Skip to main content
SpringerLink
Log in

Generalized estimator for computation of population mean under neutrosophic ranked set technique: An application to solar energy data

  • Published:
Computational and Applied Mathematics Aims and scope Submit manuscript

Abstract

Classical statistics is used so far deals with crisp or determinate types of data only but it fails if there is uncertainty in data. Neutrosophic statistics is a generalization of classical as well as fuzzy statistics and the best substitute for classical as well as fuzzy statistics to deal with such uncertainty in data. This manuscript proposes a neutrosophic ranked set sampling (NeRSS) method and then a generalized estimator for estimating the population means under indeterminacy using neutrosophic subsidiary information. We have also given neutrosophic ranked set ratio and product-type estimators which are the same as the member class of estimators from the proposed estimator. The expressions for bias and mean square error (MSE) of the proposed generalized class of estimators have been derived to the first order of approximation and compare over its member estimators and unbiased estimator through MSE criterion. The proposed estimator has shown superiority over its member estimators, unbiased estimator, and over corresponding generalized estimator under neutrosophic simple random sampling (NeSRS). To show the performance of the proposed methodology, an empirical as well simulation study through R Studio have been carried out.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

Data availability

The author confirms that the data supporting the findings of this study are available within the article and can be seen in detail through Almaraashi (2017), Aslam, and Algarni (2020). The data can be accessed by anyone from these two references.

References

  • Albassam M, Aslam M (2021) Testing internal quality control of clinical laboratory data using paired-test under uncertainty. Biomed Res Int. https://doi.org/10.1155/2021/5527845

    Article  Google Scholar 

  • Alhabib R, Ranna MM, Farah H, Salama AA (2018) Some neutrosophic probability distributions. Neutrosophic Sets Syst 22:30–38

    Google Scholar 

  • Almaraashi M (2017) Short-term prediction of solar energy in Saudi Arabia using automated-design fuzzy logic systems. PLoS ONE 12(8):e0182429

    Google Scholar 

  • Almarashi AM, Aslam M (2021) Correlated proportions test under indeterminacy. J Math 2021:5

    Google Scholar 

  • Al-Marshadi AH, Aslam M (2021) Statistical analysis for food quality in the presence of Vague information. J Food Qual 2021:1

    Google Scholar 

  • Al-Omari AI, Bouza CN (2014) Review of ranked set sampling: modifications and applications. Investigación Oper 35(3):215–235

    MathSciNet  MATH  Google Scholar 

  • Al-Omari AI, Bouza CN (2015) Ratio estimators of the population mean with missing values using ranked set sampling. Environmetrics 26(2):67–76

    MathSciNet  Google Scholar 

  • Al-Saleh MF, Al-Omari AI (2002) Multistage ranked set sampling. J Stat Plann Inference 102(2):273–286

    MathSciNet  MATH  Google Scholar 

  • Al-Saleh MF, Al-Shrafat K (2001) Estimation of average milk yield using ranked set sampling. Environmetr J Int Environmetr Soc 12(4):395–399

    Google Scholar 

  • Arif OH, Aslam M (2021) A new sudden death chart for the Weibull distribution under complexity. Compl Intell Syst 7(4):2093–2101

    Google Scholar 

  • Aslam M (2019) Neutrosophic analysis of variance: application to university students. Compl Intell Syst 5:403–407. https://doi.org/10.1007/s40747-019-0107-2

    Article  Google Scholar 

  • Aslam M (2020) Monitoring the road traffic crashes using NEWMA chart and repetitive sampling. Int J Inj Contr Saf Promot 28(1):39–45. https://doi.org/10.1080/17457300.2020.1835990

    Article  Google Scholar 

  • Aslam M (2021a) A study on skewness and kurtosis estimators of wind speed distribution under indeterminacy. Theoret Appl Climatol 143(3):1227–1234

    Google Scholar 

  • Aslam M (2021b) Analyzing Gray cast iron data using a new Shapiro-Wilks test for normality under indeterminacy. Int J Cast Met Res 34(1):1–5

    Google Scholar 

  • Aslam M (2021c) Testing average wind speed using sampling plan for Weibull distribution under indeterminacy. Sci Rep 11(1):1–9

    Google Scholar 

  • Aslam M (2021d) Clinical laboratory medicine measurements correlation analysis under uncertainty. Ann Clin Biochem 58(4):377–383

    Google Scholar 

  • Aslam M (2021e) Radar data analysis in the presence of uncertainty. Eur J Remote Sens 54(1):140–144

