The (α, β)-cut control charts for process average based on the generalised intuitionistic fuzzy number

Intuitionistic fuzzy set is very useful in providing a flexible model to elaborate uncertainty and vagueness involved in decision-making. In this paper, we introduce the generalised trapezoidal intuitionistic fuzzy number (denoted by GtrIFNB) and then construct the (α, β)-cut X‾˜-R˜$\widetilde{\overline{X}} - \widetilde{R}$ and X‾˜-S˜$\widetilde{\overline{X}} - \widetilde{S}$ control charts for GTrIFNB. We also present fuzzy decisions for in-control and out-of-control of the process, in which membership and non-membership degrees of in-control and out-of-control states of the process mean are computed. We also compare X‾$\overline{X}$ control charts with the constructed control chart by bootstrapping for generalised intuitionistic fuzzy numbers. Finally, a real data application and a numerical example are given, showing flexibility and potentiality of the proposed method.