Generalized Neutrosophic Sampling Strategy for Elevated estimation of Population Mean

SubhashKumarYadav; Florentin

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Generalized Neutrosophic Sampling Strategy for Elevated estimation of Population Mean

SubhashKumarYadav ^*

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Florentin Smarandache

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Abstract

One of the disadvantages of the point estimate in survey sampling is that it fluctuates from sample to sample due to sampling error, as the estimator only provides a point value for the parameter under discussion. The neutrosophic approach, pioneered by Florentin Smarandache, is an excellent tool for estimating the parameters under consideration in sampling theory since it yields interval estimates in which the parameter lies with a very high probability. As a result, the neutrosophic technique, which is a generalization of classical approach, is used to deal with ambiguous, indeterminate, and uncertain data. In this investigation, we suggest a new general family of ratio and exponential ratio type estimators for the elevated estimation of neutrosophic population mean of the primary variable using known neutrosophic auxiliary parameters. Up to the first order of approximation, the bias and Mean Squared Error (MSE) of the suggested estimators are computed. The neutrosophic optimum values of the characterizing constants are determined, as well as the minimum value of the neutrosophic MSE of the suggested estimator is obtained for these optimum values of the characterizing scalars. Because the minimum MSE of the classical estimators of population mean lies inside the estimated interval of the neutrosophic estimators, the neutrosophic estimators are better than the equivalent classical estimators. The empirical investigation, which used both real and simulated data sets, backs up the theoretical findings. For practical utility in various areas of applications, the estimator with the lowest MSE or highest Percentage Relative Efficiency (PRE) is recommended.

Keywords

Classical Ratio Estimators Neutrosophic Estimators Bias MSE PRE Simulation.

References

Ali, Z. and Mahmood, T. (2020). Complex neutrosophic generalized dice similarity measures and their application to decision making. CAAI Trans Intelligence Technol, 5, https://doi.org/10.1049/trit.2019.0084

Al-Omari, A.I. (2012). Ratio estimation of the population mean using auxiliary information in simple random sampling and median ranked set sampling, Statistics and Probability Letters, 82, 1883-18890.

Aslam, M. (2018). A new sampling plan using neutrosophic process loss consideration. Symmetry, 10(5), 132. https://doi.org/10.3390/sym10050132

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

Aslam, M. (2021a). 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

Aslam, M. (2021b). A new goodness of fit test in the presence of uncertain parameters, Complex Intell Syst, 7(1), 359-365. https://doi.org/10.1007/s40747-020-00214-8

Aslam, M. (2021c). A study on skewness and kurtosis estimators of wind speed distribution under indeterminacy, Theoret Appl Climatol, 143(3), 1227-1234. https://doi.org/10.1007/s00704-020-03509-5

Aslam, M. Al-Shareef, A. Khan, K. (2020). Monitoring the temperature through moving average control under uncertainty environment, Scientific Reports, 10, 12182, Doi.org/10.1038/s41598-020-69192-8

Bahl, S. and Tuteja, R.K. (1991). Ratio and product type exponential estimator, Information and Optimization Sciences, XII (I), 159-163.

Bellman R.E. and Zadeh L.A. (1970). Decision making in a fuzzy environment, Management Science, 17, 140-164.

Bouza-Herrera, C.N. Subzar, M. (2020). Estimating the Ratio of a Crisp Variable and a Neutrosophic Variable, International Journal of Neutrosophic Science, 11(1), 9-21.

Cekim, H.O. and Cingi, H. (2017). Some estimator types for population mean using linear transformation with the help of the minimum and maximum values of the auxiliary variable, Hacettepe Journal of Mathematics and Statistics, 46 (4), 685-694.

Chang, J-F., Lai, C-J., Wang, C-N., Hsueh, M-H and Nguyen, V.T. (2021). Fuzzy Optimization Model for Decision-Making in Supply Chain Management, Mathematics, 9, 312. DOI: 10.3390/math9040312

Chen, J. Ye, J. Du, S. (2017). Scale effect and anisotropy analyzed for neutrosophic numbers of rock joint roughness coefficient based on neutrosophic statistics. Symmetry, 9(10), 208. https://doi.org/10.3390/sym9100208

Chinnadurai, V. Sindhu, M.P. Bharathivelan, K. (2021). An Introduction to Neutro-Prime Topology and Decision Making Problem, Neutrosophic Sets and Systems, 41, 146-167.

