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Interval Type-2 Fuzzy c-Control Charts: An Application in a Food Company
Volume 28, Issue 2 (2017), pp. 269–283
Pub. online: 1 January 2017      Type: Research Article      Open accessOpen Access
Received
1 November 2016
Accepted
1 May 2017
Published
1 January 2017

Abstract

Many papers exist on ordinary fuzzy control charts in literature in order to consider the vagueness and uncertainty in observation data. These are on both variable and attribute control charts. Several extensions of fuzzy sets have appeared in literature since ordinary fuzzy sets emerged. Type-2 fuzzy sets are one of these extensions. Type-2 fuzzy sets take into account the imprecision of membership functions in three dimensions. The aim of this paper is to develop interval type-2 fuzzy control charts for number of nonconformities, briefly c-control charts. In this paper, the theoretical structure of interval type-2 fuzzy c-control charts is proposed for the first time and the application is implemented in a food company.

References

 
Chen, L.-H., Huang, C.-H. (2016). Design of a fuzzy zone control chart for improving the process variation monitoring capability. Journal of Applied Sciences, 16, 201–208.
 
Chen, S.-M., Lee, L.-W. (2010). Fuzzy multiple attributes group decisions-making based on the interval type-2 TOPSIS method. Expert Systems with Applications, 37, 2790–2798.
 
El-Shal, S.M., Morris, A.S. (2000). A fuzzy rule-based algorithm to improve the performance of statistical process control in quality systems. Journal of Intelligent & Fuzzy Systems, 9, 207–223.
 
Erginel, N. (2008). Fuzzy individual and moving range control charts with α-cuts. Journal of Intelligent & Fuzzy Systems, 19, 373–383.
 
Erginel, N. (2014). Fuzzy rule based p-np control charts. Journal of Intelligent & Fuzzy Systems, 27, 159–171.
 
Gildeh, B.S., Shafiee, N. (2015). X-MR control chart for autocorrelated fuzzy data using Dp, q-distance. International Journal of Advanced Manufacturing Technology, 81, 1047–1054.
 
Gülbay, M., Kahraman, C. (2006a). Development of fuzzy process control charts and fuzzy unnatural pattern analyses. Computational Statistics and Data Analysis, 51, 434–451.
 
Gülbay, M., Kahraman, C. (2006b). An alternative approach to fuzzy control charts: Direct fuzzy approach. Information Sciences, 77(6), 1463–1480.
 
Gülbay, M., Kahraman, C., Ruan, D. (2004). α-cut fuzzy control charts for linguistic data. International Journal of Intelligent Systems, 19, 1173–1196.
 
Hou, S., Wang, H., Feng, S. (2016). Attribute control chart construction based on fuzzy score number. Symmetry, 8, 3–13.
 
Kahraman, C., Öztayşi, B., Sarı, İ.U., Turanoǧlu, E. (2014). Fuzzy analytic hierarchy process with interval type 2 fuzzy sets. Knowledge – Based Systems, 59, 48–57.
 
Kanagawa, A., Tamaki, F., Ohta, H. (1993). Control charts for process average and variability based on linguistic data. Intelligent Journal of Production Research, 31(4), 913–922.
 
Karnik, N.N., Mendel, J.M. (2001). Operations on type-2 fuzzy sets. Fuzzy Sets and Systems, 122, 327–348.
 
Kaya, İ., Erdoğan, M., Yıldız, C. (2017). Analysis and control of variability by using fuzzy individual control charts. Applied Soft Computing, 51, 370–381.
 
Kaya, İ., Kahraman, C. (2011). Process capability analyses based on fuzzy measurement and fuzzy control charts. Expert Systems with Applications, 38, 3172–3184.
 
Keshavarz Ghorabaee, M., Zavadskas, E.K., Amiri, M., Antucheviciene, J. (2016a). A new method of Assessment based on fuzzy ranking and aggregated weights (AFRAW) for MCDM problems under type-2 fuzzy environment. Economic Computation and Economic Cybernetics Studies and Research, 50(1), 39–68.
 
Keshavarz Ghorabaee, M., Zavadskas, E.K., Amiri, M., Antucheviciene, J. (2016b). Evaluation by an area-based method of ranking interval type-2 fuzzy sets (EAMRIT-2f) for multi-criteria group decision-making. Transformations in Business & Economics, 15(3), 76–95.
 
