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

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 GtrIFN_B) and then construct the (α, β)-cut $\tilde{\bar{X}}-\tilde{R}$ and $\tilde{\bar{X}}-\tilde{S}$ control charts for GTrIFN_B. 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 $\bar{X}$ 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.

KEYWORDS:

• (α, β)-cut control limit
• (α, β)-level fuzzy midrange
• bootstrap method
• control charts
• fuzzy control charts

Acknowledgments

The authors would like to thank the editor and the three referees for careful reading and comments which greatly improved the paper.

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Notes on contributors

Ali Shabani

Ali Shabani is a professor at Islamic Azad University, Iran.

Saralees Nadarajah

Saralees Nadarajah is a senior lecturer at University of Manchester, UK.

Mojtaba Alizadeh

Mojtaba Alizadehis a PhD student at Statistical Center of Iran.