Solution of second order linear homogeneous fuzzy difference equation with constant coefficients by geometric approach
DOI:
https://doi.org/10.31181/jdaic10021122024aKeywords:
Second order linear homogeneous difference equation, Fuzzy difference equation, Geometric approachAbstract
In this article, we have solved an initial valued second order linear homogeneous fuzzy difference equation with constant coefficient using geometric approach. General fuzzy solution structures for the three cases are established depending on the auxiliary roots of the corresponding homogeneous difference equation. Finally, we have taken the numerical examples and solved them using the theoretical results and depicted the graphical scenarios to realize the deviation of the uncertain solution from the exact solution as well as the vagueness of the initial values.
Downloads
References
Abid, M., & Saqlain, M. (2024). Optimizing Diabetes Data Insights Through Kmapper-Based Topological Networks: A Decision Analytics Approach for Predictive and Prescriptive Modeling. Management Science Advances, 1(1), 1-19.
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.
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.
Ayub, S., Shabir, M., Riaz, M., Waqus, M., Bozanic, D., & Marinkovic, D. (2022). Linear Diophantine Fuzzy Rough Sets: A New Rough Set Approach with Decision Making. Symmetry, 14(3), 525.
Božanić, D., Pamučar, D., Badi, I., & Tešić, D. A decision support tool for oil spill response strategy selection: application of LBWA and Z MABAC methods. OPSEARCH 2023, 60(1), 24-58.
Chakraborty, J., Mukherjee, S., & Sahoo, L. (2024). An Alternative Approach for Enhanced Decision-Making using Fermatean Fuzzy Sets. Spectrum of Engineering and Management Sciences, 2(1), 135-150.
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.
Gasilov, N. A., Amrahov, Ş. E., Fatullayev, A. G., & Hashimoglu, I. F. (2015). Solution method for a boundary value problem with fuzzy forcing function. Information Sciences, 317, 349-368.
Gasilov, N. A., Hashimoglu, I. F., Amrahov, S. E., & Fatullayev, A. G. (2012). A new approach to non-homogeneous fuzzy initial value problem. Computer Modeling in Engineering & Sciences, 85(4), 367-378.
Gasilov, N., Amrahov, Ş. E., & Fatullayev, A. G. (2014). Solution of linear differential equations with fuzzy boundary values. Fuzzy Sets and Systems, 257, 169-183.
Gasilov, N., Amrahov, S. G., & Fatullayev, A. G. (2011). A geometric approach to solve fuzzy linear systems of differential equations. Applied Mathematics & Information Sciences, 5(3), 484-499.
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
Hussain, A., & Ullah, K. (2024). An Intelligent Decision Support System for Spherical Fuzzy Sugeno-Weber Aggregation Operators and Real-Life Applications. Spectrum of Mechanical Engineering and Operational Research, 1(1), 177-188.
Kamran, M., Ashraf, S., Kalim Khan, S., Hussain Khan, A., Zardi, H., & Mehmood, S. (2024). Integrated Decision-Making Framework for Hospital Development: A Single-Valued Neutrosophic Probabilistic Hesitant Fuzzy Approach With Innovative Aggregation Operators. Yugoslav Journal of Operations Research, 34(3), 515-550.
Khastan, A. (2018). Fuzzy logistic difference equation. Iranian Journal of Fuzzy Systems, 15(7), 55-66.
Kizielewicz, B., & Sałabun, W. (2024). SITW Method: A New Approach to Re-identifying Multi-criteria Weights in Complex Decision Analysis. Spectrum of Mechanical Engineering and Operational Research, 1(1), 215-226.
Lakshmikantham, V., & Vatsala, A. S. (2002). Basic theory of fuzzy difference equations. Journal of Difference Equations and Applications, 8(11), 957-968.
Mahmoodirad, A., & Niroomand, S. (2023). A heuristic approach for fuzzy fixed charge transportation problem. Journal of Decision Analytics and Intelligent Computing, 3(1), 139–147.
Mukherjee, A. K., Gazi, K. H., Salahshour, S., Ghosh, A., & Mondal, S. P. (2023). A brief analysis and interpretation on arithmetic operations of fuzzy numbers. Results in Control and Optimization, 13, 100312.
Özdağoğlu, A., Keleş, M. K., & Şenefe, M. (2024). Evaluation of banks in terms of customer preferences with fuzzy SWARA and fuzzy MOORA integrated approach. Journal of Decision Analytics and Intelligent Computing, 4(1), 216–232.
Pamučar D., Božanić D., Đorović B., & Milić A. (2011a). Modelling of the fuzzy logical system for offering support in making decisions within the engineering units of the Serbian army. International Journal of the Physical Sciences, 6(3), 592-609.
Pamučar D., Božanić D., & Đorović, B. (2011b). Fuzzy logic in decision making process in the Armed Forces of Serbia. Saarbrücken: LAP Lambert Academic Publishing & Co. KG.
Pamucar, D., & Ćirović, G. (2018). Vehicle route selection with an adaptive neuro fuzzy inference system in uncertainty conditions. Decision Making: Applications in Management and Engineering, 1(1), 13-37.
Pamucar, D., Deveci, M., Schitea, D., Erişkin, L., Iordache, M., & Iordache, I. (2020). Developing a novel fuzzy neutrosophic numbers based decision making analysis for prioritizing the energy storage technologies. International journal of hydrogen energy, 45(43), 23027-23047.
Pamucar, D., Žižović, M., & Đuričić, D. (2022). Modification of the CRITIC method using fuzzy rough numbers. Decision Making: Applications in Management and Engineering, 5(2), 362-371.
Riaz, M., Hashmi, M. R., Pamucar, D., & Chu, Y. M. (2021). Spherical linear Diophantine fuzzy sets with modeling uncertainties in MCDM. Computer Modeling in Engineering & Sciences, 126(3), 1125-1164.
Sarfraz, M. (2024). Interval-value Pythagorean Fuzzy Prioritized Aggregation Operators for Selecting an Eco-Friendly Transportation Mode Selection. Spectrum of Engineering and Management Sciences, 2(1), 172-201.
Singh, P., Gazi, K. H., Rahaman, M., Basuri, T., & Mondal, S. P. (2024a). Solution strategy and associated result for fuzzy Mellin transformation. Franklin Open, 7, 100112.
Singh, P., Gazi, K. H., Rahaman, M., Salahshour, S., & Mondal, S. P. (2024b). A fuzzy fractional power series approximation and Taylor expansion for solving fuzzy fractional differential equation. Decision Analytics Journal, 10, 100402.
Tešić, D. Z., Božanić, D. I., & Puška, A. (2024). Application of multi-criteria decision making for the selection of a location for crossing a water obstacle by fording in a defense operation. Vojnotehnički glasnik/Military Technical Courier, 72(3), 1120-1146.
Wang, Y., Hussain, A., Yin, S., Ullah, K., & Božanić, D. (2024), Decision-making for solar panel selection using Sugeno-Weber triangular norm-based on q-rung orthopair fuzzy information. Frontiers Energy Research, 11, 1293623.
Zadeh, L. A. (1965). Fuzzy sets. Information and Control, 8(3), 338-353.
Zadeh, L.A. (1972). A Rationale for Fuzzy Control. Journal of Dynamic Systems, Measurement and Control, 94(1), 3–4.
Zadeh, L.A. (1973). Outline of a new approach to the analysis of complex systems and decision processes. IEEE Transactions on Systems, Man, and Cybernetics, 3(1), 28–44.
All site content, except where otherwise noted, is licensed under the 