In the fuzzy arithmetic, the definitions of addition and multiplication of fuzzy numbers are based on Zadeh’s extension principle. From theoretical and practical points of view, this multiplication of fuzzy numbers owns several unnatural properties. Recently, to a More
In the fuzzy arithmetic, the definitions of addition and multiplication of fuzzy numbers are based on Zadeh’s extension principle. From theoretical and practical points of view, this multiplication of fuzzy numbers owns several unnatural properties. Recently, to avoid this shortcoming, a new multiplicative operation of product type is introduced, the so-called cross-product of fuzzy numbers. The main advantage is that this product preserves the shape of triangular or trapezoidal fuzzy numbers under multiplication and from computational point of view the cross product is more applicable than the usual product. The above mentioned properties motivate us to use the cross product in applications as a possible alternative of the product obtained by Zadeh's extension Principle. The aim of the present paper is to give an explicit formula for the cross product of triangular fuzzy numbers based on the scalar product of fuzzy numbers and then, explicit formulas for the length of cross product of triangular fuzzy numbers and fuzzy derivative of cross product of triangular fuzzy functions. As an application, we apply the cross product concept for the first order linear fuzzy differential equations with fuzzy variable coefficients and obtain its triangular solutions under generalized differentiability. Finally, some examples are given to illustrate the theoretical results.
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In this research, a numerical method by piecewise approximated method for solving fuzzy differential equations is introduced. In this method, the solution by piecewise fuzzy polynomial is present. The base of this method is using fuzzy Taylor expansion on initial value More
In this research, a numerical method by piecewise approximated method for solving fuzzy differential equations is introduced. In this method, the solution by piecewise fuzzy polynomial is present. The base of this method is using fuzzy Taylor expansion on initial value of fuzzy differential equations. The existence, uniqueness and convergence of the approximate solution are investigated. To show the advantage of method, this method is compared with the Euler method that was introduced in [۱], and it is shown this method is more accurate than Euler method for solving fuzzy differential equations under generalized differentiability.
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So far, many methods have been presented to solve the rst-order di erential equations. But, not many studies have been conducted for numerical solution of high-order fuzzy di erential equations. In this research, First, the equation by reducing time, we transform the rs More
So far, many methods have been presented to solve the rst-order di erential equations. But, not many studies have been conducted for numerical solution of high-order fuzzy di erential equations. In this research, First, the equation by reducing time, we transform the rst-order equation. Then we have applied Adams-Bashforth multi-step methods for the initial approximation of one order di erential equations. Finally, we examine the accuracy of method by presenting examples.
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در این مقاله، ما یک کلاس از مسائل مقداراولیه فازی مرتبه دوم که در حالت معمول، به معادلات دیفرانسیل کوشی-اویلر معروف هستند، را مطالعه می کنیم. این کار با مطالعه کردن ساختار تابع جواب در حالت معمول و فراهم کردن فضایی مطلوب از توابع مشتق پذیر توسعه یافته، آغاز می شود. در ا More
در این مقاله، ما یک کلاس از مسائل مقداراولیه فازی مرتبه دوم که در حالت معمول، به معادلات دیفرانسیل کوشی-اویلر معروف هستند، را مطالعه می کنیم. این کار با مطالعه کردن ساختار تابع جواب در حالت معمول و فراهم کردن فضایی مطلوب از توابع مشتق پذیر توسعه یافته، آغاز می شود. در ادامه، فرایند تولید و ساخت فرمول های جواب همراه با جزئیات بحث شده است. در نهایت، بوسیله حل چند مثال، فرمول های یافت شده، مورد استفاده قرار گرفته و تشریح شده اند.
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در این مقاله، یک روش عددی برای حل معادلات دیفرانسیل فازی هیبریدی مرتبه دوم با استفاده از بسط تیلور فازی تحت دیفرانسیل پذیری تعمیم یافته هاکوهارا و همچنین قضیه همگرایی ارائه شده است. همچنین کاربرد روش با حل چندین مثال عددی نشان داده شده است. نتایج نهایی نشان دهنده& More
در این مقاله، یک روش عددی برای حل معادلات دیفرانسیل فازی هیبریدی مرتبه دوم با استفاده از بسط تیلور فازی تحت دیفرانسیل پذیری تعمیم یافته هاکوهارا و همچنین قضیه همگرایی ارائه شده است. همچنین کاربرد روش با حل چندین مثال عددی نشان داده شده است. نتایج نهایی نشان دهنده جواب معادلات دیفرانسیل فازی هیبریدی مرتبه دوم است.
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