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La Estadística Neutrosófica es una generalización de la Estadística Clásica y de la Estadística de Intervalos
Mientras que la Estadística Clásica (EC) solo aborda datos determinados y métodos de inferencia determinados, la Estadística Neutrosófica (EN) aborda datos indeterminados, es decir, datos con cierto grado de indeterminación (poco claros, vagos, parcialmente desconocidos, contradictorios, incompletos, etc.) y métodos de inferencia indeterminados que también contienen grados de indeterminación (por ejemplo, en lugar de argumentos y valores precisos para las distribuciones de probabilidad, gráficos, diagramas, algoritmos, funciones, etc., se pueden encontrar argumentos y valores inexactos o ambiguos). Por ejemplo, el tamaño de la población o de la muestra podría no conocerse con exactitud debido a que algunos individuos pertenecen parcialmente a la población o muestra y parcialmente no, o a individuos cuya pertenencia se desconoce por completo. Además, existen individuos de la población o muestra cuyos datos podrían ser indeterminados. La Estadística Neutrosófica fue fundada por el Prof. Dr. Florentin Smarandache, de la Universidad de Nuevo México, Estados Unidos, en 1998, quien la desarrolló en 2014 con la introducción de la Estadística Descriptiva Neutrosófica (NDS). Posteriormente, el Prof. Dr. Muhammad Aslam, de la Universidad Rey Abdulaziz, Arabia Saudita, introdujo en 2018 la Estadística Inferencial Neutrosófica (NIS), la Estadística Aplicada Neutrosófica (NAS) y el Control de Calidad Estadístico Neutrosófico (NSQC). La Estadística Neutrosófica es también una generalización de la Estadística de Intervalos, debido, entre otras cosas, a que, mientras que la Estadística de Intervalos se basa en el Análisis de Intervalos, la Estadística Neutrosófica se basa en el Análisis de Conjuntos (es decir, todo tipo de conjuntos, no solo intervalos, por ejemplo, conjuntos discretos finitos). Además, al calcular la media, la varianza, la desviación estándar, las distribuciones de probabilidad, etc., en la estadística clásica y de intervalos, se asume automáticamente que todos los individuos pertenecen al 100% a la muestra o población respectiva. Sin embargo, en nuestro mundo, es frecuente encontrar individuos que solo pertenecen parcialmente, que no pertenecen parcialmente y que su pertenencia es parcialmente indeterminada. Los resultados de la estadística neutrosófica son más precisos que los de la estadística clásica y de intervalos, ya que, por ejemplo, los individuos que pertenecen solo parcialmente no tienen que considerarse al mismo nivel que aquellos que pertenecen completamente. Las distribuciones de probabilidad neutrosóficas pueden representarse mediante tres curvas: una que representa la probabilidad de que el evento ocurra, otra la probabilidad de que el evento no ocurra y una tercera la probabilidad indeterminada de que el evento ocurra o no. La estadística neutrosófica es más elástica que la estadística clásica. Si todos los datos y métodos de inferencia son determinados, la estadística neutrosófica coincide con la estadística clásica. Si todos los conjuntos utilizados son intervalos, y todos los individuos pertenecen al 100% de la muestra y la población, y solo existe una curva de distribución de probabilidad, entonces la Estadística Neutrosófica coincide con la Estadística de Intervalos. Sin embargo, dado que en nuestro mundo existen más datos indeterminados que determinados, se requieren más procedimientos estadísticos neutrosóficos que los clásicos. Por supuesto, los Conjuntos de Datos Neutrosóficos (donde los datos presentan cierto grado de indeterminación) se utilizan en la Estadística Neutrosófica. Los Números Neutrosóficos de la forma N = a + bI fueron definidos por W. B. Vasantha Kandasamy y F. Smarandache en 2003, y fueron interpretados como: "a" es la parte determinada del número N, y "bI" es la parte indeterminada del número N por F. Smarandache en 2014. Para la estadística neutrosófica, "I" es un subconjunto. La Estadística Neutrosófica es el análisis de eventos descritos por la Probabilidad Neutrosófica. La Probabilidad Neutrosófica es una generalización de la probabilidad clásica y la probabilidad imprecisa, donde la probabilidad de que ocurra un evento A es t% verdadera (donde t varía en el subconjunto T), i% indeterminada (donde i varía en el subconjunto I) y f% falsa (donde f varía en el subconjunto F). En la probabilidad clásica, la suma de todas las probabilidades espaciales es igual a 1, mientras que en la Probabilidad Neutrosófica es igual a 3.
