216 156
Full Length Article
International Journal of Neutrosophic Science
Volume 17 , Issue 1, PP: 41-60 , 2021 | Cite this article as | XML | Html |PDF


Multi-criteria Decision-making Applications Based on Set Valued Generalized Neutrosophic Quadruple Sets for Law

Authors Names :   Necmiye Merve Sahin   1 *     Merve Sena Uz   2  

1  Affiliation :  Faculty of Law, Hasan Kalyoncu University, Gaziantep 27410, Turkey

    Email :  necmiyemerve.sahin@gmail.com

2  Affiliation :  Department of Mathematics, Gaziantep University, Gaziantep27310-Turkey

    Email :  evrem_anes@yahoo.com

Doi   :   https://doi.org/10.54216/IJNS.170103

Received: August 25, 2021 Accepted: December 02, 2021

Abstract :

In this article, an algorithm has been introduced that enables judges to see the decisions that should be made in a way that is closest to the conscience and the law, without transferring the cases to the higher authorities, without anyone objecting to their decisions. This algorithm has been introduced depending on the generalized set-valued neutrosophic quadruple numbers and the Euclidean similarity measure in sets, what the decision is made by considering all the situations, regardless of which case the defendants come before the judge, how similar these decisions are to the legal decisions that should be made. In this way, we can easily see the decisions given to the accused in all kinds of cases, and we can arrange the decisions according to the similarity value. The closer the similarity value is to 1, the more correct the judge's decision from a legal point of view.

Keywords :

generalized set valued neutrosophic quadruple numbers , generalized Euclid similarity measure , law , decision making

References :

[1] Smarandache, F. (1999) “A Unifying Field in Logics. Neutrosophy: Neutrosophic Probability, Set and Logic” American Research Press: Rehoboth, DE, USA, 1999

[2] Wang H., Smarandache F., Zhang Y. Q., Sunderraman R. “Single valued neutrosophic sets” Multispace Multistructure, vol 4, pp. 410 – 413, 2010

[3] Biswas, P., Pramanik, S., & Giri, B. C. “A new methodology for neutrosophic multi-attribute decision making with unknown weight information” Neutrosophic Sets and Systems, 3, 42-52, 2014

[4] Mukherjee, A., Sarkar, S. “Several Similarity Measures of Neutrosophic Soft Sets and its Application in Real Life Problem”. Ann. Pure Appl. Math., vol. 7, pp. 1– 6, 2014

[5] Ye, S., Fu, J., & Ye, J. Medical diagnosis using distance-based similarity measures of single valued neutrosophic multisets. Neutrosophic Sets and Systems, vol 7, pp. 47-52, 2015

[6] Broumi, S., Deli, I., & Smarandache, F “N-valued interval neutrosophic sets and their application in medical diagnosis” Critical Review, Center for Mathematics of Uncertainty, Creighton University, Omaha, NE, USA, vol 10, pp. 45-69, 2015

[7] Smarandache F.  “Neutrosophic quadruple numbers, refined neutrosophic quadruple numbers, absorbance law, and the multiplication of neutrosophic quadruple numbers” Neutrosophic Set and Systems, vol 10, pp. 96 -98, 2014

[8] Şahin, M., Kargın “A. Neutrosophic triplet groups based on set valued neutrosophic quadruple numbers” Neutrosophic Sets and Systems, vol 30, pp. 122 – 131, 2019

[9] Şahin, M., Kargın, A. “Generalized set – valued neutrosophic quadruple sets and numbers” In Quadruple Neutrosophic Theory and Applications.Pons Editions Brussels, Belgium, EU, vol 2, pp. 23 -40, 2020

[10] Zadeh, L. A. “Fuzzy sets” Information and control, vol 8(3), pp. 338-353, 1965

[11] Atanassov T. K. “Intuitionistic fuzzy sets” Fuzzy Sets Syst, vol 20, pp. 87–96, 1986

[12] Smarandache, F. “Neutrosophy: neutrosophic probability, set, and logic” analytic synthesis & synthetic analysis, 1998

[13] F. Smarandache and M. Ali “Neutrosophic triplet group” Neural Computing and Applications, vol 29, pp. 595-601, (2016)

[14] Smarandache, F., & Ali, M. “Neutrosophic triplet ring and its applications”  Bulletin of the American Physical Society, vol 62, 2017

[15] Şahin, M., & Kargın, A. “Single valued neutrosophic quadruple graphs” Asian Journal of Mathematics and Computer Research, pp. 243-250, 2019

[16] Şahin, M., Kargın, A., & Yıldız, İ. “Neutrosophic Triplet Field and Neutrosophic Triplet Vector Space Based on Set Valued Neutrosophic Quadruple Number” Quadruple Neutrosophic Theory And Applications, vol 1, pp. 52, 2020

