International Journal of Nonlinear Analysis and Applications

Acceptance single sampling plan using generalized intuitionistic fuzzy number

Document Type : Research Paper

Authors

Department of Statistics, Qaemshahr Branch, Islamic Azad University, Qaemshahr, Iran

Abstract

In the present paper, the acceptance single sampling plan is developed by the generalized intuitionistic fuzzy numbers. The $\alpha_1$-cut and $\alpha_2$-cut sets of the generalized intuitionistic fuzzy numbers are applied to construct the acceptance single sampling plan. We also investigate the operating characteristic curve, where the parameter is considered the generalized intuitionistic fuzzy number. The $(\alpha_1,\alpha_2)$-cut set of generalized intuitionistic fuzzy operating characteristics is constructed. The bands are represented with upper and lower bounds instead of curves for operating characteristics and evaluated in detail. Finally, the numerical example is given to illustrate the proposed approach.

Keywords

[1] R. Afshari, B. Sadeghpour Gildeh and M. Sarmad, Fuzzy multiple deferred state attribute sampling plan in the presence of inspection errors, J. Intell. Fuzzy Syst. 33 (2017), no. 1, 503–514.
[2] R. Afshari, B. Sadeghpour Gildeh and M. Sarmad, Multiple deferred state sampling plan with fuzzy parameter, J. Intell. Fuzzy Syst. 20 (2018), 549–557.
[3] M. Aslam and C.-H. Jun, A double acceptance sampling plan for generalized log-logistic distributions with known shape parameters, J. Appl. Stat. 37 (2010), 405–414.
[4] M. Aslam, G.S. Rao and N. Khan, Single-stage and two-stage total failure-based group-sampling plans for the Weibull distribution under neutrosophic statistics, Complex Intell. Syst. 7 (2021), 891–900.
[5] K.T. Atanassov, Intuitionistic fuzzy sets, Fuzzy Sets Syst. 20 (1986), 87–96.
[6] E. Baloui Jamkhaneh, B. Sadeghpour Gildeh and G. Yari, Acceptance double sampling plan with fuzzy parameter, Proc. 11th Joint Conf. Inf. Sci. (JCIS 2008), Atlantis Press, 2008, pp. 1–9.
[7] E. Baloui Jamkhaneh, B. Sadeghpour Gildeh and G. Yari, Acceptance single sampling plan with fuzzy parameter with the using of Poisson distribution, Proc. World Acad. Sci. Eng. Technol. 49 (2009a), no. 1, 1017–1021.
[8] E. Baloui Jamkhaneh, B. Sadeghpour Gildeh and G. Yari, Preparation important criteria of rectifying inspection for single sampling plan with fuzzy parameter, Proc. World Acad. Sci. Eng. Technol. 38 (2009b), 956–960.
[9] E. Baloui Jamkhaneh, B. Sadeghpour Gildeh and G. Yari, Acceptance single sampling plan with fuzzy parameter, Iran. J. Fuzzy Syst. 8 (2011a), no. 2, 47–55.
[10] E. Baloui Jamkhaneh, B. Sadeghpour Gildeh and G. Yari, Inspection error and its effects on single sampling plans with fuzzy parameters, Struct. Multidiscipl. Optim. 43 (2011b), 555–560.
[11] E. Baloui Jamkhaneh and B. Sadeghpour Gildeh, Chain sampling plan using fuzzy probability theory, J. Appl. Sci. 11 (2011), 3830–3838.
[12] E. Baloui Jamkhaneh and B. Sadeghpour Gildeh, Sequential Sampling Plan with Fuzzy Parameters, Int. J. Oper. Res. 2 (2012), no. 1, 85–95.
[13] E. Baloui Jamkhaneh and S. Nadarajah, A new generalized intuitionistic fuzzy sets, Hacettepe J. Math. Stat. 44 (2015), no. 6, 1537–1551.
[14] E. Baloui Jamkhaneh, The operators over the GIFS, Int. J. Nonlinear Anal. Appl. 8 (2017), no. 1, 11–21.
[15] G. Isik and I. Kaya, Design and analysis of acceptance sampling plans based on intuitionistic fuzzy linguistic terms, Iran. J. Fuzzy Syst. 18 (2021), no. 6, 101–118.
[16] M.Z. Khan, M.F. Khan, M. Aslam and A.R. Mughal, Design of fuzzy sampling plan using the Birnbaum-Saunders distribution, Math. 7 (2019), 1–9.
[17] M.Z. Khan, M.F. Khan, M. Aslam and A.R. Mughal, Fuzzy acceptance sampling plan for transmuted Weibull distribution, Complex Intell. Syst. (2022), https://doi.org/10.1007/s40747-022-00725-6.
[18] D.C. Montgomery, Introduction to statistical quality control, 6th edn. Wiley, New York, 2009.
[19] F. Rasheed, S. Kousar, J. Shabbir, N. Kausar, D. Pamucar and Y.U. Gaba, Use of intuitionistic fuzzy numbersin survey sampling analysis with application in electronic data interchange, Complexity 2021 (2021), Article ID 9989477, 12 pages.
[20] Z. Roohanizadeh, E. Baloui Jamkhaneh and E. Deiri, A novel approach for analyzing system reliability using generalized intuitionistic fuzzy Pareto lifetime distribution, J. Math. Ext. 16 (2022a), no 10, 1–41.
[21] Z. Roohanizadeh, E. Baloui Jamkhaneh and E. Deiri, The reliability analysis based on the generalized intuitionistic fuzzy two-parameter Pareto distribution, Soft Comput. (2022b), https://doi.org/10.1007/s00500-022-07494-x
[22] A. Shabani and E. Baloui Jamkhaneh, A new generalized intuitionistic fuzzy number, J. Fuzzy Set Valued Anal. 2014 (2014), 1–10.
[23] E. Turanoglu, I. Kaya and C. Kahraman, Fuzzy acceptance sampling and characteristic curves, Int. J. Comput. Intell. Syst. 5 (2012), no. 1, 13–29.
International Journal of Nonlinear Analysis and Applications
Volume 14, Issue 6
June 2023
Pages 31-43
  • Receive Date: 20 June 2022
  • Accept Date: 25 September 2022