Type‐2 fuzzy linear system of equations with application in static problem of structures

Abstract

In this paper, a new method is proposed to solve type-2 fuzzy linear system of equations by converting the system into three interval linear systems and one crisp linear system of equations. In this work, three possible cases of type-2 fuzzy linear system is considered depending upon uncertainty (as type-2 fuzzy number) in right-hand side vector B, in co-efficient matrix Ã, and both in co-efficient matrix à as well as right-hand side vector B. Triangular perfect quasi type-2 fuzzy numbers are taken to propose the new method. The main significance of the proposed method is that it uses the arithmetic of interval theory, which makes this method easier to handle. Five numerical examples are solved to show the validation of the proposed technique. Further, two application problems related to 6-bar truss and rectangular sheet are encountered in type-2 fuzzy environment. Comparison among the results obtained by the present method and previously achieved results is also made in this work, which shows that the results are close enough and, in some cases, better bounds for the solution are obtained.

Legendre wavelets based approach for the solution of type-2 fuzzy uncertain smoking model of fractional order

“…Instead, few works have been conducted assuming impreciseness as type-2 (generalised type-2/interval type-2) and type-3 (interval type-3) fuzzy numbers (Mazandarani and Najariyan, 2014a; Tolga et al. , 2020; Mohapatra and Chakraverty, 2022, 2023; Castillo, 2012; Mohammadzadeh et al. , 2021).…”