Khademi, M., Amırzadeh, V. (2014). Fuzzy rules for fuzzy $\bar{X}$ and R control charts. Iranian Journal of Fuzzy systems, 11(5), 55–56.
 
Mendel, J.M., John, R.I. (2002). Type-2 fuzzy sets made simple. IEE Transactions on Fuzzy Systems, 10(2), 117–127.
 
Mendel, J.M., John, R.I., Liu, F. (2006). Interval type-2 fuzzy logic systems made simple. IEE Transactions on Fuzzy Systems, 14(6), 808–821.
 
Mendel, J.M., Rajati, M.R., Sussner, P. (2016). On clarifying some definitions and notations used for type-2 fuzzy sets as well as some recommended changes. Information Sciences, 340–341, 337–345.
 
Mizumoto, M., Tanaka, K. (1976). Some properties of fuzzy sets of type-2. Information and Control, 31, 312–340.
 
Montgomery, D.C. (1991). Introduction to Statistical Quality Control. John Wiley & Sons.
 
Niewiadomski, A., Ochelsca, J., Szczepaniak, P.S. (2006). Interval-valued linguistic summaries of databases. Control and Cybernetic, 35(2), 415–443.
 
Poongodi, T., Muthulakshmi, S. (2015). Fuzzy control chart for number of customer of E${_{k}}$/M/1 queueing model. International Journal of Advanced Scientific and Technical Research, 3(5), 9–22.
 
Raz, T., Wang, J.H. (1990). Probabilistic and memberships approaches in the construction of control chart for linguistic data. Production Planning and Control, 1(3), 147–157.
 
Rowlands, H., Wang, L.R. (2000). An approach of fuzzy logic evaluation and control in SPC. Quality Reliability Engineering Intelligent, 16, 91–98.
 
Şentürk, S. (2010). Fuzzy regression control chart based on α-cut approximation. International Journal of Computational Intelligence Systems, 3(1), 123–140.
 
Şentürk, S., Erginel, N. (2009). Development of fuzzy $\tilde{\bar{X}}-\tilde{R}$ and $\tilde{\bar{X}}-\tilde{S}$ control charts using α-cuts. Information Sciences, 179, 1542–1551.
 
Şentürk, S., Erginel, N., Kaya, I., Kahraman, C. (2011). Design of fuzzy $\tilde{u}$ control chart. Journal of Multiple-Valued Logic and Soft Computing, 17(5–6), 459–473.
 
Tsaur, S.-H., Chang, T., Yen, C. (2002). The evaluation of airline service quality by fuzzy MCDM. Tourism Management, 23, 107–115.
 
Wang, D., Hyrnıewıcz, O. (2015). A fuzzy nonparametric shewhart charts based on the bootstrap approach. International Journal of Applied Mathematics and Computer Science, 25, 389–401.
 
Wang, J.H., Raz, T. (1990). On the construction of control charts using linguistic variables. Intelligent Journal of Production Research, 28, 477–487.
 
Wang, D., Li, P., Yasuda, M. (2014). Construction of fuzzy control charts based on weighted possibilisitic mean. Communication in Statistics-Theory and Methods, 43(3), 3186–3207.
 
Zadeh, L.A. (1965). Fuzzy sets. Information and Control, 8, 338–353.
 
Zadeh, L.A. (1975). The concept of a linguistic variable and its applications to approximate reasoning-I. Information Science, 8(3), 199–249.
 
Zarandi, M.H.F., Alaeddini, A., Turksen, I.B. (2008). A hybrid fuzzy adaptive sampling – run rules for Shewhart control charts. Information Sciences, 178, 1152–1170.

Biographies

Şentürk Sevil
sdeligoz@anadolu.edu.tr

S. Ṣentürk is an assoc. professor at the Department of Statistics, Anadolu University, Turkey. She received her PhD from Anadolu University, in 2006. She is interested in statistics, quality control, fuzzy sets, decision-making theories and multi-criteria analysis.

Antucheviciene Jurgita
jurgita.antucheviciene@vgtu.lt

J. Antucheviciene is a professor at the Department of Construction Technology and Management at Vilnius Gediminas Technical University, Lithuania. She received her PhD in 2005. Her research interests include multi-criteria analysis, decision-making theories and decision support systems, sustainable development, construction management and investment.


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© 2017 Vilnius University
Open access article under the CC BY license.

Keywords
fuzzy control charts interval type-2 fuzzy sets c-control charts nonconformity process control

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