برآورد پارامترهای فازی از طریق شبکه‌های عصبی فازی با استفاده از داده‌های ذوزنقه‌ای

محورهای موضوعی : آمار

راضیه نادرخانی ¹ (گروه آمار، واحد علوم و تحقیقات ، دانشگاه آزاد اسلامی، تهران، ایران.)
محمد حسن بهزادی ² (دانشگاه آزاد اسلامی، واحد علوم وتحقیقات،گروه آمار، تهران، ایران)
طاهره رزاق نیا ³ (گروه آمار، واحد تهران شمال، دانشگاه آزاد اسلامی، تهران ، ایران)
رحمان فرنوش ⁴ (دانشکده ریاضی، دانشگاه علم و صنعت ایران، تهران، ایران)

تاریخ دریافت : 1399/02/10 تاریخ پذیرش : 1399/12/19 تاریخ انتشار : 1401/04/01

کلید واژه: Nonparametric Fuzzy Regression, Trapezoidal Fuzzy Numbers, Adaptive Fuzzy Neural Inference System (ANFIS), Leans squares error,

چکیده مقاله :

رگرسیون فازی یک مدل رگرسیونی تعمیم یافته است که نشان دهنده ارتباط متغیرهای مستقل و وابسته در محیط فازی می‌باشد. تجزیه و تحلیل رگرسیون خطی فازی تعمیم مدل‌های رگرسیونی است که با استفاده از تمامی داده‌ها بر اساس یک معیار خاص مناسب می‌باشد. در این مقاله یک سیستم استنتاج فازی عصبی تطبیقی (انفیس)برای تجزیه و تحلیل و پیش بینی یک تابع رگرسیون فازی غیر پارامتری با ورودی‌های غیر فازی و خروجی‌های فازی ذوزنقه‌ای متقارن استفاده می‌شود. بدین منظور، یک الگوریتم جدید هیبریدی پیشنهاد می‌شود که در آن حداقل مربعات فازی و برنامه‌نویسی خطی برای بهینه‌سازی وزن‌های ثانویه مورد استفاده قرار می‌گیرند. الگوریتم‌ها به روش اعتبارسنجی چند لایه برای تأیید اعتبار مدل ها اعمال میشود. به طور دقیق‌تر، دقت الگوریتم‌ها با شبیه‌سازی ها به طورکامل تایید می‌شود. در نهایت برای بررسی کارایی مدل از دو مثال شبیه سازی استفاده شده است که در آن، داده ها به صورت اعداد ذوزنقه ای تعریف شده اند و با آموزش آنها و مشخص کردن تعداد قوانین استفاده شده، پارامترهای مجهول برآورد شده اند.

چکیده انگلیسی:

Fuzzy regression is a generalized regression model that shows the relationship between independent and dependent variables in the fuzzy environment. Fuzzy linear regression analysis is the generalization of regression models that is appropriate using all data based on a specific criterion. This paper uses an adaptive neural fuzzy inference system to analyze and predict a non-parametric fuzzy regression function with non-fuzzy inputs and symmetrical trapezoidal fuzzy outputs. To this end, a new hybrid algorithm is proposed in which fuzzy minimum squares and linear programming are used to optimize secondary weights. Algorithms are applied by multi layer validation to validate models. More precisely, the accuracy of the algorithms with simulations is fully confirmed. Finally, two simulation examples were used to examine the efficiency of the model, in which the data were defined as trapezoidal numbers and by teaching them and specifying the number of rules used, the unknown parameters were estimated.

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