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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.

PurposeInvestigation of the smoking model is important as it has a direct effect on human health. This paper focuses on the numerical analysis of the fractional order giving up smoking model. Nonetheless, due to observational or experimental errors, or any other circumstance, it may contain some incomplete information. Fuzzy sets can be used to deal with uncertainty. Yet, there may be some inconsistency in the membership as well. As a result, the primary goal of this proposed work is to numerically solve the model in a type-2 fuzzy environment.Design/methodology/approachTriangular perfect quasi type-2 fuzzy numbers (TPQT2FNs) are used to deal with the uncertainty in the model. In this work, concepts of r2-cut at r1-plane are used to model the problem's uncertain parameter. The Legendre wavelet method (LWM) is then utilised to solve the giving up smoking model in a type-2 fuzzy environment.FindingsLWM has been effectively employed in conjunction with the r2-cut at r1-plane notion of type-2 fuzzy sets to solve the model. The LWM has the advantage of converting the non-linear fractional order model into a set of non-linear algebraic equations. LWM scheme solutions are found to be well agreed with RK4 scheme solutions. The existence and uniqueness of the model's solution have also been demonstrated.Originality/valueTo deal with the uncertainty, type-2 fuzzy numbers are used. The use of LWM in a type-2 fuzzy uncertain environment to achieve the model's required solutions is quite fascinating, and this is the key focus of this work.

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