küme, esnek küme, VFP-esnek küme, algoritma, karar verme

Innovative Decision-Making with VFP-Soft Sets: A Comparative Analysis

Abstract

This study delves into fundamental set properties within the framework of virtual fuzzy parameterized (VFP-)soft set theory. It provides a comprehensive examination of these properties, offering essential insights and considerations. The study also simplifies the definition of VFP-soft sets to streamline data analysis, making it more accessible and less complex. Furthermore, the paper explores the integration of two distinct approaches for parameter weighting in VFP-soft sets. Notably, the research introduces a novel decision-making algorithm grounded in VFP-soft sets and conducts a comparative analysis to evaluate its effectiveness. This work contributes to the field by enhancing the understanding of VFP-soft sets and their applications, while also providing a practical decision-making tool for real-world scenarios.

Keywords

Fuzzy set, soft set, VFP-soft set, algorithm, decision-making

References

• Zadeh LA. Fuzzy sets. Inf & Cont 1965; 8: 338-353.
• Pawlak Z. Rough sets. Int J Comput Inform Sci 1982; 11: 341-356.
• Molodtsov D. Soft set theory-first results. Comput & Math Appl 1999; 37: 19-31.
• Maji PK, Roy AR, Biswas R. Soft set theory. Comput & Math Appl 2003; 45(4-5): 555–562.
• Maji PK, Roy AR, Biswas R. Fuzzy soft sets. J Fuzzy Math 2001; 9(3): 589-602.
• Maji PK, Roy AR, Biswas R. An application of soft sets in a decision making problem. Comput & Math Appl 2002; 44: 1077-1083.
• Çağman N, Enginoglu S. Soft matrices and its decision makings. Comput & Math Appl 2010; 59: 3308-3314.
• Çağman N, Çıtak F, Enginoglu S. Fuzzy parameterized fuzzy soft set theory and its applications. Turkish J Fuzzy Syst 2010; 1(1): 21-35.
• Chen D, Tsang ECC, Yeung DS, Wang X. The parameterization reduction of soft sets and its applications. Comput & Math Appl 2005; 49: 757-763.
• Feng F, Jun YB, Liu X, Li L. An adjustable approach to fuzzy soft set based decision making. J Comput & Appl Math 2010; 234: 10-20.
• Çağman N, Enginoglu S, Çıtak F. Fuzzy soft set theory and its applications. Iranian J Fuzzy Syst 2011; 8(3): 137-147.
• Demirtaş N, Dalkılıç O. An application in the diagnosis of prostate cancer with the help of bipolar soft rough sets. In: Mathematics and Mathematics Education (ICMME 2019), Konya, 283, 2019.
• Dalkılıç O, Demirtaş N. Bipolar soft filter. J Univ Math 2020; 3(1): 21-27.
• Demirtaş N, Hussaın S, Dalkılıc O. New approaches of inverse soft rough sets and their applications in a decision making problem. J Appl Math & Inf 2020; 38(3-4): 335-349.
• Demirtaş N, Dalkılıç O. Decompositions of soft α-continuity and soft A-continuity. J New Theory 2020; (31): 86-94.
• Roy AR, Maji PK. A fuzzy soft set theoretic approach to decision making problems. J Comput & Appl Math 2007; 203(2): 412-418.
• Peng X, Jingguo D. Hesitant fuzzy soft decision making methods based on WASPAS, MABAC, and COPRAS with combined weights. J Intell Fuzzy Syst 2017; 33: 1313-1325.
• Özlü, Ş. Interval valued q-rung orthopair hesitant fuzzy choquet aggregating operators in multi-criteria decision making problems. Gazi Univ J Sci Part C Des & Technol 2022; 10(4): 1006-1025.
• Özlü, Ş. Interval valued bipolar fuzzy prioritized weighted dombi averaging operator based on multi-criteria decision making problems. Gazi Univ J Sci Part C Des & Technol 2022; 10(4): 841-857.
• Özlü, Ş. Generalized Dice measures of single valued neutrosophic type-2 hesitant fuzzy sets and their application to multi-criteria decision making problems. Int J Mach Learn & Cybern 2023; 14(1): 33-62.
• Özlü, Ş. Multi-criteria decision making based on vector similarity measures of picture type-2 hesitant fuzzy sets. Granular Comput 2023; 8(6): 1505-1531.
• Çağman N, Çıtak F, Enginoglu S. FP-soft set theory and its applications. Annals Fuzzy Math & Inf 2011; 2: 219-226.
• Dalkılıç O, Demirtas N. VFP-soft sets and its application on decision making problems. J Polytech 2021; 24(4): 1391-1399.
• Dalkılıç O. An application of VFPFSS’s in decision making problems. J Polytech 2021; 25(2): 491-501.
• Dalkılıç O. On topological structures of virtual fuzzy parametrized fuzzy soft sets. Complex & Intell Syst 2022; 8(1): 337-348.