En la Probabilidad Imprecisa: la probabilidad de un evento es un subconjunto T en [0, 1], no un número p en [0, 1]; se supone que el resto es el opuesto, el subconjunto F (también del intervalo unitario [0, 1]); no existe un subconjunto indeterminado I en la probabilidad imprecisa [véase B9].
La función que modela la probabilidad neutrosófica de una variable aleatoria x se denomina distribución neutrosófica: NP(x) = ( T(x), I(x), F(x) ), donde T(x) representa la probabilidad de que el valor x ocurra, F(x) representa la probabilidad de que el valor x no ocurra e I(x) representa la probabilidad indeterminada/desconocida del valor x. Comparación entre la estadística neutrosófica (EN) y la estadística de intervalos (IS) Mostramos que la EN y la EI son diferentes, y que en muchas aplicaciones la EN es más general que la EI. La EN no se limita únicamente al uso de números neutrosóficos en aplicaciones estadísticas, como algunos creen.
La Probabilidad Plitogénica y la Estadística Plitogénica son generalizaciones de la Probabilidad MultiVariada y la Estadística MultiVariada
El Análisis de Variantes Plitogénico (AVP) es una extensión del Análisis Multivariado clásico, donde se permiten datos o procedimientos indeterminados, denominados datos neutrosóficos y, respectivamente, procedimientos neutrosóficos.
Por lo tanto, el AVP aborda variables neutrosóficas indeterminadas, sub-sistemas neutrosóficos/indeterminados y sistemas-de-sistemas neutrosóficos/indeterminados en su conjunto.
Por lo tanto, el Análisis de Variantes Plitogénico estudia un sistema neutrosófico/indeterminado en su conjunto, caracterizado por numerosas variables neutrosóficas/indeterminadas (es decir, sub-sistemas neutrosóficos/indeterminados) y numerosas relaciones neutrosóficas/indeterminadas. Por lo tanto, se requieren numerosas mediciones y observaciones neutrosóficas. La probabilidad plitogénica de que ocurra un evento se compone de las probabilidades de que dicho evento ocurra con respecto a todas las variables aleatorias (parámetros) que lo determinan. La probabilidad plitogénica, basada en el análisis de variables plitogénicas, es una probabilidad multidimensional («plitho» significa «muchas», sinónimo de «multi»). Podríamos decir que es una probabilidad de sub-probabilidades, donde cada sub-probabilidad describe el comportamiento de una variable.
