## $$\alpha$$-cut fuzzy control charts for linguistic data.(English)Zbl 1063.93003

In crisp control charts, all parameters should be well defined. Very often, such an assumption appears too rigid for real-life problems, especially when dealing with linguistic or imprecise data. To relax this rigidity, fuzzy methods are incorporated into control charts. Especially in the control charts for attributes, fuzzy methods should be used because the data are usually linguistic. The representation of linguistic variables as fuzzy sets, which can be manipulated with the rules of fuzzy arithmetics, retains the ambiguity and vagueness inherent in natural languages and improves the expressive ability of quality assurance inspectors.
In this article, the authors have defined the tightness of inspection by the use of $$\alpha$$-cut control charts.
The $$\alpha$$-level is determined according to the nature of the products and manufacturing processes.
For a toy factory, the $$\alpha$$-level might be accepted between 0.6 and 0.8, whereas it is between 0.95 and 1.0 for a motor factory. In the case of fuzzy data, the presented approach is more usable. It is flexible, not complex, easy in computation and similar to the crisp control charts for attributes. It has the ability of detecting control points at least as effectively as the other approaches do.

### MSC:

 93A30 Mathematical modelling of systems (MSC2010) 93C42 Fuzzy control/observation systems 62G10 Nonparametric hypothesis testing 90B25 Reliability, availability, maintenance, inspection in operations research 90B30 Production models
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