[17] Kargın, A., Dayan, A., & Şahin, N. M. “Generalized Hamming Similarity Measure Based on Neutrosophic Quadruple Numbers and Its Applications to Law Sciences” Neutrosophic Sets and Systems, vol 40(1), pp. 4, 2021

[18] Şahin, S., Kargın, A., & Yücel, M. “Hausdorff Measures on Generalized Set Valued Neutrosophic Quadruple Numbers and Decision Making Applications for Adequacy of Online Education” Neutrosophic Sets and Systems, vol 40, pp. 86-116, 2021

[19] Şahin, M., Kargın, A., & Kılıç, A. “Generalized neutrosophic quadruple sets and numbers” Quadruple Neutrosophic Theory and Applications, vol 1, pp. 11-22, 2020

[20] Şahin, M., Kargın, A., & Kılıç, A. “Generalized set valued neutrosophic quadruple sets and numbers” Quadruple Neutrosophic Theory and Applications, vol. 1(2), pp. 23-40, 2020

[21] Ibrahim, M., Agboola, A., Adeleke, E., & Akinleye, S. “On Neutrosophic, Quadruple Hypervector Spaces” International Journal of Neutrosophic Science (IJNS), vol 4, pp. 20-35, 2020

[22] Aslan, C., Kargın, A., & Şahin, M. “Neutrosophic modeling of Talcott Parsons’s action and decision-making applications for it” Symmetry, vol. 12(7), pp. 1166, 2020

[23] Kargın, A., Dayan A., Yıldız, İ., Kılıç, A. “Neutrosophic Triplet m – Banach   Space  ”Neutrosophic Set and Systems, vol 38, pp. 383 – 398, 2020

 [24] Şahin, M., Kargın, A., Uz, M. S., & Kılıç, A. “Neutrosophic Triplet Bipolar Metric Spaces” Quadruple Neutrosophic Theory And Applications, vol 1, pp. 150, 2020

[25] Kandasamy, V., Kandasamy, I., & Smarandache, F. “Neutrosophic quadruple vector spaces and their properties” Mathematics, vol 7(8), pp. 758, 2019

[26] Şahin, M., Kargın, A., & Yücel, M. “Neutrosophic Triplet Partial g-Metric Spaces” Neutrosophic Sets and Systems, vol 33, pp. 116-133, 2020

[27] Rezaei, G. R., Jun, Y. B., & Borzooei, R. A. “Neutrosophic quadruple a-ideals” Neutrosophic Sets and Systems, vol 31(1), pp. 19, 2020

[28] Şahin, M., and Kargın, A. “New Similarity Measure between Single-Valued Neutrosophic Sets and Decision-Making Applications in Professional Proficiencies” In Neutrosophic Sets in Decision Analysis and Operations Research, IGI Global vol. 7, pp. 129-149, 2020

[29] Şahin, M. Kargın, A., Uz, M. S. “Generalized Euclid Measures Based on Generalized Set Valued Neutrosophic Quadruple Numbers and Multi Criteria Decision Making Applications” Neutrosophic Sets and Systems, 2021, accepted

[30] Borzooei, R. A., Jun, Y. B., Takallo, M. M., & Ahn, S. S. “Positive implicative neutrosophic quadruple BCK-algebras and ideals” New Mathematics and Natural Computation (NMNC), vol 17(02), pp. 403-423, 2021

[31] Şahin, M., & Kargın, A. “Neutrosophic triplet Lie Algebra” Neutrosophic Triplet Research, vol 1(6), pp.        68-78, 2019

[32] Şahin M. and Kargın A. “Neutrosophic triplet partial inner product space” Neutrosophic Triplet Structures, vol 1, pp. 10-21, 2019

[33] Saqlain, M., Jafar, N., Moin, S., Saeed, M., & Broumi, S. “Single and multi-valued neutrosophic hypersoft set and tangent similarity measure of single valued neutrosophic hyper soft sets” Neutrosophic Sets and Systems, vol 32(1), pp. 317-329, 2020

[34] Şahin, M., Kargın, A., & Smarandache, F. “Neutrosophic triplet topology” Neutrosophic Triplet Research, vol 1(4), pp. 43-54, 2019

[35] Tan, R. P., & Zhang, W. D. Decision-making method based on new entropy and refined single-valued neutrosophic sets and its application in typhoon disaster assessment. Applied Intelligence, vol 51(1), pp. 283-307, 2021

Cite this Article as :
Necmiye Merve Sahin , Merve Sena Uz, Multi-criteria Decision-making Applications Based on Set Valued Generalized Neutrosophic Quadruple Sets for Law, International Journal of Neutrosophic Science, Vol. 17 , No. 1 , (2021) : 41-60 (Doi   :  https://doi.org/10.54216/IJNS.170103)