Suponemos que el evento que estudiamos es producido por una o más variables. Cada variable se representa mediante una función de distribución de probabilidad (Densidad) (PDF). Las subclases de la estadística plitogénica son: - Estadística de intervalos - Estadística neutrosófica - Estadística multivariante - Estadística neutrosófica plitogénica - Estadística indeterminada plitogénica - Estadística difusa intuicionista plitogénica - Estadística difusa de imagen plitogénica - Estadística difusa esférica plitogénica - y, en general: Estadística plitogénica (cualquier extensión difusa) - y Estadística híbrida plitogénica. La estadística plitogénica refinada es, de manera similar, la forma más general de estadística que estudia el análisis y las observaciones de los eventos descritos por la probabilidad refinada plitogénica. Referencia:
F. Smarandache, Neutrosophic Statistics vs. Interval Statistics, and Plithogenic Statistics
as the most general form of statistics http://fs.unm.edu/NS/NeutrosophicStatistics-vs-IntervalStatistics.pdf
Contribuciones Latinoamericanas a la Estadística Neutrosófica y Plitogénica
Referencias Libros B1. Florentin Smarandache: A Unifying Field in Logics: Neutrosophic Logic. Neutrosophy, Neutrosophic Set, Neutrosophic Probability and Statistics (sixth edition). InfoLearnQuest, 1998 - 2007, 156 p. http://fs.unm.edu/eBook-Neutrosophics6.pdf B2. W. B. Vasantha Kandasamy, Florentin Smarandache, Fuzzy Cognitive Maps and Neutrosophic Cognitive Maps, Xiquan, Phoenix, 211 p., 2003, http://fs.unm.edu/NCMs.pdf B3. Florentin Smarandache: Introduction to Neutrosophic Statistics. Sitech & Education Publishing, 2014, 124 p. http://fs.unm.edu/NeutrosophicStatistics.pdf B4. Florentin Smarandache: Neutrosophic Overset, Neutrosophic Underset, and Neutrosophic Offset. Similarly for Neutrosophic Over-/Under-/Off- Logic, Probability, and Statistics. Pons Editions, Brussels, 2016, 168 p. http://fs.unm.edu/NeutrosophicOversetUndersetOffset.pdf B5. Maikel Leyva Vázquez, Florentin Smarandache: Neutrosofía: Nuevos avances en el tratamiento de la incertidumbre. Pons Editions, Bruselas, 2018, 74 p. http://fs.unm.edu/NeutrosofiaNuevosAvances.pdf B6. Tatiana Veronica Gutierrez Quinonez, Fabian Andres Espinoza, Ingrid Kathyuska Giraldo, Angel Steven Asanza, Mauricio Daniel Montenegro: Estadistica y Probabilidades: Una Vision Neutrosofica desde el Aprendizaje Basado en Problemas en la Construccion del Conocimiento. Pons Editions, Bruselas, 2020, 131 p. http://fs.unm.edu/EstadisticaYProbabilidadNeutrosofica.pdf B7. F. Smarandache, Neutrosophic Statistics vs. Classical Statistics, section in Nidus Idearum / Superluminal Physics, Vol. 7, third edition, p. 117, 2019, http://fs.unm.edu/NidusIdearum7-ed3.pdf . B8. F. Smarandache, Nidus Idearum de Neutrosophia (Book Series), Editions Pons, Brussels, Belgium, Vols. 1-7, 2016-2019; http://fs.unm.edu/ScienceLibrary.htm B9. F. Smarandache, Introduction to Neutrosophic Measure, Neutrosophic
Integral, and Neutrosophic Probability, Sitech Publishing House, Craiova, 2013,
http://fs.unm.edu/NeutrosophicMeasureIntegralProbability.pdf
Tesis Doctoral PhD1. Rafif Alhabib: Formulation of the classical probability and some probability distributions due to neutrosophic logic and its impact on Decision Making. PhD Thesis in Arabic, held under the supervision of Dr. M. M. Ranna, Dr. H. Farah, Dr. A. A. Salama, Faculty of Science, Department of Mathematical Statistics, University of Aleppo, Syrian Arab Republic, 2019. http://fs.unm.edu/NS/FormulationOfTheClassicalProbability-PhDThesis.pdf Presentaciones Cientificas SP1. Muhammad Aslam, Testing wind speed using
Neutrosophic Weibull distribution,
Articulos 1. Florentin Smarandache: Operators on Single-Valued Neutrosophic Oversets, Neutrosophic Undersets, and Neutrosophic Offsets. Journal of Mathematics and Informatics, Vol. 5, 2016, 63-67. 2. Florentin Smarandache: Interval-Valued Neutrosophic Oversets, Neutrosophic Undersets, and Neutrosophic Offsets. International Journal of Science and Engineering Investigations, Vol. 5, issue 54, 2016, Paper ID: 55416-01, 4 p. 3. Nouran M. Radwan, M. Badr Senousy, Alaa El Din M. Riad: Approaches for Managing Uncertainty in Learning Management Systems. Egyptian Computer Science Journal, vol. 40, no. 2, May 2016, 10 p.
