Modelling with Neutrosophic Fuzzy Sets for Financial Applications in Discrete System

Authors

DOI:

https://doi.org/10.31181/sems21202433a

Keywords:

Fuzzy difference equation, Neutrosophic fuzzy sets, Financial modelling

Abstract

A unique branch of philosophy known as "Neutrosophy" describes the nature, genesis and scope of neutralities. F. Smarandache originated the neutrosophic set. As an extension of the intuitionistic set, he showed the degree of indeterminacy as an independent component. The application of the neutrosophic numbers, that is, the financial applications in discrete systems is analysed here. In this research paper, we consider the two cases of the financial applications of the neutrosophic environment with its numerical illustration on the basis of fuzzy difference equations. 

References

Gazi, K. H., Raisa, N., Biswas, A., Azizzadeh, F., & Mondal, S. P. (2025). Finding the most important criteria in women's empowerment for sports sector by pentagonal fuzzy DEMATEL methodology. Spectrum of Decision Making and Applications, 2(1), 28-52. https://doi.org/10.31181/sdmap21202510

Alamin, A., Rahaman, M., & Mondal, S. P. (2025). Geometric approach for solving first order non homogenous fuzzy difference equation. Spectrum of Operational Research, 2(1), 61-71. https://doi.org/10.31181/sor2120257

Biswas, A., Gazi, K. H., Bhaduri, P., & Mondal, S. P. (2024). Neutrosophic fuzzy decision-making framework for site selection. Journal of Decision Analytics and Intelligent Computing, 4(1), 187-215. https://doi.org/10.31181/jdaic10004122024b

Biswas, A., Gazi, K. H., & Mondal, S. P. (2024). Finding Effective Factor for Circular Economy Using Uncertain MCDM Approach. Management Science Advances, 1(1), 31-52. https://doi.org/10.31181/msa1120245

Rangarajan, K., Singh, P., Salahshour, S., & Mondal, S. P. (2024). Analysis of Second-Order Linear Fuzzy Differential Equation Under an Innovative Fuzzy Derivative Approach and Its Application. Journal of Uncertain Systems, 2450022. https://doi.org/10.1142/S1752890924500223

Rahaman, M., Das, M., Alam, S., Salahshour, S., & Mondal, S. P. (2024). Metric Space and Calculus of Type-2 Interval-Valued Functions. Journal of Uncertain Systems. https://dx.doi.org/10.1142/s1752890924500181

Alamin, A., Gazi, K. H., & Mondal, S. P. (2024). Solution of second order linear homogeneous fuzzy difference equation with constant coefficients by geometric approach. Journal of Decision Analytics and Intelligent Computing, 4(1), 241–252. https://doi.org/10.31181/jdaic10021122024a

Gazi, K. H., Biswas, A., Singh, P., Rahaman, M., Maity, S., Mahata, A., & Mondal, S. P. (2024). A comprehensive literature review of fuzzy differential equations with applications. Journal of Fuzzy Extension and Applications, https://doi.org/10.22105/jfea.2024.449970.1426

Alamin, A., Rahaman, M., Salahshour, S., Mondal, S. P., Alam, S., Gazi, K. H., & Mian, M. J. (2024). A Discussion of Newton's Law of Cooling using Difference Equations in Fuzzy Frames as an Alternative to the Traditional Continuous Dynamical System. International Journal of Mathematics in Operational Research, https://doi.org/10.1504/IJMOR.2024.10067203

Adhikari, D., Gazi, K. H., Sobczak, A., Giri, B. C., Salahshour, S., & Mondal, S. P. (2024). Ranking of Different States in India Based on Sustainable Women Empowerment using MCDM Methodology under Uncertain Environment. Journal of Uncertain Systems, 17(4), 2450010. https://doi.org/10.1142/S1752890924500107

Singh, P., Gazi, K. H., Rahaman, M., Basuri, T., & Mondal, S. P. (2024). Solution strategy and associated result for fuzzy Mellin transformation. Franklin Open, 100112.

