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International Journal of Neutrosophic Science
Volume 17 , Issue 2, PP: 96-109 , 2021 | Cite this article as | XML | Html |PDF


Neutrosophic Perspective of Neutrosophic Probability Distributions and its Application

Authors Names :   M. Lathamaheswari   1 *     Said Broumi   2     Florentin Smarandache   3     S. Sudha   4  

1  Affiliation :  Department of Mathematcs, Hindustan Institute of Technology & Science, Chennai-603 103, India

    Email :  lathamax@gmail.com

2  Affiliation :  Regional Center for the Professions of Education and Training, Casablanca-Settat, Morocco

    Email :  broumisaid78@gmail.com

3  Affiliation :  Laboratory of Information processing, Faculty of Science Ben M’Sik, University Hassan II, B.P 7955, Sidi Othman, Casablanca, Morocco

    Email :  broumisaid78@gmail.com

4  Affiliation :  Research Scholar, Department of Mathematcs, Hindustan Institute of Technology & Science, Chennai-603 103, India

    Email :  India. sudha.aarpitha@gmail.com

Doi   :   https://doi.org/10.54216/IJNS.170202

Received: October 15, 2021 Accepted: December 07, 2021

Abstract :

Neutrosophical probability is concerned with inequitable and defective topics and processes. This is a subset of Neutrosophic measures that includes a prediction of an event (as opposed to indeterminacy) as well as a prediction of some unpredictability. When there is no such thing as a non-stochastic occurrence, the Neutrosophic probability is the probability of determining a stochastic process. It is a generalisation of classical probability, which states that the probability of correctly predicting an occurrence is zero. Until now, neutrosophic probability distributions have been derived directly from conventional statistical distributions, with fewer contributions to the determination of the for statistical distribution. We introduced the Poission distribution as a limiting case of the Binomial distribution for the first time in this study, and we also proposed Neutrosophic Exponential Distribution and Uniform Distribution for the first time. With numerical examples, the validity and soundness of the proposed notions were also tested

Keywords :

Neutrosophic Statistics , Poisson , Uniform , Exponential , Probability distribution

References :

[1] Zadeh. L,Fuzzy Sets. Inform.Control 8,(1965).

[2] Atanassov.K, Intuitionistic fuzzy sets. In V.Sgurev, ed., ITKRS Session, Sofia, June 1983, Central Sci. and Techn. Library, Bulg. Academy of Sciences, (1984).

[3] Smarandache, F, Neutrosophy and Neutrosophic Logic, First International Conference on Neutrosophy, Neutrosophic Logic, Set Probability, and Statistics University of New Mexico, Gallup, NM 87301,USA,(2002).

[4] Smarandache, F.A Unifying Field in Logics: Neutrosophic Logic. Neutrosophy, Neutrosophic Set, Neutrosophic Probability,American Research Press, Rehoboth, NM,1999.

[5] Smarandache, F.Neutrosophic set a generalization of the intuitionistic fuzzy sets. Inter. J.Pure Appl. Math.,24,287-297,(2005).

[6] Smarandache.F, Introduction to Neutrosophic Measure, Integral, Probability. Sitech Education Publisher, (2015).

[7] Hanafy, I.M,Salama,A.A and Mahfouz, K,Correlation of Neutrosophic Data, International Refereed Journal of Engineering and Science (IRJES),1(2),PP39-33,2012.

[8] Hanafy,I.M.,Salama,A.A, and Mahfouz, K.M Neutrosophic Classical Events and its Probability. International Journal of Mathematics and Computer Applications Research (IJMCAR), 3(1),171-178,(2013).

[9] Salama, A.A, and Alblowi,S.A,Generalized Neutrosophic Set and Generalized Neutrosophic Sapace. Journal Computer Sci. Engineering, 2(7),129-132,(2012).

[10] Salama,A.A, and Alblowi, S.A,Neutrosophic Set and Neutrosophic Topological Spaces, ISOR J. Mathematics, 3(3),31-35,(2012).

[11] Mondal, K., Pramanik, S., & Smarandache, F. NN-harmonic mean aggregation operators-based MCGDM strategy in a Neutrosophic number environment. Axoims 2018,7.12: DOI:10.3390/axioms7010012.

[12] Pramanik,S., & Dey,P.P (2018). Bi-level linear programming problem with Neutrosophic numbers. Neutrosophic Sets and Systems, 21,110-121. Https://doi.org/10.5281/zenoda.1408663.

[13] Pramanik, S., Banerjee, D.(2018). Neutrosophic number goal programming for multi-objective linear programming problem inneutrosophic number environment. MOJ Current Research & Review, 1(3),135-141. DOI:10.15406/mojcrr.2018.01.0021.

[14] Banerjee, D.Pramanik,S (2018). Single-objective linear goal programming problem with Neutrosophic numbers. International, Journal of Engineering Science & Research Technology, 7(5),454-469.

[15] Florentin Smarandache: A Unifying Field in Logic,Neutorsophy, Neutrosophic Set,Neutrosophic Probability and Statistics (Sixth Edition). InfoLearn Quest, 1998-2007,156 p.http://fs.unm.edu/eBook-Neutrosophics6.pdf.

[16] Florentin Smarandache: Neurosophic Overset, Neutrosophic Underset, and Neutrosophic Offset.Similarly for Neutrosophic Over-/Under-/Off-Logic,Probability, and Statistics. Pons Editions, Brussels, 2016, 168p.http://fs.unm.edu/Neutosophic Overset UndersetOffset.pdf.

[17] Salama.A.A, Smarandache. F, Neutrosophic Crisp Set Theory. Education Publishing, Columbus, (2015).

[18] Salama. A.A, Smarandache. F, and Kroumov. V,Neutrosophic Crisp Sets & Neutrosophic Crisp Topological Spaces. Neutrosophic Sets and Systems, Vol. 2, pp.25-30, (2014).

[19] Smarandache.F, Neutorsophical statistics Sitech & Education publishing,(2014).

[20] Patro.S.K,Smarandache. F. The Neutrosophic Statistics Distribution, More Problems, More Solutions. Neutrosophic Sets and Systems, Vol.12,(2016).

[21] Rafif Alhabib, Moustafa Mzher Ranna et.al “Some Neutrosophic Probability Distributions” Neutrosophic Sets and Systems, Vol.22,(2018).

[22] S.K. Patr,F.Smarandache “The Neutrosophic Statistical Distribution, more problems, more solutions” Neutrosophic  Sets and Systems,Vol.12,(2016).

[23] Gupta.A.C.Kapoor.V.K.Mathematics Statistics, Schand publisher, India,(2009).

Cite this Article as :
M. Lathamaheswari , Said Broumi , Florentin Smarandache , S. Sudha, Neutrosophic Perspective of Neutrosophic Probability Distributions and its Application, International Journal of Neutrosophic Science, Vol. 17 , No. 2 , (2021) : 96-109 (Doi   :  https://doi.org/10.54216/IJNS.170202)