4. Muhammad
Aslam: A
Variable Acceptance Sampling Plan under Neutrosophic Statistical Interval Method. Symmetry 2019,
11, 114, DOI: 10.3390/sym11010114. 5. Soumyadip Dhar, Malay K. Kundu: Accurate segmentation of complex document image using digital shearlet transform with neutrosophic set as uncertainty handing tool. Applied Soft Computing, vol. 61, 2017, 412–426. 6. B. Kavitha, S. Karthikeyan, P. Sheeba Maybell: An ensemble design of intrusion system for handling uncertainty using Neutrosophic Logic Classifier. Knowlwdge-Based Systems, vol. 28, 2012, 88-96. 7. Muhammad Aslam: A new attribute sampling plan using neutrosophic statistical interval method. Complex & Intelligent Systems, 6 p. DOI: 10.1007/s40747-018-0088-6
8. Muhammad
Aslam, Nasrullah Khan, Mohammed Albassam: Control
Chart for Failure-Censored Reliability Tests under Uncertainty Environment. Symmetry 2018,
10, 690, DOI: 10.3390/sym10120690.
9. Muhammad
Aslam, Nasrullah Khan, Ali Hussein AL-Marshadi: Design
of Variable Sampling Plan for Pareto Distribution Using Neutrosophic Statistical
Interval Method. Symmetry 2019,
11, 80, DOI: 10.3390/sym11010080. 10. Jun Ye, Jiqian Chen, Rui Yong, Shigui Du: Expression and Analysis of Joint Roughness Coefficient Using Neutrosophic Number Functions. Information, Volume 8, 2017, 13 pages. 11. Jiqian Chen, Jun Ye, Shigui Du, Rui Yong: Expressions of Rock Joint Roughness Coefficient Using Neutrosophic Interval Statistical Numbers. Symmetry, Volume 9, 2017, 7 pages. 12. Adrian Rubio-Solis, George Panoutsos: Fuzzy Uncertainty Assessment in RBF Neural Networks using neutrosophic sets for Multiclass Classification. Presented at 2014 IEEE International Conference on Fuzzy Systems (FUZZ-IEEE) July 6-11, 2014, Beijing, China, 8 pages. 13. Pierpaolo D’Urso: Informational Paradigm, management of uncertainty and theoretical formalisms in the clustering framework: A review. Information Sciences, 400–401 (2017), pp. 30-62, 33 pages.
14. Muhammad
Aslam, Mohammed Albassam: Inspection
Plan Based on the Process Capability Index Using the Neutrosophic Statistical
Method. Mathematics 2019,
7, 631, DOI: 10.3390/math7070631. 15. Mirela Teodorescu, Florentin Smarandache, Daniela Gifu: Maintenance Operating System Uncertainties Approached through Neutrosophic Theory. 8 p.
16. Muhammad
Aslam, Rashad A. R. Bantan, Nasrullah Khan: Monitoring
the Process Based on Belief Statistic for Neutrosophic Gamma Distributed Product. Processes 2019,
7, 209, DOI: 10.3390/pr7040209. 17. Rafael Rojas-Gualdron, Florentin Smarandache, Carlos Diaz-Bohorquez: Application of The Neutrosophical Theory to Deal with Uncertainty in Supply Chain Risk Management. AGLALA 2019; 10 (2): 1-19. 18. Florentin Smarandache, Gheorghe Savoiu: Neutrosophic Index Numbers: Neutrosophic Logic Applied In The Statistical Indicators Theory. Critical Review, Vol. XI, 2015, pp. 67-100. 19. Murat Kirisci, Necip Simsek: Neutrosophic normed spaces and statistical convergence. Journal of Analysis, 11 April 2020, DOI: 10.1007/s41478-020-00234-0. 20. S.K. Patro: The Neutrosophic Statistical Distribution: More Problems, More Solutions. 17 p. 21. Deepesh Kunwar, Jayant Singh, Florentin Smarandache: Neutrosophic statistical evaluation of migration with particular reference to Jaipur. Octogon Mathematical Magazine, vol. 26, no. 2, October 2018, 560-568. 22. Deepesh Kunwar, Jayant Singh, Florentin Smarandache: Neutrosophic statistical techniques to find migration pattern in Jaipur. Octogon Mathematical Magazine, vol. 26, no. 2, October 2018, 583-592. 23. Muhammad Aslam, Osama H. Arif, Rehan Ahmad Khan Sherwani: New Diagnosis Test under the Neutrosophic Statistics: An Application to Diabetic Patients. Hindawi, BioMed Research International, Volume 2020, Article ID 2086185, 7 pages; DOI: 10.1155/2020/2086185. 24. Jose L. Salmeron, Florentin Smarandache: Processing Uncertainty and Indeterminacy in Information Systems success mapping. 13 p., arXiv:cs/0512047v2. 25. Wenzhong Jiang, Jun Ye, Wenhua Cui: Scale Effect and Anisotropic Analysis of Rock Joint Roughness Coefficient Neutrosophic Interval Statistical Numbers Based on Neutrosophic Statistics. Journal of Soft Computing in Civil Engineering, 2-4 / 2018, 62-71; DOI: 10.5281/zenodo.3130240.
