حل دستگاه معادلات چندجملهای فازی با استفاده از روش وو | ||
| پژوهش های نظری و کاربردی هوش ماشینی | ||
| دوره 2، شماره 1، شهریور 1403، صفحه 155-170 اصل مقاله (807.62 K) | ||
| نوع مقاله: مقاله پژوهشی | ||
| شناسه دیجیتال (DOI): 10.22034/abmir.2025.22565.1085 | ||
| نویسنده | ||
| حامد فراهانی* | ||
| دانشگاه دریانوردی و علوم دریایی چابهار، چابهار، ایران | ||
| چکیده | ||
| در این مقاله، روشی مبتنی بر الگوریتم وو برای تعیین راهحلهای واقعی دستگاههای معادلات چندجملهای فازی معرفی میشود. در ابتدا، -rبرشهای یک دستگاه معادلات چندجملهای فازی محاسبه شده و نمایش پارامتری برای این سیستم استخراج میگردد. سپس، الگوریتم وو به کار گرفته میشود تا نمایش پارامتری دستگاه معادلات چندجملهای فازی را به مجموعهای متناهی از مجموعههای مشخصه تبدیل کند. ارتباط قویای میان راهحلهای این مجموعههای مشخصه و راهحلهای دستگاهه چندجملهای وجود دارد. الگوریتم وو بهطور مؤثر دستگاههای چندجملهای را با ایجاد مجموعههای مشخصه به سیستمهای مثلثی تبدیل میکند، که این امر حل آنها را ساده و کارآمد میسازد. این روش نه تنها روابط میان متغیرها را روشن میکند، بلکه کارایی محاسباتی در حل معادلات چندجملهای را نیز افزایش میدهد. مزیت بزرگ روش پیشنهادی در این است که تمامی جوابهای فازی مسئله را بهطور همزمان به دست میآورد. در نهایت، مثالهای محاسباتی عملی متنوعی برای نشان دادن اثربخشی این روش ارائه شده است. | ||
| کلیدواژهها | ||
| مجموعههای مشخصه؛ سیستمهای مثلثی؛ جوابهای دقیق؛ تحلیل فازی؛ روشهای جبری | ||
| عنوان مقاله [English] | ||
| Solving Fuzzy Polynomial Equations Systems Using Wu’s Method | ||
| نویسندگان [English] | ||
| Hamed Farahani | ||
| Chabahar Maritime University, Chabahar, Iran | ||
| چکیده [English] | ||
| In this paper, we introduce a method grounded in Wu’s algorithm for determining real solutions of systems of fuzzy polynomial equations. We initially calculate the r-cuts of a fuzzy polynomial equations system and derive a parametric representation for the system. Wu’s algorithm is subsequently utilized to convert the parametric representation of the FPES into a finite set of characteristic sets. There is a strong connection between the solutions of these characteristic sets and the solutions of the polynomial system. Wu’s algorithm effectively transforms polynomial systems into triangular systems through the creation of characteristic sets, enabling straightforward and efficient solutions. This method not only clarifies the relationships between variables but also enhances computational efficiency in solving polynomial equations. The big advantage of the proposed method lies in the fact that it attains all fuzzy solutions of problem at a time. Finally, various practical computational examples are provided to illustrate the method’s effectiveness. | ||
| کلیدواژهها [English] | ||
| Characteristic sets, Triangular systems, Exact solutions, Fuzzy analysis, Algebraic methods | ||
| مراجع | ||
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