Fuzzy Differential Equations with Application in Electrical Circuit
محورهای موضوعی : Fuzzy Optimization and Modeling JournalNemat Taghi-Nezhad 1 , F. Amiri 2 , M. Shahini 3
1 - Department of Mathematics & Statistics, Gonbad Kavous University, Gonbad Kavous, Golestan, Iran.
2 - Department of Mathematics & Statistics, Gonbad Kavous University, Gonbad Kavous, Golestan, Iran.
3 - Department of Mathematics & Statistics, Gonbad Kavous University, Gonbad Kavous, Golestan, Iran
کلید واژه: Fuzzy set, First order differential equations, Fuzzy differential equations, Electrical circuit,
چکیده مقاله :
Today, the production and services field faces a change in the competition pattern among independent companies and supply chains. The food supply chain is among the complex supply chains with special characteristics that can toughly be adapted to general evaluation systems. The current research aims to determine the effective indicators for evaluating the performance of the sustainable food supply chain. This research is descriptive-survey in terms of method and practical in terms of purpose. In line with the research implementation, based on the study of the theoretical foundations and the background of the research conducted concerning the effective indicators in evaluating the performance of the sustainable supply chain, the effective criteria were extracted and given to 25 research experts in the form of a questionnaire. Finally, to investigate the relationships between these 26 basic criteria, another questionnaire was prepared and given to the research experts. The final factors were structured based on the answers received and using the methods of fuzzy cognitive mapping and fuzzy DEMATEL. Regarding the centrality criterion in the fuzzy cognitive mapping method, the factors "income distribution, sustainable investment, and average annual training time of employees" have the most centrality, so they were recognized as the main factors influencing the performance evaluation of the sustainable food supply chain.
Today, the production and services field faces a change in the competition pattern among independent companies and supply chains. The food supply chain is among the complex supply chains with special characteristics that can toughly be adapted to general evaluation systems. The current research aims to determine the effective indicators for evaluating the performance of the sustainable food supply chain. This research is descriptive-survey in terms of method and practical in terms of purpose. In line with the research implementation, based on the study of the theoretical foundations and the background of the research conducted concerning the effective indicators in evaluating the performance of the sustainable supply chain, the effective criteria were extracted and given to 25 research experts in the form of a questionnaire. Finally, to investigate the relationships between these 26 basic criteria, another questionnaire was prepared and given to the research experts. The final factors were structured based on the answers received and using the methods of fuzzy cognitive mapping and fuzzy DEMATEL. Regarding the centrality criterion in the fuzzy cognitive mapping method, the factors "income distribution, sustainable investment, and average annual training time of employees" have the most centrality, so they were recognized as the main factors influencing the performance evaluation of the sustainable food supply chain.
1. Abbasi, S.M.M., & Jalali, A. (2020) Some new performance definitions of second-order fuzzy systems. Soft Computing
24(6), 4109–4120.
2. Bede, B., & Gal, S.G. (2005) Generalizations of the differentiability of fuzzy-number valued functions with applications
to fuzzy differential equations. Fuzzy sets and systems 151(3), 581–599.
3. Bede, B., Rudas, I.J., & Bencsik, A.L. (2007) First order linear fuzzy differential equations under generalized
differentiability. Information sciences 177(7), 1648–1662.
4. Betounes, D. (2010) Differential Equations: Theory and Applications. Springer.
5. Bhaskar, T.G., Lakshmikantham, V., & Devi, V. (2004) Revisiting fuzzy differential equations. Nonlinear Analysis: Theory, Methods & Applications 58(3-4), 351–358.
6. Braun, M., & Golubitsky, M. (1983) Differential Equations and Their Applications vol. 2. Springer.
7. Buckley, J.J., & Feuring, T. (1999) Introduction to fuzzy partial differential equations. Fuzzy sets and systems 105(2), 241–248.
