Type-2 fuzzy initial value problems under granular differentiability

IF 5.4 3区材料科学 Q2 CHEMISTRY, PHYSICAL

ACS Applied Energy Materials Pub Date : 2024-10-05 DOI:10.1016/j.matcom.2024.10.002

Dhabaleswar Mohapatra , S. Chakraverty

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Abstract

This article investigates type-2 fuzzy initial value problems and introduces a novel strategy that capitalises on granular differentiability. Incorporating type-2 fuzzy numbers to depict the problem’s uncertainty may be advantageous from a practical standpoint. This work employs triangularly perfect quasi type-2 fuzzy numbers (TPQT2FNs) and defines the granular differentiability of TPQT2FN-valued functions. In addition, the solution approach for initial value problems with type-2 fuzzy initial conditions is discussed in the context of granular differentiability by transforming the type-2 fuzzy problem into a type-1 fuzzy problem using the lower membership function (LMF) and upper membership function (UMF) concepts. A couple of numerical examples are then examined to determine the applicability of the proposed method, and comparisons are made with existing type-2 fuzzy results and, in a special case, type-1 fuzzy results. In order to aid readers’ comprehension and study the behaviour of the numerical solution, three-dimensional graphical results are also shown.

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颗粒可微分性下的第二类模糊初值问题

本文研究了 2 型模糊初值问题，并介绍了一种利用粒度可微分性的新策略。从实用的角度来看，用 2 型模糊数来描述问题的不确定性可能是有利的。这项研究采用了三角完全准 2 型模糊数（TPQT2FN），并定义了 TPQT2FN 值函数的微分性。此外，通过使用下成员函数（LMF）和上成员函数（UMF）概念将 2 型模糊问题转化为 1 型模糊问题，在粒度可微分的背景下讨论了具有 2 型模糊初始条件的初值问题的求解方法。然后研究了几个数值示例，以确定所提方法的适用性，并与现有的 2 型模糊结果以及特殊情况下的 1 型模糊结果进行了比较。为了帮助读者理解和研究数值解决方案的行为，还展示了三维图形结果。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

ACS Applied Energy Materials Materials Science-Materials Chemistry

CiteScore

10.30

自引率

6.20%

发文量

1368

期刊介绍： ACS Applied Energy Materials is an interdisciplinary journal publishing original research covering all aspects of materials, engineering, chemistry, physics and biology relevant to energy conversion and storage. The journal is devoted to reports of new and original experimental and theoretical research of an applied nature that integrate knowledge in the areas of materials, engineering, physics, bioscience, and chemistry into important energy applications.