26. Muhammad
Aslam, P. Jeyadurga, Saminathan Balamurali, Ali Hussein Al-Marshadi: Time-Truncated
Group Plan under aWeibull Distribution based on Neutrosophic Statistics. Mathematics 2019,
7, 905; DOI: 10.3390/math7100905 27. A.A. Salama, M. Elsayed Wahed, Eman Yousif: A Multi-objective Transportation Data Problems and their Based on Fuzzy Random Variables. Neutrosophic Knowledge, vol. 1, 2020, 41-53; DOI: 10.5281/zenodo.4269558. 28. Philippe Schweizer: Uncertainty: two probabilities for the three states of neutrosophy. International Journal of Neutrosophic Science (IJNS), Volume 2, Issue 1, 2020, 18-26; DOI: 10.5281/zenodo.3989350.
29. Carlos
N. Bouza-Herrera, Mir Subzar: Estimating
the Ratio of a Crisp Variable and a Neutrosophic Variable. International
Journal of Neutrosophic Science (IJNS), Volume 11, Issue 1, 2020, 9-21; DOI:
10.5281/zenodo.4275712 30. Angel Carlos Yumar Carralero, Darvin Manuel Ramirez Guerra, Giorver Perez Iribar: Analisis estadistico neutrosofico en la aplicacion de ejercicios fisicos en la rehabilitacion del adulto mayor con gonartrosis. Neutrosophic Computing and Machine Learning, Vol. 13, 1-9, 2020; DOI: https://zenodo.org/record/3901770. 31. Alexandra Dolores Molina Manzo, Rosa Leonor Maldonado Manzano, Blanca Esmeralda Brito Herrera, Johanna Irene Escobar Jara: Analisis estadistico neutrosofico de la incidencia del voto facultativo de los jovenes entre 16 y 18 anos en el proceso electoral del Ecuador. Neutrosophic Computing and Machine Learning, Vol. 11, 9-14, 2020; DOI: https://zenodo.org/record/3474439. 32. Johana Cristina Sierra Morán, Jenny Fernanda Enríquez Chuga, Wilmer Medardo Arias Collaguazo And Carlos Wilman Maldonado Gudiño:Neutrosophic statistics applied to the analysis of socially responsible participation in the community , Neutrosophic Sets and Systems, vol. 26, 2019, pp. 19 -28. DOI: 10.5281/zenodo.3244232 33. Paúl Alejandro Centeno Maldonado, Yusmany Puertas Martinez, Gabriela Stephanie Escobar Valverde, and Juan Danilo Inca Erazo: Neutrosophic statistics methods applied to demonstrate the extra-contractual liability of the state from the Administrative Organic Code, Neutrosophic Sets and Systems, vol. 26, 2019, pp. 29-34. DOI: 10.5281/zenodo.3244262 34. S. K. Patro, F. Smarandache: The Neutrosophic Statistical Distribution - More Problems, More Solutions, Neutrosophic Sets and Systems, vol. 12, 2016, pp. 73-79. doi.org/10.5281/zenodo.571153 35. Lilia Esther Valencia Cruzaty, Mariela Reyes Tomalá, Carlos Manuel Castillo Gallo and Florentin Smarandache, A Neutrosophic Statistic Method to PredictTax Time Series in Ecuador, Neutrosophic Sets and Systems, vol. 34, 2020, pp. 33-39. DOI: 10.5281/zenodo.3843289; http://fs.unm.edu/NSS/NeutrosophicStatisticMethod.pdf
36. Somen Debnath: Neutrosophication
of statistical data in a study to assess the knowledge, attitude and symptoms
on reproductive tract infection among women. Journal
of Fuzzy Extension & Applications (JFEA),