    Google Scholar 

  • Aslam M (2021f) Chi-square test under indeterminacy: an application using pulse count data. BMC Med Res Methodol 21(1):1–5

    Google Scholar 

  • Aslam M (2021g) On Testing autocorrelation in metrology data under indeterminacy. Mapan 36(3):515–519

    Google Scholar 

  • Aslam M (2021h) Neutrosophic statistical test for counts in climatology. Sci Rep 11(1):1–5

    Google Scholar 

  • Aslam M, Albassam M (2021) Monitoring Road accidents and injuries using variance chart under resampling and having indeterminacy. Int J Environ Res Public Health 18(10):5247

    Google Scholar 

  • Aslam M, Algarni A (2020) Analyzing the solar energy data using a new Anderson-Darling test under indeterminacy. Int J Photoenergy. https://doi.org/10.1155/2020/6662389

    Article  Google Scholar 

  • Aslam M, Khan N (2021) Normality test of temperature in jeddah city using Cochran’s test under indeterminacy. Mapan 36(3):589–598

    Google Scholar 

  • Aslam M, Arif OH, Sherwani RAK (2020) New diagnosis test under the neutrosophic statistics: an application to diabetic patients. Biomed Res Int 00:7. https://doi.org/10.1155/2020/2086185

    Article  Google Scholar 

  • Aslam M, Shafqat A, Albassam M, Malela-Majika JC, Shongwe SC (2021a) A new CUSUM control chart under uncertainty with applications in petroleum and meteorology. PLoS ONE 16(2):e0246185

    Google Scholar 

  • Aslam M, Sherwani RAK, Saleem M (2021b) Vague data analysis using neutrosophic Jarque-Bera test. PLoS ONE 16(12):e0260689

    Google Scholar 

  • Aslam M, Saleem M (2021) Radar circular data analysis using a new watson’s goodness of test under complexity. J Sens 20:87

    Google Scholar 

  • Atanassov K (1986) Intuitionistic fuzzy sets. Fuzzy Sets Syst 20(1):87–96

    MATH  Google Scholar 

  • Atanassov K (1999) New operations defined over the intuitionistic fuzzy sets. Fuzzy Sets Syst 61(2):137–142

    MathSciNet  MATH  Google Scholar 

  • Bouza CN (2002) Ranked set sub-sampling the non-response strata for estimating the difference of means. Biomet J J Math Methods Biosci 44(7):903–915

    MathSciNet  MATH  Google Scholar 

  • Bouza CN (2008) Ranked set sampling for the product estimator. Rev Invest Oper 29(3):201–206

    MathSciNet  MATH  Google Scholar 

  • Chakraborty A, Mondal SP, Alam S, Dey A (2021) Classification of trapezoidal bipolar neutrosophic number, de-bipolarization technique and its execution in cloud service-based MCGDM problem. Compl Intell Syst 7(1):145–162

    Google Scholar 

  • Chen CT (2000) Extensions of the TOPSIS for group decision-making under fuzzy environment. Fuzzy Sets Syst 114(1):1–9

    MATH  Google Scholar 

  • Chen J, Ye J, Du S (2017a) Scale effect and anisotropy analyzed for neutrosophic numbers of rock joint roughness coefficient based on neutrosophic statistics. Symmetry 9(10):208

    Google Scholar 

  • Chen J, Ye J, Du S, Yong R (2017b) Expressions of rock joint roughness coefficient using neutrosophic interval statistical numbers. Symmetry 9(7):123

    Google Scholar 

  • Chen Z, Bai Z, Sinha B (2003) Ranked set sampling: theory and applications (Vol 176). Springer Science & Business Media, Berlin

    Google Scholar 

  • Cobby JM, Ridout MS, Bassett PJ, Large RV (1985) An investigation into the use of ranked set sampling on grass and grass-clover swards. Grass Forage Sci 40(3):257–263

    Google Scholar 

  • Cochran G (1940) Some properties of estimators based on sampling scheme with varying probabilities. Aust J Stat 17:22–28

    MathSciNet  Google Scholar 

  • Dell TR, Clutter JL (1972) Ranked set sampling theory with order statistics background. Biometrics 28:545–555

    MATH  Google Scholar 

  • Dong X, Cui L, Liu F (2012) A further study on reliable life estimation under ranked set sampling. Commun Stat Theory Methods 41(21):3888–3902

    MathSciNet  MATH  Google Scholar 

  • Evans MJ (1967) Application of ranked set sampling to regeneration, surveys in areas direct-seeded to long leaf pine, Master Thesis, school for Forestry and Wild-life Management, Louisiana state University, Baton Rouge, Louisiana