8. Buckley, J.J., & Feuring, T. (2001) Fuzzy initial value problem for nth-order linear differential equations. Fuzzy sets and systems 121(2), 247–255.
9. Chang, S.S., & Lofti Zadeh, A. (1972) On fuzzy mapping and control. IEEE transactions on systems, man, and
cybernetics 2(1), 30–34.
10. Chakraverty, S., Tapaswini, S., & Behera, D. (2016) Fuzzy Differential Equations and Applications for Engineers and Scientists. CRC Press.
11. Dubois, D., & Prade, H. (1982) Towards fuzzy differential calculus part 3: Differentiation. Fuzzy sets and systems 8(3), 225–233.
12. Goetschel Jr, R., & Voxman, W. (1983) Topological properties of fuzzy numbers. Fuzzy Sets and Systems 10(1-3),87–99.
13. Goetschel Jr, R., & Voxman, W. (1986) Elementary fuzzy calculus. Fuzzy sets and systems 18(1), 31–43.
14. Hukuhara, M. (1967) Integration des applications mesurables dont la valeur est un compact convexe. Funkcialaj Ekvacioj 10(3), 205–223.
15. Hullermeier, E. (1997) An approach to modelling and simulation of uncertain dynamical systems. International
Journal of Uncertainty, Fuzziness and Knowledge-Based Systems 5(02), 117–137.
16. Kaleva, O. (1987) Fuzzy differential equations. Fuzzy sets and systems 24(3), 301–317.
17. Mazandarani, M., & Pariz, N. (2018) Sub-optimal control of fuzzy linear dynamical systems under granular
differentiability concept. ISA transactions 76, 1–17.
18. Mazandarani, M., & Zhao, Y. (2018) Fuzzy bang-bang control problem under granular differentiability. Journal of the Franklin Institute 355(12), 4931–4951.
19. Najariyan, M., & Farahi, M.H. (2013) Optimal control of fuzzy linear controlled system with fuzzy initial conditions. Iranian Journal of Fuzzy Systems 10(3), 21–35.
20. Najariyan, M., & Farahi, M.H. (2014) A new approach for the optimal fuzzy linear time invariant controlled system with fuzzy coefficients. Journal of Computational and Applied Mathematics 259, 682–694.
21. Najariyan, M., & Farahi, M.H. (2015) A new approach for solving a class of fuzzy optimal control systems under generalized hukuhara differentiability. Journal of the Franklin Institute 352(5), 1836–1849.
22. Oberguggenberger, M., & Pittschmann, S. (1999) Differential equations with fuzzy parameters. Mathematical and Computer Modelling of Dynamical Systems 5(3), 181–202.
23. Parand, K., Dehghan, M., & Shahini, M. (2010) New method for solving a nonlinear ordinary differential equation. Nonlinear Functional Analysis Applications 2.
24. Parand, K., Shahini, M., & Dehghan, M. (2009) Rational Legendre pseudo spectral approach for solving nonlinear differential equations of lane–emden type. Journal of Computational Physics 228(23), 8830–8840.
25. Puri, M.L., & Ralescu, D.A. (1983) Differentials of fuzzy functions. Journal of Mathematical Analysis and Applications 91(2), 552–558.
26. Seikkala, S. (1987) On the fuzzy initial value problem. Fuzzy sets and systems 24(3), 319–330.
27. Taghi-Nezhad, N., & Babakordi, F. (2023) Fully hesitant parametric fuzzy equation. Soft Computing 27(16), 11099–11110.
28. Taghi-Nezhad, N.A., & Taleshian, F. (2023) A new approach for solving fuzzy single facility location problem under l1 norm. Fuzzy Optimization and Modeling Journal 4(2), 66–80.
29. Friedman, M., Ma, M., & Kandel, A. (1996) Fuzzy derivatives and fuzzy cauchy problems using lp metric. Fuzzy Logic Foundations and Industrial Applications, 57–72.