Volume 2, Issue 1, Winter 2021, 33-40; DOI: 10.22105/JFEA.2021.272508.1073. 37. Muhammad Aslam, Rashad A.R. Bantan, Nasrullah Khan: Design of tests for mean and variance under complexity-an application to rock measurement data. Elsevier: Measurement, Volume 177, June 2021, 109312; DOI: 10.1016/j.measurement.2021.109312. 38. O.H. Arif, Muhammad Aslam: A new sudden death chart for the Weibull distribution under complexity. Springer: Complex & Intelligent Systems (2021); DOI: 10.1007/s40747-021-00316-x. 39. Nasrullah Khan, Muhammad Aslam, Asma Arshad, Ambreen Shafqat: Tracking Temperature Under Uncertainty Using EWMA-MA Control Chart. Springer: Journal of Metrology Society of India (2021); DOI: 10.1007/s12647-021-00436-2. 40. Muhammad Aslam: Analyzing wind power data using analysis of means under neutrosophic statistics. Springer: Soft Computing (2021); DOI: 10.1007/s00500-021-05661-0. 41. Muhammad Aslam: On Testing Autocorrelation in Metrology Data Under Indeterminacy. Springer: Journal of Metrology Society of India (2021); DOI: 10.1007/s12647-021-00429-1. 42. Muhammad Aslam, Nasrullah Khan: Normality Test of Temperature in Jeddah City Using Cochran’s Test Under Indeterminacy. Springer: Journal of Metrology Society of India (2021); DOI: 10.1007/s12647-020-00428-8. 43. Muhammad Aslam, Gadde Srinivasa Rao, Nasrullah Khan, Liaquat Ahmad: Two-stage sampling plan using process loss index under neutrosophic statistics. Taylor&Francis: Communications in Statistics - Theory and Methods (2020); DOI: 10.1080/03610918.2019.1702212. 44. Ali Hussein Al-Marshadi, Ambreen Shafqat, Muhammad Aslam, Abdullah Alharbey: Performance of a New Time-Truncated Control Chart for Weibull Distribution Under Uncertainty. Atlantis Press: International Journal of Computational Intelligence Systems, Volume 14, Issue 1, 2021, 1256 - 1262; DOI: 10.2991/ijcis.d.210331.001. 45. Muhammad Aslam: Testing average wind speed using sampling plan for Weibull distribution under indeterminacy. Nature: Scientific Reports, 11, Article number: 7532 (2021); DOI: 10.1038/s41598-021-87136-8. 46. Muhammad Aslam, G. Srinivasa Rao, Nasrullah Khan: Single-stage and two-stage total failure-based group-sampling plans for the Weibull distribution under neutrosophic statistics. Springer: Complex & Intelligent Systems, 7, 891–900 (2021); DOI: 10.1007/s40747-020-00253-1. 47. Muhammad Aslam, G. Srinivasa Rao, Ambreen Shafqat, Liaquat Ahmad, Rehan Ahmad Khan Sherwani: Monitoring circuit boards products in the presence of indeterminacy. Elsevier: Measurement, Volume 168, 15 January 2021, 108404; DOI: 10.1016/j.measurement.2020.108404. 48. Mohammed Albassam, Nasrullah Khan, Muhammad Aslam: Neutrosophic D’Agostino Test of Normality: An Application to Water Data. Hindawi: Journal of Mathematics - Theory, Algorithms, and Applications within Neutrosophic Modelling and Optimisation, 2021, Article ID 5582102, 5 pages; DOI: 10.1155/2021/5582102. 49. Mohammed Albassam: Radar data analysis in the presence of uncertainty. Taylor&Francis: European Journal of Remote Sensing, 54:1, 140-144, 2021; DOI: 10.1080/22797254.2021.1886597. 