Intuitionistic fuzzy X- R control chart based on IF-WABL defuzzification method

Abstract

Control charts are one of the most important tools used for process monitoring. Traditional control charts use crisp data, but in the real world the processes to be monitored have uncertainties, due to human subjectivity, measurement instruments among other factors. In this case Shewhart charts may not be adequate and fuzzy control charts should be used. In this paper X-R fuzzy control chart for triangular intuitionistic fuzzy numbers (TIFNs) using Intuitionistic Fuzzy - Weighted Averaging Based on Levels (IFWABL) defuzzification method is proposed. An interesting aspect in the defuzzification method that is considered, which differs from others, is the property of flexibility. The method is considered flexible because users can adjust the coefficients according to the problem being solved. Therefore, it is possible to obtain different defuzzification values for the same triangular intuitionistic fuzzy number. This is completely in accordance with the principles of fuzzy set theory. Intuitionistic fuzzy control charts are able to represent both uncertainty and hesitation present at various stages of the process. An illustrative example is developed in order to understand and show the use of the proposed control chart and finally the results are interpreted.