  • Jana C, Pal M (2019) A robust single-valued neutrosophic soft aggregation operators in multi-criteria decision making. Symmetry 11(1):110

    Google Scholar 

  • Kadilar C, Cingi H (2004) Ratio estimators in simple random sampling. Appl Math Comput 151:893–902

    MathSciNet  MATH  Google Scholar 

  • Kadilar C, Cingi H (2006) An improvement in estimating the population mean by using the correlation co-efficient. Hacettepe J Math Stat 35(1):103–109

    MathSciNet  MATH  Google Scholar 

  • Kadilar C, And UY, Cingi H (2009) Ratio estimator for the population mean using ranked set sampling. Stat Pap 50:301–309

    MathSciNet  MATH  Google Scholar 

  • Mandowara VL, Mehta N (2013) Efficient generalized ratio-product type estimators for finite population mean with ranked set sampling. Austr J Stat 42(3):137–148

    Google Scholar 

  • McIntyre GA (1952) A method for unbiased selective sampling using ranked sets. Crop Pasture Sci 3:385–390

    Google Scholar 

  • Mode NA, Conquest LL, Marker DA (2002) Incorporating prior knowledge in environmental sampling: ranked set sampling and other double sampling procedures. Environmetrics 13:513–521

    Google Scholar 

  • Murthy MN (1964) Product method of estimation. Sankhya Indian J Stat Ser A 1964:69–74

    MathSciNet  MATH  Google Scholar 

  • Nabeeh NA, Smarandache F, Abdel-Basset M, El-Ghareeb HA, Aboelfetouh A (2019) An integrated neutrosophic-TOPSIS approach and its application to personnel selection: A new trend in brain processing and analysis. IEEE Access 7:29734–29744

    Google Scholar 

  • Rao GS, Aslam M (2021) Inspection plan for COVID-19 patients for Weibull distribution using repetitive sampling under indeterminacy. BMC Med Res Methodol 21(1):1–15

    Google Scholar 

  • Saini M, Kumar A (2019) Ratio estimators using stratified random sampling and stratified ranked set sampling. Life Cycle Reliab Saf Eng 8(1):85–89

    MathSciNet  Google Scholar 

  • Samawi HM, Muttlak HA (1996) Estimation of ratio using rank set sampling. Biom J 38(6):753–764

    MathSciNet  MATH  Google Scholar 

  • Shalabh, Tsai JR (2017) Ratio and product methods of estimation of population mean in the presence of correlatedmeasurement errors. Commun Stat-Simul Comput 46(7):5566–5593

  • Singh A, Vishwakarma GK (2021) Improved predictive estimation for mean using the Searls technique under ranked set sampling. Commun Stat Theory Methods 50(9):2015–2038

    MathSciNet  MATH  Google Scholar 

  • Singh HP, Tailor R, Tailor R, Kakran MS (2004) An Improved Estimator of population mean using Power transformation. J Indian Soc Agric Stat 58(2):223–230

    MathSciNet  MATH  Google Scholar 

  • Sisodia BVS, Dwivedi VK (1981) A modified ratio estimator using co-efficient of variation of auxiliary variable. J Indian Soc Agric Stat 33(1):13–18

    Google Scholar 

  • Smarandache F (1998) Neutrosophy: neutrosophic probability, set, and logic: analytic synthesis & synthetic analysis. ProQuest Inf Learn 105:118–123

    MATH  Google Scholar 

  • Smarandache F (2005) Neutrosophic set a generalization of the intuitionistic fuzzy set. Int J Pure Appl Math 24(3):287

    MathSciNet  MATH  Google Scholar 

  • Smarandache F (2019) Neutrosophic set is a generalization of intuitionistic fuzzy set, inconsistent intuitionistic fuzzy set (picture fuzzy set, ternary fuzzy set), Pythagorean fuzzy set, spherical fuzzy set, and q-rung orthopair fuzzy set, while neutrosophication is a generalization of regret theory, grey system theory, and three-ways decision (revisited). J New Theory 29:1–31

    Google Scholar 

  • Smarandache F (1999) A unifying field in logics: neutrosophic logic. In: Philosophy (pp 1–141). American Research Press

  • Smarandache F (2001) A unifying field in logics: Neutrosophic logic, neutrosophic set, neutrosophic probability, and statistics. arXiv preprint math/0101228

  • Smarandache F (2010) Neutrosophic logic—a generalization of the intuitionistic fuzzy logic. Multispace Multi Struct Neutrosophic Transdiscipl 4:396