Zadeh, L. A. (1965). Fuzzy sets. Information and Control, 8(5), 338- 353. https://doi.org/10.1016/S0019-9958(65)90241-X

Atanassov, K. (1986). Intuitionistic fuzzy sets. Fuzzy Sets and Systems, 20, 87-96. https://doi.org/10.1016/S0165-0114(86)80034-3

Smarandache, F. (1998). Neutrosophy: neutrosophic probability, set, and logic: analytic synthesis & synthetic analysis, 105.

Rahaman, M., Alam, S., Alamin, A., & Mondal, S. P. (2023). Solution of the Second-Order Linear Intuitionistic Fuzzy Difference Equation by Extension Principle Scheme. In Fuzzy Optimization, Decision-making and Operations Research: Theory and Applications (pp. 703-724). Cham: Springer International Publishing. https://doi.org/10.1007/978-3-031-35668-1_31.

Das, S., Roy, B. K., Kar, M. B., Kar, S., & Pamučar, D. (2020). Neutrosophic fuzzy set and its application in decision making. Journal of Ambient Intelligence and Humanized Computing, 11, 5017-5029. https://doi.org/10.1007/s12652-020-01808-3

Long, H. V., Ali, M., Khan, M., & Tu, D. N. (2019). A novel approach for fuzzy clustering based on neutrosophic association matrix. Computers & Industrial Engineering, 127, 687-697. https://doi.org/10.1016/j.cie.2018.11.007.

Wang, H., Smarandache, F., Zhang, Y., & Sunderraman, R. (2010). Single valued neutrosophic sets. Infinite study.

Ye, J. (2014). Single-valued neutrosophic minimum spanning tree and its clustering method. Journal of intelligent Systems, 23(3), 311-324. https://doi.org/10.1515/jisys-2013-0075.

Peng, J. J., Wang, J. Q., Wang, J., Zhang, H. Y., & Chen, X. H. (2016). Simplified neutrosophic sets and their applications in multi-criteria group decision-making problems. International journal of systems science, 47(10), 2342-2358. https://doi.org/10.1080/00207721.2014.994050.

Peng, J. J., Wang, J. Q., Wu, X. H., Zhang, H. Y., & Chen, X. H. (2015). The fuzzy cross-entropy for intuitionistic hesitant fuzzy sets and their application in multi-criteria decision-making. International Journal of Systems Science, 46(13), 2335-2350. https://doi.org/10.1080/00207721.2014.993744.

Chakraborty, A., Mondal, S. P., Ahmadian, A., Senu, N., Alam, S., & Salahshour, S. (2018). Different forms of triangular neutrosophic numbers, de-neutrosophication techniques, and their applications. Symmetry, 10(8), 327. https://doi.org/10.3390/sym10080327.

Smarandache, F. (2017). Neutrosophic Perspectives: Triplets, Duplets, Multisets, Hybrid Operators, Modal Logic, Hedge Algebras. And Applications. Infinite Study.

Deli, I., Broumi, S., & Smarandache, F. (2015). On neutrosophic refined sets and their applications in medical diagnosis. Journal of new theory, (6), 88-98.

Broumi, S., & Smarandache, F. (2015). Interval‐Valued Neutrosophic Soft Rough Sets. International Journal of Computational Mathematics, 2015(1), 232919. https://doi.org/10.1155/2015/232919.

Broumi, S. (2013). Generalized neutrosophic soft set. Infinite Study,3(2).

Edalatpanah, S. A. (2020). A direct model for triangular neutrosophic linear programming. International journal of neutrosophic science, 1(1), 19-28. https://doi.org/10.5281/zenodo.3679499

Deli, I., & Subas, Y. (2014). Single valued neutrosophic numbers and their applications to multicriteria decision making problem. Neutrosophic Sets Syst, 2(1), 1-13.

