Analyzing of process capability indices under uncertain information and hesitancy by using Pythagorean fuzzy sets

KAYA İ., Yalçın S.

Iranian Journal of Fuzzy Systems, vol.20, no.7, pp.85-99, 2023 (SCI-Expanded) identifier

  • Publication Type: Article / Article
  • Volume: 20 Issue: 7
  • Publication Date: 2023
  • Doi Number: 10.22111/ijfs.2023.7632
  • Journal Name: Iranian Journal of Fuzzy Systems
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Academic Search Premier, zbMATH
  • Page Numbers: pp.85-99
  • Keywords: Process capability analysis, process capability indices, Pythagorean fuzzy sets, the fuzzy set theory
  • Yıldız Technical University Affiliated: Yes


Process capability analysis (PCA) is a completely effective statistical tool for ability of a process to meet predetermined specification limits (SLs). Unfortunately, especially the real case problems include many uncertainties, it is one of the critical necessities to define the parameters of PCIs by using crisp numbers. So, the results obtained may be incorrect, if the PCIs are calculated without taking into account the uncertainty. To overcome this problem, the fuzzy set theory (FST) has been successfully used to design of PCA. We also know that fuzzy set extensions have an important role in modelling the case that include uncertainty, incomplete and inconsistent information and they are more powerful than traditional FST to model uncertainty. Defining of main parameters of PCIs such as SLs, mean (µ) and variance (σ2) by using the flexible of fuzzy set extensions rather than precise values due to uncertainty, time, cost, inspectors hesitancy and the results based on fuzzy sets for PCIs contain more, flexible and sensitive information. In this study, two of well-known PCIs called Cp and Cpk have been re-designed at the first time by using one of fuzzy set extensions named Pythagorean fuzzy sets (PFSs). Defining PCIs with more than one membership function instead of an only one membership function is enabling to evaluate the process more broadly more flexibility. For this aim, the main parameters of PCIs have been defined and analyzed by using PFSs. Finally, four new PCIs based on PFSs such as˜Csp, ˜Cspk,˜Cfp and˜Cfpk have been derived. The proposed new PCIs based on PFSs have been also applied on manufacturing process and capability for gears have been analyzed. It is shown that the flexibility of the PFSs on PCIs enables the PCA to give more realistic, more sensitive, and more comprehensive results.