Cochran, W. G. (1940)The Estimation of the Yields of the Cereal Experiments by Sampling for the Ratio of Grain to Total Produce. The Journal of Agric. Science, 30, 262-275.

Das, S. Kumar, S. Kar, S. Pal, T. (2019). Group decision making using neutrosophic soft matrix: An algorithmic approach, Journal of King Saud University-Computer and Information Sciences. 31, 459-468.

Grover, L.K. and Kaur, P. (2014). A generalized class of ratio type exponential estimators of population mean under linear transformation of auxiliary variable. Communications in Statistics-Simulation and Computation, 43, 1552-1574.

Jan, N. Zedam, L. Mahmood, T. Ullah, K. Ali, Z. (2019). Multiple attribute decision making method under linguistic cubic informa tion. Journal of Intell Fuzzy Syst, 36, 253-269. https://doi.org/10.3233/JIFS-181253

Jerajuddin, M. and Kishun, J. (2016). Modified Ratio Estimators for Population Mean Using Size of the Sample, Selected From Population, IJSRSET, 2(2), 10-16.

Kadilar, C. and Cingi, H. (2006). Improvement in estimating the population mean in simple random sampling, Applied Mathematics Letters, 19, 75-79.

Khan, H. Sanaullah, A. Amjad, M. Siddiqi, A. (2014). Improved exponential ratio type estimators for estimating population mean regarding full information in survey sampling, World Applied Science Journal, 26(5), 1897-1902.

Li D-F, Mahmood T, Ali Z, Dong Y (2020) Decision making based on interval-valued complex single-valued neutrosophic hesitant fuzzy generalized hybrid weighted averaging operators. J Intell Fuzzy Syst 38:4359–4401. https://doi.org/10.3233/JIFS-191005

Liu P, Ali Z, Mahmood T (2020) The distance measures and cross-entropy based on complex fuzzy sets and their application in decision making. J Intell Fuzzy Syst 39:1–24. https://doi.org/10.3233/JIFS-191718

Mohanta, K. Dey, A. Pal, A. (2021). A note on different types of product of neutrosophic graphs, Complex & Intelligent Systems, 7, 857-871. Doi.org/10.1007/s40747-020-00238-0

Rahman, A.U. Saeed, M. Dhital, A. (2021). Decision Making Application Based on Neutrosophic Parameterized Hypersoft Set Theory, Neutrosophic Sets and Systems, 41, 1-14.

Riaz, M. Hamid, M.T. Afzal, D. Pamucar, D. Chu, Y-M. (2021). Multi-criteria decision making in robotic agri-farming with q-rung orthopair m-polar fuzzy sets. PLoS ONE, 16(2), e0246485. https://doi. org/10.1371/journal.pone.0246485

Searls, D. T. (1964). The Utilization of a Known Coefficient of Variation in the Estimation Procedure, Journal of the American Statistical Association, 59, 1225-1226.

Sherwani, R.A.K. Shakeel, H. Saleem, M. Awan, W.B. Aslam, M. Farooq, M. (2021). A new neutrosophic sign test: An application to COVID-19 data, PLoS ONE, 16(8), e0255671. https://doi.org/10.1371/journal.pone.0255671

Singh, H.P. and Solanki, R.S. (2012). Improved estimation of population mean in simple random sampling using information on auxiliary attribute, Applied Mathematics and Computation, 218, 15, 7798-7812.

Singh, H.P. and Tailor, R. (2003). Use of known correlation coefficient in estimating the finite population mean, Statistics in Transition, 6, 4, 555-560.

Singh, R. Chauhan, P. Sawan, N. Smarandache, F. (2007). Auxiliary information and a priori values in construction of improved estimators: Infinite Study.

Sisodia, B.V.S. and Dwivedi, V.K. (1981). A modified ratio estimator using coefficient of variation of auxiliary variable, Journal of the Indian Society of Agricultural Statistics, 33, 13-18.

Smarandache, F. (1998). Neutrosophy: neutrosophic probability, set, and logic: analytic synthesis & synthetic analysis.: American Research Press.

