Generalization of Neutrosophic Parametrized Soft Set Theory and Its Applications

Yıl 2022, , 675 - 684, 01.06.2022

Orhan Dalkılıç

https://doi.org/10.2339/politeknik.783237

Cited By: 1

Öz

This study focuses on two important theories, neutrosophy and soft sets, in order to expand the application area of uncertainty problems that can be encountered especially in the fields of science and engineering. For this purpose, the virtual neutrosophic parametrized soft set theory are defined and some important properties of the theory are given. Then, it is proposed to use virtual neutrosophic parametrized soft sets to solve similar problems by using an algorithm to show that virtual neutrosophic parametrized soft set theory is more successful than neutrosophic parametrized soft set theory in approximation of uncertainty to the ideal solution. In addition, in this study, specific parameter sets make more alternative solutions available for solving uncertainty problems. This makes it easier to choose the most ideal solution from many solutions.

Anahtar Kelimeler

Neutrosophic parametrized soft set, virtual neutrosophic parametrized soft set, decision making

Nötrosofik Parametreli Esnek Kümelerin Genelleştirilmesi ve Uygulamaları

Öz

Bu çalışma özellikle bilim ve mühendislik alanlarında karşılaşılabilen belirsizlik problemlerinin uygulama alanını genişletebilmek için iki önemli teori olan nötrosofi ve esnek kümelere odaklanmaktadır. Bunun için sanal nötrosofik parametreli esnek küme teorisi tanımlanarak önemli bazı özellikleri verilmiştir. Daha sonra, belirsizliğin ideal çözüme yaklaştırılmasında sanal nötrosofik parametreli esnek küme teorisinin nötrosofik parametreli esnek küme teorisinden daha başarılı olduğu bir algoritma yardımıyla gösterilerek benzeri problemlerin çözümü için sanal nötrosofik parametreli esnek kümelerin kullanılması önerilmiştir. Ayrıca çalışmadaki özel parametre kümeleri, belirsizlik problemlerinin çözümünde daha fazla alternatif çözüm yolunu mevcut kılmaktadır. Bu sayede birçok çözüm yolundan ideale en yakın olanı seçmeyi kolaylaştırmaktadır.

Anahtar Kelimeler

Nötrosofik parametreli esnek küme, sanal nötrosofik parametreli esnek küme, karar verme

Kaynakça

• [1] Zadeh L.A., “Fuzzy sets”, Information and Control, 8: 338-353, (1965).
• [2] Pawlak Z., “Rough sets”, Int J Comput Inf Sci, 11: 341-356, (1982).
• [3] Maji P.K., Roy A.R. and Biswas R., “Fuzzy soft sets”, Journal of Fuzzy Mathematics, 9(3):589-602, (2001).
• [4] Molodtsov D., “Soft set theory-first results”, Comput. Math. Appl., 37: 19-31, (1999).
• [5] Çağman N., Çıtak F. and Enginoğlu S., “FP-soft Set Theory and Its Applications”, Annals of Fuzzy Mathematics and Informatics, 2: 219-226, (2011).
• [6] Dalkılıç O. and Demirtas N., “VFP-Soft Sets and Its Application on Decision Making Problems”, Journal of Polytechnic, https://doi.org/10.2339/politeknik.685634, (2020).
• [7] Smarandache F., “Neutrosophic set, a generalisation of the intuitionistic fuzzy sets”, Int. J. Pure Appl. Math., 24: 287–297, (2005).
• [8] Broumi S., Deli I. and Smarandache F., “Neutrosophic parametrized soft set theory and its decision making”, International Frontier Science Letters, 1(1): 1-11, (2014).
• [9] Çağman N., Çıtak F. and Enginoğlu S., “Fuzzy parameterized fuzzy soft set theory and its applications”, Turkish Journal of Fuzzy System, 1: 21-35, (2010).
• [10] Çağman N. and Karataş S., “Intuitionistic fuzzy soft set theory and its decision making”, Journal of Intelligent and Fuzzy Systems, 24(4): 829-836, (2013).
• [11] Deli I. and Çağman N., “Intuitionistic fuzzy parameterized soft set theory and its decision making”, Applied Soft Computing, 28: 109-113, (2015).
• [12] Smarandache F., “A unifying field in logics. Neutrosophy: neutrosophic probability, set and logic”, American Research Press, Rehoboth, (1999).
• [13] Grattan-Guiness I., “Fuzzy membership mapped onto interval and many-valued quantities”, Z Math Logik Grundladen Math, 22: 149–160, (1975).
• [14] Jahn K.U., “Intervall-wertige Mengen”, Math Nachr, 68:115–132, (1975).
• [15] Zadeh L., “The concept of a linguistic variable and its application to approximate reasoning-I”, Inf Sci, 8: 199–249, (1975).
• [16] Atanassov K., “Intuitionistic fuzzy sets”, Fuzzy Sets Syst, 20: 87–96, (1986).
• [17] Das S. and Kar D.S., “Group decision making in medical system: an intuitionistic fuzzy soft set approach”, Appl Soft Comput, 24: 196–211, (2014).
• [18] Atanassov K. and Gargov G., “Interval valued intuitionistic fuzzy sets”, Fuzzy Set Syst, 31:343–349, (1989).
• [19] Wang H., Smarandache F., Zhang Y.Q. and Sunderraman R., “Single valued neutrosophic sets”, Multispace Multistruct, 4: 410–413, (2010).
• [20] 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).
• [21] 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).
• [22] Abu Qamar M. and Hassan N. “An approach toward a Q-neutrosophic soft set and its application in decision making”, Symmetry, 11(2): 139, (2019).
• [23] Jana C. and Pal M. “A robust single-valued neutrosophic soft aggregation operators in multi-criteria decision making”, Symmetry, 11(1): 110, (2019).
• [24] Deli I. “Interval-valued neutrosophic soft sets and its decision making”, International Journal of Machine Learning and Cybernetics, 8(2): 665-676, (2017).
• [25] Deli I., Eraslan S. and Çağman N. “ivnpiv-Neutrosophic soft sets and their decision making based on similarity measure”, Neural Computing and applications, 29(1): 187- 203, (2018).
• [26] Saha A. and Broumi S. “Parameter Reduction of Neutrosophic Soft Sets and Their Applications”, Neutrosophic Sets and Systems, 32(1): 1, (2020).
• [27] Khalil A.M., Cao D., Azzam A.A., Smarandache F. and Alharbi W. “Combination of the single-valued neutrosophic fuzzy set and the soft set with applications in decision- making”, Symmetry, 12(8): 1361, (2020).