Control charts, used in many areas, are important for providing information about the status of the product control. Control charts allow us observation of abnormal conditions about a product and/or a process. These situations usually need to be interpreted by an expert. At this point, fuzzy numbers can be beneficial in reducing the differences between experts’ opinions and information loss. This is especially true for qualitative data, and for this reason, fuzzy numbers can be used to transform linguistic expressions into data. Although some recent studies have created control charts with fuzzy sets, most focused on type-1 fuzzy sets. Nevertheless, in real life, it may not always be possible to express these data as type-1 fuzzy sets; it may be more realistic to express some data as type-2 fuzzy sets. The purpose of this study is to create control charts using interval type-2 fuzzy numbers. Interval type-2 fuzzy control charts can be obtained by using different approaches, including defuzzification, centroid, type reduction and likelihood approaches. Comparisons are made between the interval type-2 fuzzy control charts and classical control charts. This study introduces likelihood method as a new approach to generate fuzzy control charts. The significant contribution of this paper to the relevant literature is that interval type-2 fuzzy set methods applied to different areas—such as likelihood, centroid, type reduction—are adapted to c-control charts for the first time.
This is a preview of subscription content, log in to check access.
The authors are grateful to Eskisehir Osmangazi University Bilimsel Arastirmalar Projesi (Scientific Research Project) whose funding is useful for our paper.
Compliance with ethical standards
Conflict of interest
The authors declare that they have no conflict of interest.
This article does not contain any studies with human participants or animals performed by any of the authors.
Alaeddini A, Ghanzanfari M, Nayeri MA (2009) A hybrid fuzzy-statistical clustering approach for estimating the time of changes in fixed and variable sampling control charts. Inf Sci 179:1769–1784CrossRefGoogle Scholar
Chen SM, Lee LW (2010) Fuzzy multiple attributes group-decision making based on the ranking values and the arithmetic operations of interval type-2 fuzzy sets. Expert Syst 37:824–833CrossRefGoogle Scholar
Coupland S, John R (2007) Geometric type-1 and type-2 fuzzy logic systems. IEEE Trans Fuzzy Syst 15:3–15CrossRefMATHGoogle Scholar
Ercan-Teksen H, Anagun AS (2017a) Type-2 fuzzy control charts using likelihood and defuzzification methods. Advances in fuzzy logic and technology proceedings of EUSFLAT-2017-10th conference of the European society for fuzzy logic and technology, September 11–15, 2017, Warsaw, PolandGoogle Scholar
Ercan-Teksen H, Anagun AS (2017b) Type-2 fuzzy control charts using ranking methods. In: The 5th international fuzzy systems symposium (FUZZYSS’17) October 14–15, 2017 Ankara, TurkeyGoogle Scholar
Mendel JM, John RIB (2002) Type-2 fuzzy sets made simple. IEEE Trans Fuzzy Syst 10:117–127CrossRefGoogle Scholar
Mendel JM, Liu F (2008) On new quasi-type-2 fuzzy logic systems. In: Proceedings of 2008 international conference on fuzzy systems (FUZZ 2008), WCCI 2008, Hong Kong, China, June 1–6Google Scholar
Mendel JM, Wu H (2007) New results about the centroid of an interval type-2 fuzzy set including the centroid of a fuzzy granule. Inf Sci 177:360–377MathSciNetCrossRefMATHGoogle Scholar
Montgomery DC (2009) Introduction to statistical quality control. Wiley, HobokenMATHGoogle Scholar
Raz T, Wang JH (1990) Probabilistic and membership approaches in the construction of control charts for linguistic data. Prod Plan Control 1:147–157CrossRefGoogle Scholar
Senvar O, Kahraman C (2014) Fuzzy process capability indices using Clement’s method for non-normal processes. J Mult Valued Logic Soft Comput 22:95–121MATHGoogle Scholar
Shewhart WA (1931) Economic control of quality of manufactured product. D.Van Nosrrand Inc., PrincetonGoogle Scholar
Shu MH, Wu HC (2011) Fuzzy X and R control charts: fuzzy dominance approach. Comput Ind Eng 613:676–686Google Scholar
Şentürk S, Antuchieviciene J (2017) Interval type-2 fuzzy c-control charts: an application in a food company. Informatica 28:269–283CrossRefGoogle Scholar
Şentürk S, Erginel N (2009) Development of fuzzy X–R and X–S control charts using \(\upalpha \)-cuts. Inf Sci 179:1542–1551CrossRefGoogle Scholar
Wang JH, Raz T (1990) On the construction of control charts using linguistic variables. Int J Prod Res 28:477–487CrossRefGoogle Scholar
Woodall WH, Tsui KL, Tucker GR (1997) A review of statistical and fuzzy quality control charts based on categorical data. In: Lenz HJ, Wilrich PT (eds) Frontiers in statistical quality control. vol 5. Physica, HeidelbergGoogle Scholar
Wu D, Mendel JM (2009) Enhanced Karnik–Mendel algorithms. IEEE Trans Fuzzy Syst 17:923–934CrossRefGoogle Scholar
Zadeh LA (1975) The concept of linguistic variable and its application to approximate reasoning. Inf Sci 8:338–353MathSciNetGoogle Scholar