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

Ali Shabani, Saralees Nadarajah and Mojtaba Alizadeh

International Journal of Systems Science, 2018, vol. 49, issue 2, 392-406

Abstract: 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.

Date: 2018
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DOI: 10.1080/00207721.2017.1406550

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