Reig-Mullor, J., & Salas-Molina, F. (2022). Non-linear neutrosophic numbers and its application to multiple criteria performance assessment. International Journal of Fuzzy Systems, 24(6), 2889-2904. https://doi.org/10.1007/s40815-022-01295-y

Deveci, M., Erdogan, N., Cali, U., Stekli, J., & Zhong, S. (2021). Type-2 neutrosophic number based multi-attributive border approximation area comparison (MABAC) approach for offshore wind farm site selection in USA. Engineering Applications of Artificial Intelligence, 103, 104311. https://doi.org/10.1016/j.engappai.2021.104311

Deeba, E. Y., Korvin, A. D., & Koh, E. L. (1996). A fuzzy difference equation with an application. Journal of Difference Equations and applications, 2(4), 365-374. https://doi.org/10.1080/10236199608808071

Deeba, E. Y., & De Korvin, A. (1999). Analysis by fuzzy difference equations of a model of CO2 level in the blood. Applied mathematics letters, 12(3), 33-40. https://doi.org/10.1016/S0893-9659(98)00168-2

Lakshmikantham, V., & Vatsala, A. S. (2002). Basic theory of fuzzy difference equations. Journal of Difference Equations and Applications, 8(11), 957-968. https://doi.org/10.1080/1023619021000048850

Papaschinopoulos, G., & Papadopoulos, B. K. (2002). On the fuzzy difference equation x n+ 1= A+ B/xn. Soft Computing, 6, 456-461. https://doi.org/10.1007/s00500-001-0161-7

Papaschinopoulos, G., & Stefanidou, G. (2003). Boundedness and asymptotic behavior of the solutions of a fuzzy difference equation. Fuzzy sets and systems, 140(3), 523-539. https://doi.org/10.1016/S0165-0114(03)00034-4

Umekkan, S. A., Can, E., & Bayrak, M. A. (2014). Fuzzy difference equation in finance. IJSIMR, 2(8), 729-735.

Zhang, Q. H., Yang, L. H., & Liao, D. X. (2012). Behavior of solutions to a fuzzy nonlinear difference equation. Iranian Journal of Fuzzy Systems, 9(2), 1-12.

Memarbashi, R., & Ghasemabadi, A. (2013). Fuzzy difference equations of volterra type. International Journal of Nonlinear Analysis and Applications, 4(1), 74-78. https://doi.org/10.22075/ijnaa.2013.56

Stefanidou, G., & Papaschinopoulos, G. (2005). A fuzzy difference equation of a rational form. Journal of Nonlinear Mathematical Physics, 12(sup2), 300-315. https://doi.org/10.2991/jnmp.2005.12.s2.21

Chrysafis, K. A., Papadopoulos, B. K., & Papaschinopoulos, G. (2008). On the fuzzy difference equations of finance. Fuzzy Sets and Systems, 159(24), 3259-3270. https://doi.org/10.1016/j.fss.2008.06.007

Biswas, A., Gazi, K. H., Bhaduri, P., & Mondal, S. P. (2025). Site selection for girls hostel in a university campus by mcdm based strategy. Spectrum of Decision Making and Applications, 2(1), 68-93. https://doi.org/10.31181/sdmap21202511

Momena, A. F., Gazi, K. H., Rahaman, M., Sobczak, A., Salahshour, S., Mondal, S. P., & Ghosh, A. (2024). Ranking and challenges of supply chain companies using MCDM methodology. Logistics, 8(3), 87. https://doi.org/10.3390/logistics8030087

Pamučar, D., Puška, A., Stević, Ž., & Ćirović, G. (2021). A new intelligent MCDM model for HCW management: The integrated BWM–MABAC model based on D numbers. Expert Systems with Applications, 175, 114862. https://doi.org/10.1016/j.eswa.2021.114862

Mukhametzyanov, I., & Pamucar, D. (2018). A sensitivity analysis in MCDM problems: A statistical approach. Decision Making: Applications in Management and Engineering, 1(2), 51-80. https://doi.org/10.31181/dmame1802050m

Görçün, Ö. F., Pamucar, D., & Biswas, S. (2023). The blockchain technology selection in the logistics industry using a novel MCDM framework based on Fermatean fuzzy sets and Dombi aggregation. Information Sciences, 635, 345-374. https://doi.org/10.1016/j.ins.2023.03.113

Pamučar, D. Hybrid Spatial Mathematical Model for the Selection of the Most Suitable Wind Farm Locations. eNergetics 2016, 61.