Smarandache, F. (2014). Introduction to neutrosophic statistics: Sitech & Education Publishing

Subramani, J. and Kumarapandiyan, G. (2012). Estimation of Population Mean Using Coefficient of Variation and Median of an Auxiliary Variable, International Journal of Probability and Statistics, 1(4), 111-118.

Subzar, M. Maqbool, S. Raja, T.A. Pal, S.K. and Sharma, P. (2018). Efficient Estimators of Population Mean Using Auxiliary Information under Simple Random Sampling, Statistics in Transition new series, 19 (2), 219-238.

Tahir, Z. Khan, H. Aslam, M. Shabbir, J. Mahmood, Smarandache, F. (2021). Neutrosophic ratio-type estimators for estimating the population mean, Complex & Intelligent Systems, Doi.org/10.1007/s40747-021-00439-1

Upadhyaya, L. N. and Singh, H. P. (1999). Use of transformed auxiliary variable in estimating the finite population mean, Biometrical Journal, 41, 627-636.

Vishwakarma, G.K. and Kumar, M. (2015). A general family of dual to ratio-cum-product estimators of population mean in simple random sampling, Chilean Journal of Statistics, 6 (2), 69-79.

Xue, Y. and Deng, Y. (2021). Decision making under measure-based granular uncertainty with intuitionistic fuzzy sets. Appl Intell 51, 6224-6233. DOI: 10.1007/s10489-021-02216-6

Yadav, S.K. and Kadilar, C. (2013). Improved class of ratio and product estimators. Applied Mathematics and Computation, 219 (2)2, 10726-10731.

Yadav, S.K. and Zaman, T. (2021). Use of some conventional and non-conventional parameters for improving the efficiency of ratio-type estimators, Journal of Statistics and Management Systems, DOI: 10.1080/09720510.2020.1864939.

Yadav, S.K. Sharma, D.K. and Baghel, S. (2021). Upgraded family of estimators of population mean using known parameters of auxiliary and study variables. International Journal of Mathematical Modelling and Numerical Optimisation, 11(3), 252-274.

Yadav, S.K. Sharma, D.K. and Brown, K. (2020). New class of estimators of the population mean using the known population median of the study variable, International Journal of Mathematics in Operational Research, 16 (2), 179-201.

Yan, Z. and Tian, B. (2010). Ratio method to the mean estimation using coefficient of skewness of auxiliary variable. ICICA, Part II, CCIS, 106, 103-110.

Zaman, T. and Dunder, E. (2020). Proposing Novel Modified Ratio Estimators by Adding an Exponential Parameter, Lobachevskii Journal of Mathematics, 41 (3), 451-458.

Zulqarnain, R.M. Garg, H. Siddique, I. Ali, R. Alsubie, A. Hamadneh, N.N Khan, I. (2021). Algorithms for a Generalized Multipolar Neutrosophic Soft Set with Information Measures to Solve Medical Diagnoses and Decision-Making Problems, Journal of Mathematics, https://doi.org/10.1155/2021/6654657

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, SubhashKumarYadav, Smarandache, Florentin. "Generalized Neutrosophic Sampling Strategy for Elevated estimation of Population Mean." Journal of Neutrosophic and Fuzzy Systems, vol. , no. , , pp. . DOI:

, S., Smarandache, F. (). Generalized Neutrosophic Sampling Strategy for Elevated estimation of Population Mean. Journal of Neutrosophic and Fuzzy Systems, (), . DOI:

, SubhashKumarYadav, Smarandache, Florentin. "Generalized Neutrosophic Sampling Strategy for Elevated estimation of Population Mean." Journal of Neutrosophic and Fuzzy Systems , no. (): . DOI:

, S., Smarandache, F. () 'Generalized Neutrosophic Sampling Strategy for Elevated estimation of Population Mean', Journal of Neutrosophic and Fuzzy Systems, (), pp. . DOI:

S, Smarandache F. Generalized Neutrosophic Sampling Strategy for Elevated estimation of Population Mean. Journal of Neutrosophic and Fuzzy Systems. ;():. DOI:

S. , F. Smarandache, "Generalized Neutrosophic Sampling Strategy for Elevated estimation of Population Mean," Journal of Neutrosophic and Fuzzy Systems, vol. , no. , pp. , . DOI:

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