جواب‌های مدل ریاضی عملکرد کبد انسان با داده‌های فازی تحت مفهوم مشتق‌پذیری هاکوهارای توسعه‌یافته

چه لابی, مهران

doi:10.22052/scj.2024.253988.1203

جواب‌های مدل ریاضی عملکرد کبد انسان با داده‌های فازی تحت مفهوم مشتق‌پذیری هاکوهارای توسعه‌یافته

نوع مقاله : مقاله پژوهشی

نویسنده

مهران چه لابی

گروه علوم پایه، واحد سوادکوه، دانشگاه آزاد اسلامی، سوادکوه، ایران.

10.22052/scj.2024.253988.1203

چکیده

یک مدل ریاضی ساده از عملکرد کبد انسان، دستگاهی خطی متشکل از دو معادله دیفرانسیل مرتبه اول است. از آنجا که داده‌های آزمایشگاهی و مقادیر بالینی از روی اندازه‌گیری و سنجش ثبت می‌شوند، از ویژگی عدم قطعیت و نادقیقی برخوردارند. لحاظ نمودن عدم قطعیت داده‌ها، منجر به تولید نتایج با کیفیت بیشتر می‌شود. منطق فازی یک ابزار توانا جهت برخورد با عدم قطعیت است که امکان مشاهده اثرات عدم قطعیت داده‌ها، در فرآیند حل مساله را فراهم می‌کند. در این مقاله، به مطالعه نظری و یافتن جواب‌های مدل مذکور همراه با داده‌های فازی، می‌پردازیم. برای این منظور، از مفهوم مشتق هاکوهارای توسعه‌یافته مربوط به تابع‌های فازی مقدار، استفاده می‌کنیم. ابتدا به تحلیل فرآیند حل مساله در حالت کاملا فازی، می‌پردازیم و شرایط کافی وجود جواب یکتا را به دست می‌آوریم. سپس، مساله را در دو حالت خاص مجزا، مورد مطالعه قرار می‌دهیم: (1) حالتی که ضرایب اعداد حقیقی باشند و مقدار اولیه فازی باشد و (2) حالتی که ضرایب اعداد فازی مثلثی متقارن و هم پهنا باشند و مقدار اولیه، عددی حقیقی باشد. در هر دو حالت، فرمول‌های جواب را به دست می‌آوریم و در انتها، با ارائه دو مثال، به تشریح و بکارگیری عملی نتایج، می‌پردازیم.

کلیدواژه‌ها

موضوعات

منطق فازی

عنوان مقاله [English]

Solutions to the mathematical model of human liver with fuzzy data under generalized Hukuhara differentiability

نویسنده [English]

Mehran Chehlabi

Department of Mathematics, Savadkooh Branch, Islamic Azad University, Savadkooh, Iran.

چکیده [English]

A simple mathematical model of human liver action is a linear system consisting of two first-order differential equations. Since laboratory data and clinical values are recorded through measurement and estimation, they have the characteristic of uncertainty and inaccuracy. Taking into account the uncertainty of the data leads to the production of higher-quality results. Fuzzy logic is a powerful tool for dealing with uncertainty, which provides the possibility of observing the effects of data uncertainty in the problem-solving process. In this paper, from a theoretical point of view, we study and obtain the solutions of the mentioned model along with fuzzy data. To this end, we use the generalized Hukuhara differentiability concept related to fuzzy-valued functions. First, we analyze the process of solving the problem in the fully fuzzy case and obtain the sufficient conditions for the existence of a unique solution. Next, we study the problem in two separate special cases: (1) the case where the coefficients are real numbers and the initial value is fuzzy, and (2) the case where the coefficients are symmetric triangular fuzzy numbers with the same width and the initial value is a real number. In both cases, we obtain the solution formulas and, at the end, by presenting two examples, we practically explain and apply the results.

کلیدواژه‌ها [English]

Fuzzy numbers
Fuzzy-valued functions
Fuzzy differential equations
Generalized Hukuhara differentiability

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