Bayeğ, SelamiMert, RaziyeAkın, ÖmerKhaniyev, Tahir2025-01-062025-01-0620221432-764310.1007/s00500-021-06607-22-s2.0-85123239998https://doi.org/10.1007/s00500-021-06607-2https://hdl.handle.net/20.500.14669/1437In this paper, we have proposed a new representation of the triangular type-2 fuzzy numbers called the perfect triangular type-2 fuzzy numbers and defined their level sets by the (?, ?) -cut representation. With respect to this (?, ?) -cut representation, we have defined the algebraic operations for perfect triangular type-2 fuzzy numbers by using interval arithmetics. And then, we have proposed a method to find the solutions for second-order initial value problems with perfect triangular type-2 fuzzy initial conditions and forcing coefficients based on the Zadeh’s extension principle. Finally, we have used the proposed method for the mechanical vibration and RLC circuit models with perfect triangular type-2 fuzzy numbers. © 2021, The Author(s), under exclusive licence to Springer-Verlag GmbH Germany, part of Springer Nature.eninfo:eu-repo/semantics/closedAccess(?, ?) -cut representationMechanical vibrationPerfect triangular type-2 fuzzy numberRLC circuitType-2 fuzzy second order differential equationArticle16834Q1167126