Type-2 fuzzy initial value problems under granular differentiability

Dhabaleswar Mohapatra and S. Chakraverty

Mathematics and Computers in Simulation (MATCOM), 2025, vol. 229, issue C, 435-447

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.

Keywords: Horizontal membership; Granular derivative; Triangularly perfect quasi type-2 fuzzy number; Type-2 fuzzy number valued function; Type-2 fuzzy initial value problem (search for similar items in EconPapers)
Date: 2025
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Persistent link: https://EconPapers.repec.org/RePEc:eee:matcom:v:229:y:2025:i:c:p:435-447

DOI: 10.1016/j.matcom.2024.10.002

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