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A neuro-fuzzy approach to compute the solution of a $Z$-numbers system with Trapezoidal fuzzy data | ||
| Journal of Mathematical Modeling | ||
| مقاله 10، دوره 12، شماره 4، اسفند 2024، صفحه 753-767 اصل مقاله (428.45 K) | ||
| نوع مقاله: Research Article | ||
| شناسه دیجیتال (DOI): 10.22124/jmm.2024.28020.2466 | ||
| نویسندگان | ||
| Seyed Mohammad Reza Hashemi Moosavi1؛ Mohammad Ali Fariborzi Araghi* 1؛ Shokrollah Ziari2 | ||
| 1Department of Mathematics, Central Tehran Branch, Islamic Azad University, Tehran, Iran | ||
| 2Department of Mathematics, South Tehran Branch, Islamic Azad University, Tehran, Iran | ||
| چکیده | ||
| Linear systems of equations with $Z$-numbers have recently attracted some interest. Some approaches have been developed for solving these systems. Since, there are many ambiguities and uncertainties in such issues, there is no analytic solution for these kinds of systems. Therefore, numerical schemes are usually used to estimate the solution of them. In this research, a computational scheme for solving linear systems involving trapezoidal $Z$-numbers is presented. The proposed approach is designed in such a way that it is firstly converted the $Z$-numbers coefficients to the corresponding fuzzy numbers and then using a ranking function, the fuzzy coefficients are converted to real coefficients. In this trend, after two stages, firstly, the original $Z$-numbers system becomes a fuzzy linear system and the fuzzy system is converted to a real system. Then, the obtained crisp linear system is solved based on the artificial neural network algorithm. Finally, two sample trapezoidal $Z$-numbers systems are solved based on the given approach to illustrate the process of the proposed algorithm. | ||
| کلیدواژه‌ها | ||
| $Z$-numbers؛ trapezoidal fuzzy number؛ weighted $Z$-number؛ linear system of equations؛ artificial neural networks؛ ranking function | ||
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آمار تعداد مشاهده مقاله: 75 تعداد دریافت فایل اصل مقاله: 58 |
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