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International Journal of Neutrosophic Science
Volume 11 , Issue 1, PP: 09-21 , 2020 | Cite this article as | XML | Html |PDF

Title

Estimating the Ratio of a Crisp Variable and a Neutrosophic Variable

Authors Names :   Carlos N. Bouza-Herrera   1 *     Mir Subzar   2  

1  Affiliation :  Universidad de La Habana La Habana , Cuba

    Email :  bouza@matcom.uh.cu


2  Affiliation :   Jammu and Kashmir Institute of mathematical sciences, India

    Email :  subzarstat@gmail.com



Doi   :   https://doi.org/10.54216/IJNS.0110101

Received: May 03, 2020 Accepted: September 02, 2020

Abstract :

The estimation of the ratio of two means is studied within the neutrosophic theory framework. The variable of interest Y is measured in a sample of units and the auxiliary variable X is obtainable for all units using records  or predictions. They are correlated and the sample is selected using simple random sampling. The indeterminacy of the auxiliary variable is considered and is modeled as a neutrosophic variable.  The bias and variance of the proposed estimator are derived.

Keywords :

Ratio of Means , Neutrosophic Variable , Bias , Mean Squared Errors , Taylor Series.

References :

[1] Ajay, D., J. Aldring, S. Abirami, D. Jeni Seles Martina, “A SVTrN-number approach of multi-objective optimisation on the basis of simple ratio analysis based on MCDM method”International Journal of Neutrosophic Science Vol. 5, pp. 16-28, 2020 

[2] Alhabib , R., M. M. Ranna , H. Farah , A.A. Salama “Some Neutrosophic Probability Distributions”, Neutrosophic Sets and Systems, Vol. 22, pp 30-38, 2018. 

[3] Atanassov K. T. “Intuitionistic Fuzzy Sets, Physica–Verlag” , Heidelberg, New York, 1999. International Journal of Neutrosophic Science (IJNS) Vol. 11, No. 1 PP. 9-21, 2020 DOI: 10.5281/zenodo.4030309 21 

[4] Aslam, M. “A new sampling plan using neutrosophic process loss consideration”. Symmetry, Vol.10, 132, 2018. 

[5] Aslam, M. “Neutrosophic analysis of variance application to university students”. Complex & Intelligent Systems Vol. 5, pp 403–407 (2019a) 

[6] Aslam, M. “Control Chart for Variance Using Repetitive Sampling Under Neutrosophic Statistical Interval System”. IEEE Access, (2019b) 

[7] Aslam, M. “Design of the Bartlett and Hartley tests for homogeneity of variances under indeterminacy environment”. Journal of Taibah University for Science, Vol. 14 , pp 6–10, 2020. 

[8] Aslam A., O. H. Arif, 1 and R. A. K. Sherwani “New Diagnosis Test under the Neutrosophic Statistics An Application to Diabetic Patients”. BioMed Research International , 2020a, https//doi.org/10.1155/2020/2086185. 

[9] Aslam, A., O. H. Arif, and R. A. K. Sherwani “A new attribute sampling plan using neutrosophic statistical interval method”. BioMed Research International” Vol 2020, pp 1-6, 2020b 

[10] Bouza, C. N. and A. Alomari Ranked Set Sampling. 65 Years Improving The Accuracy In Data Gathering. Elsevier, ISBN 978-0-12-815044-3, 2019. 

[11] Cacuango Almeida, G.; J. Cadena Morillo ; M. Carrillo Palacio “Discernimiento e inferencia de la reinserción social en Ecuador, basada en conjuntos de números de 2-tuplas”. Inv. Operacional, Vol. 41, pp 637-646, 2020. 

[12] Crespo Berti L. A. “Application of the neutrosophic system to tax havens with a criminal approach”, International Journal of Neutrosophic Science , Vol. 5, pp. 91-106, 2020. 

[13] Hanafy, I.M. , A.A.Salama and K. Mahfouz “Correlation of Neutrosophic Data. International Refereed Journal of Engineering and Science”, Vol. 1, pp 39-43, 2012. 

[14] Hatip A. “The Special Neutrosophic Functions” International Journal of Neutrosophic Science , Vol. 4, pp. 104-116, 2020. 

[15] Patro S.K. and F. Smarandache “The Neutrosophic Statistical Distribution, More Problems, More Solutions “. Neutrosophic Sets and Systems, Vol. 12, pp 73-79, 2016. 

[16] Saqlain M. , A. Hamza and S. Farooq “Linear and Non-Linear Octagonal Neutrosophic Numbers: Its Representation, − and Application”, International Journal of Neutrosophic Science,Vol. 3, pp. 29- 43, 2020 

[17] Singh, S. “Advanced Sampling Theory with Applications. How Michael selected Amy”. Kluwer, Dordrecht 2003. 

[18] Smarandache, F. Neutrosophy “A New Branch of Philosophy”, in Multiple valued logic, An International Journal, Vol. 8, pp 297-384, 2002. 

[19] Smarandache F. “Neutrosophic set a generalization of the intuitionistic fuzzy sets” , In Proceedings of the third conference of the European Society for fuzzy logic and Technolgye, EUSFLAT, Septamper Zittau Geamany; Univ. of Applied Sciences at Zittau Goerlit Vol. 2, pp 141-146, 2003. 

[20] Smarandache, F. “Introduction to Neutrosophic Measure, Neutrosophic Integral, and Neutrosophic Probability”, Sitech-Education Publisher, Craiova – Columbus, 2013. 

[21] Smarandache, F. Introduction to Neutrosophic Statistics. Infinite Study. 2014. 

[22] Smarandache, F. “Neutrosophic Overset, Neutrosophic Underset, and Neutrosophic Offset Similarly for Neutrosophic Over-/Under-/Off- Logic, Probability, and Statistics”, Pons Editions Brussels, Belgium, 2016. 

[23] Subzar, M., C., N. Bouza, S. Maqbool, T A Raja and B. A. Para Robust ratio type estimators in simple random sampling using Huber m estimation Inv. Operacional Vol. 40, pp 201-209, 2019. 

[24] Schweizer P. “The Natural Bases of Neutrosophy”, International Journal of Neutrosophic Science , Vol. 9, pp. 100-109, 2020


Cite this Article as :
Carlos N. Bouza-Herrera , Mir Subzar, Estimating the Ratio of a Crisp Variable and a Neutrosophic Variable, International Journal of Neutrosophic Science, Vol. 11 , No. 1 , (2020) : 09-21 (Doi   :  https://doi.org/10.54216/IJNS.0110101)