Pamučar, D., Ćirović, G., Sekulović, D., & Ilić, A. (2011). A new fuzzy mathematical model for multi criteria decision making: An application of fuzzy mathematical model in a SWOT analysis. Scientific Research and Essays, 6(25), 5374-5386.

Pamučar, D., Marinković, D., & Kar, S. (2021). Dynamics under uncertainty: Modelling simulation and complexity. Mathematics, 9(12), 1416. https://doi.org/10.3390/books978-3-0365-1575-5

Zadeh, L. A. (1965). Information and control. Fuzzy sets, 8(3), 338-353. https://doi.org/10.1016/S0019-9958(65)90241-X

Atanassov, K. T., & Atanassov, K. T. (1999). Intuitionistic fuzzy sets (pp. 1-137). Physica-Verlag HD. https://doi.org/10.1007/978-3-7908-1870-3_1

Mondal, S. P., Mandal, M., Mahata, A., & Roy, T. K. (2018). Integral equations with pentagonal intuitionistic fuzzy numbers. Notes Intuitionistic Fuzzy Sets, 24(3), 40-52. https://doi.org/10.1007/978-3-7908-1870-3_1

Pamucar, D., Yazdani, M., Obradovic, R., Kumar, A., & Torres‐Jiménez, M. (2020). A novel fuzzy hybrid neutrosophic decision‐making approach for the resilient supplier selection problem. International Journal of Intelligent Systems, 35(12), 1934-1986. https://doi.org/10.1002/int.22279

Chakraborty, A., Mondal, S. P., Mahata, A., & Alam, S. (2021). Different linear and non-linear form of trapezoidal neutrosophic numbers, de-neutrosophication techniques and its application in time-cost optimization technique, sequencing problem. RAIRO-Operations Research, 55, S97-S118. https://doi.org/10.1051/ro/2019090

Mondal, S. P., Goswami, A., & Kumar De, S. (2019). Nonlinear triangular intuitionistic fuzzy number and its application in linear integral equation. Advances in Fuzzy Systems, 2019(1), 4142382. https://doi.org/10.1155/2019/4142382

Chakraborty, A., Mondal, S. P., Ahmadian, A., Senu, N., Alam, S., & Salahshour, S. (2018). Different forms of triangular neutrosophic numbers, de-neutrosophication techniques, and their applications. Symmetry, 10(8), 327. https://doi.org/10.3390/sym10080327

Jensen, A. (2011). Lecture notes on difference equations. Department of mathematical science, Aalborg University, Denmark, July, 18.

Alamin, A., Mondal, S. P., Alam, S., Ahmadian, A., Salahshour, S., & Salimi, M. (2020). Solution and interpretation of neutrosophic homogeneous difference equation. Symmetry, 12(7), 1091. https://doi.org/10.3390/sym12071091

Alamin, A., Mondal, S. P., Alam, S., & Goswami, A. (2020). Solution and stability analysis of non-homogeneous difference equation followed by real life application in fuzzy environment. Sādhanā, 45, 1-20. https://doi.org/10.1007/s12046-020-01422-1

Kwapisz, M. (1997). On difference equations arising in mathematics of finance. Nonlinear Analysis: Theory, Methods & Applications, 30(2), 1207-1218. https://doi.org/10.1016/S0362-546X(97)00235-6

Ümekkan, S. A., Can, E., & Bayrak, M. A. (2014). Fuzzy Difference Equations in Finance. International Journal of Scientific and Innovative Mathematical Research (IJSIMR), 2(8), 729-735.

Chrysafis, K. A., Papadopoulos, B. K., & Papaschinopoulos, G. (2008). On the fuzzy difference equations of finance. Fuzzy Sets and Systems, 159(24), 3259-3270. https://doi.org/10.1016/j.fss.2008.06.007

Published

2024-12-24

How to Cite

Alamin, A., Biswas, A., Gazi, K. H., & Sankar, S. P. M. (2024). Modelling with Neutrosophic Fuzzy Sets for Financial Applications in Discrete System. Spectrum of Engineering and Management Sciences, 2(1), 263-280. https://doi.org/10.31181/sems21202433a

Most read articles by the same author(s)

<< < 1 2 3 > >>