    Google Scholar 

  • Smarandache F (2013) Introduction to neutrosophic measure, neutrosophic integral, and neutrosophic probability. In: Infinite study

  • Smarandache F (2014) Introduction to neutrosophic statistics. In: Infinite Study

  • Stokes L (1977) Ranked set sampling with concomitant variables. Commun Stat Theory Methods 6:1207–1211

    Google Scholar 

  • Tahir Z, Khan H, Aslam M, Shabbir J, Mahmood Y, Smarandache F (2021) Neutrosophic ratio-type estimators for estimating the population mean. Compl Intell Syst 7:2991–3001. https://doi.org/10.1007/s40747-021-00439-1

    Article  Google Scholar 

  • Takahasi K, Wakimoto K (1968) On unbiased estimates of the population mean based on the sample stratified by means of ordering. Ann Inst Stat Math 20:1–31

    MATH  Google Scholar 

  • Tiwari N, Pandey GS (2013) Application of ranked set sampling design in environmental investigations for real data set. Thailand Stat 11(2):173–184

    MATH  Google Scholar 

  • Upadhyaya LN, Singh HP (1999) Use of transformed auxiliary variable in estimating the finite population mean. Biom J 41(5):627–636

    MathSciNet  MATH  Google Scholar 

  • Vishwakarma GK, Singh A, Singh N (2020) Calibration under measurement errors. J King Saud Univ Sci 32(7):2950–2961

    Google Scholar 

  • Wang YG, Yang YE, Milton DA (2009) Efficient designs for sampling and subsampling in fisheries research based on ranked sets. J Mar Sci 66:928–934

    Google Scholar 

  • Wang H, Smarandache F, Sunderraman R, Zhang YQ (2005) Interval neutrosophic sets and logic: theory and applications in computing: theory and applications in computing (Vol. 5). In: Infinite Study

  • Wolfe DA (2004) Ranked set sampling: an approach to more efficient data collection. Stat Sci 19:636–643

    MathSciNet  MATH  Google Scholar 

  • Yan Z, Tian B (2010) Ratio method to the mean estimation using co-efficient of skewness of auxiliary variable. In: ICICA 2010, Part II, CCIS, vol 106, pp 103–110

  • Zadeh LA (1965) Fuzzy sets. Inf Control 8(3):338–353

    MATH  Google Scholar 

  • Zadeh LA (1996) Fuzzy sets. In: Zadeh LA (ed) Fuzzy sets, fuzzy logic, and fuzzy systems: selected papers (pp 394–432)

Download references

Acknowledgements

Authors are heartily thankful to Editors and anonymous learned reviewers for their valuable comments which have made substantial improvements to bring the original manuscript to its present form.

Author information

Authors and Affiliations

  1. Department of Mathematics and Computing, Indian Institute of Technology (ISM) Dhanbad, Dhanbad, 826004, Jharkhand, India

    Gajendra K. Vishwakarma & Abhishek Singh

Authors
  1. Gajendra K. Vishwakarma
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Abhishek Singh
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Abhishek Singh.

Additional information

Communicated by Anibal Tavares de Azevedo.

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Appendices

Appendix A

A flow chart diagram for the proposed method of estimation.

figure a

Appendix B

See Figs. 1 and 2.

Fig. 1
figure 1

REs of the proposed estimators (Neutrosophic vs Classical)

Full size image
Fig. 2
figure 2

REs of the proposed estimators (Neutrosophic vs Classical), where \(T_{\left[ u \right]N} = t0\); \(T_{\left[ R \right]N} = tr\); \(T_{\left[ P \right]N} = tp\); \(T_{\left[ 1 \right]N} = t1\); \(T_{\left[ 2 \right]N} = t2\); \(T_{\left[ 3 \right]N} = t3\); \(T_{\left[ 4 \right]N} = t4\); \(T_{\left[ 5 \right]N} = t5\); \(T_{\left[ 6 \right]N} = t6\); \(T_{\left[ 7 \right]N} = t7\); \(T_{\left[ 8 \right]N} = t8\); \(T_{\left[ g \right]N} = tg\)

Full size image

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Vishwakarma, G.K., Singh, A. Generalized estimator for computation of population mean under neutrosophic ranked set technique: An application to solar energy data. Comp. Appl. Math. 41, 144 (2022). https://doi.org/10.1007/s40314-022-01820-7

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • DOI: https://doi.org/10.1007/s40314-022-01820-7

Keywords

Mathematics Subject Classification

Search

Navigation