A more ideal Approach to Uncertainty Problems: VFPIVFSS

Öz

The aim of this study is to reach a more ideal result by generalizing the approach proposed by fuzzy parametrized interval valued fuzzy soft sets (FPIVFSSs) for uncertainty problems. For this purpose, the virtual FPIVFSS (VFPIVFSS) concept was defined. In addition, an algorithm is proposed for how to handle VFPIVFSSs in solving an uncertainty problem. Finally, by comparing the decision-making processes for the FPIVFSS and VFPIVFSS through an application, both clusters were analyzed in detail.

Anahtar Kelimeler

• FPIVFSS
• virtual FPIVFSS
• decision making

Belirsizlik Problemleri için Daha İdeal Bir Yaklaşım: VFPIVFSS

Öz

Bu çalışmanın amacı belirsizlik problemleri için bulanık parametreli aralık değerli bulanık esnek küme (FPIVFSS)’lerin önerdiği yaklaşımı genelleştirerek daha ideale yakın bir sonuca ulaşabilmektir. Bu amaçla sanal FPIVFSS (VFPIVFSS) kavramı tanımlandı. Ayrıca bir belirsizlik probleminin çözümünde VFPIVSS’lerin nasıl ele alınması gerektiğine yönelik bir algoritma önerildi. Son olarak bir uygulama üzerinden FPIVFSS ve VFPIVFSS için karar verme süreçleri karşılaştırılarak her iki küme detaylı bir şekilde analiz edildi.

Anahtar Kelimeler

• FPIVFSS
• sanal FPIVFSS
• karar verme

Kaynakça

1. [1] Zadeh L.A., “Fuzzy sets”, Information and Control, 8:338-353, (1965).
2. [2] Pawlak Z., “Rough sets”, Int J Comput Inf Sci, 11:341-356, (1982).
3. [3] Molodtsov D., “Soft set theory-first results”, Comput. Math. Appl., 37:19-31, (1999).
4. [4] Maji P.K., Roy A.R. and Biswas R., “Fuzzy soft sets”, Journal of Fuzzy Mathematics, 9(3):589-602, (2001).
5. [5] Gorzalczany M.B., “A method of inference in approximate reasoning based on interval valued fuzzy sets”, Fuzzy Sets and Systems, 21:1-17, (1987).
6. [6] Demirtaş N., Hussaın S. and Dalkılıç O. “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, (2020).
7. [7] Demirtaş N. and 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, (2019).
8. [8] Dalkılıç O, Demirtas N. “VFP-Soft Sets and Its Application on Decision Making Problems”, Journal of Polytechnic, https://doi.org/10.2339/politeknik.685634, (2021).

9. [9] Dalkılıç O. “An Application of VFPFSS’s in Decision Making Problems”, Journal of Polytechnic, https://doi.org/10.2339/politeknik.758474, (2021).
10. [10] Dalkılıç O. and Demirtaş N. “Bipolar soft filter”, Journal of Universal Mathematics, 3(1): 21-27, (2020).
11. [11] Demirtaş N. and Dalkılıç O. “Decompositions of Soft α-continuity and Soft A-continuity, Journal of New Theory, (31): 86-94, (2020).
12. [12] Alkhazaleh S., Salleh A.R. and Hassan N. “Fuzzy parameterized interval-valued fuzzy soft set”, Applied Mathematical Sciences, 5(67): 3335-3346, (2011).
13. [13] Maji P.K., Roy A.R. and Biswas R., “Soft set theory”, Computers and Mathematics with Applications, 45(4-5): 555–562, (2003).
14. [14] Maji P.K., Roy A.R. and Biswas R., “An application of soft sets in a decision making problem”, Computers and Mathematics with Applications, 44: 1077-1083, (2002).
15. [15] Cağman N., Citak F. and Enginoglu S., “Fuzzy parameterized fuzzy soft set theory and its applications”, Turkish Journal of Fuzzy Systems, 1(1): 21-35, (2010).
16. [16] Cağman N. and Enginoğlu S.,” Soft matrices and its decision makings”, Computers and Mathematics with Applications, 59: 3308-3314, (2010).
17. [17] Chen D., Tsang E.C.C., Yeung D.S. and Wang X., “The parameterization reduction of soft sets and its applications”, Computers and Mathematics with Applications, 49: 757-763, (2005).
18. [18] Feng F., Jun Y.B., Liu X. and Li L., “An adjustable approach to fuzzy soft set based decision making”, Journal of Computational and Applied Mathematics, 234: 10-20, (2010).
19. [19] Zadeh L.A., “The concept of a linguistic variable and its application to approximate reasoning-I”, Information Sciences, 8: 199-249, (1975).
20. [20] Roy A.R. and Maji P.K., “A fuzzy soft set theoretic approach to decision making problems”, Journal of computational and Applied Mathematics, 203 (2): 412-418, (2007).
21. [21] Peng X. and Jingguo D., "Hesitant fuzzy soft decision making methods based on WASPAS, MABAC and COPRAS with combined weights", Journal of Intelligent and Fuzzy Systems, 33: 1313-1325, (2017).
22. [22] Peng X. and Harish G., "Algorithms for interval-valued fuzzy soft sets in emergency decision making based on WDBA and CODAS with new information measure", Computers and Industrial Engineering, 119: 439-452, (2018).
23. [23] Çağman N., Çıtak F. and Enginoğlu S., “FP-soft Set Theory and Its Applications”, Annals of Fuzzy Mathematics and Informatics, 2: 219-226, (2011).
24. [24] Yang X., Lin T.Y., Yang J., Li Y. and Yu D., Combination of interval-valued fuzzy set and soft set, Computers and Mathematics with Application, 58: 521-527, (2009).