50. Muhammad Aslam: A new goodness of fit test in the presence of uncertain parameters. Springer: Complex & Intelligent Systems, 7, 359–365, 2021; DOI: 10.1007/s40747-020-00214-8. 51. Abdullah M. Almarashi, Muhammad Aslam: Process Monitoring for Gamma Distributed Product under Neutrosophic Statistics Using Resampling Scheme. Hindawi: Journal of Mathematics: Soft Computing Algorithms Based on Fuzzy Extensions, Volume 2021, Article ID 6635846, 12 pages; DOI: 10.1155/2021/6635846. 52. Muhammad Aslam: A study on skewness and kurtosis estimators of wind speed distribution under indeterminacy. Springer: Theoretical and Applied Climatology, 143, 1227–1234, 2021; DOI: 10.1007/s00704-020-03509-5. 53. Muhammad Aslam, Ali Algarni: Analyzing the Solar Energy Data Using a New Anderson-Darling Test under Indeterminacy. Hindawi: International Journal of Photoenergy, Volume 2020, Article ID 6662389, 6 pages; DOI: 10.1155/2020/6662389. 54. Muhammad Aslam: Forecasting of the wind speed under uncertainty. Nature: Sc. Rep., Volume 10 (2020). 55. Azhar Ali Janjua, Muhammad Aslam, Naheed Sultana: Evaluating the relationship between climate variability and agricultural crops under indeterminacy. Springer: Theoretical and Applied Climatology, Volume 142, pages 1641–1648 (2020); DOI: 10.1007/s00704-020-03398-8. 56. Rehan Ahmad Khan Sherwan, Mishal Naeem, Muhammad Aslam, Muhammad Ali Raza, Muhammad Abid, Shumaila Abbas: Neutrosophic Beta Distribution with Properties and Applications. University of New Mexico: Neutrosophic Sets and Systems, Vol. 41, 209-214, 2021; DOI: 10.5281/zenodo.4625715. 57. Muhammad Aslam, Ambreen Shafqat, Mohammed Albassam, Jean-Claude Malela-Majika, Sandile C. Shongwe: A new CUSUM control chart under uncertainty with applications in petroleum and meteorology. PLoS ONE 16(2): e0246185, 2021; DOI: 10.1371/journal.pone.0246185. 58. Muhammad Aslam: Monitoring the road traffic crashes using NEWMA chart and repetitive sampling. Taylor&Francis: International Journal of Injury Control and Safety Promotion, Volume 28, 2021 - Issue 1, 39-45; DOI: 10.1080/17457300.2020.1835990. 59. Muhammad Aslam: Analysing Gray Cast Iron Data using a New Shapiro-Wilks test for Normality under Indeterminacy. Taylor&Francis: International Journal of Cast Metals Research, Volume 34, 2021 - Issue 1, 1-5; DOI: 10.1080/13640461.2020.1846959. 60. Ishmal Shahzadi, Muhammad Aslam, Hussain Aslam: Neutrosophic Statistical Analysis of Income of YouTube Channels. University of New Mexico: Neutrosophic Sets and Systems, Vol. 39, 101-106, 2020. 61. Nasrullah Khan, Muhammad Aslam, P. Jeyadurga, S. Balamurali: Monitoring of production of blood components by attribute control chart under indeterminacy. Nature: Sc. Rep., volume 11 (2021). 62. Muhammad Aslam, Rashad A.R. Bantan: A study on measurement system analysis in the presence of indeterminacy. Elsevier: Measurement, Volume 166, December 2020, 108201; DOI: 10.1016/j.measurement.2020.108201. 63. Muhammad Aslam, Rashad A. R. Bantan, Nasrullah Khan: Design of NEWMA np control chart for monitoring neutrosophic nonconforming items. Springer: Soft Computing, Volume 24, 16617–16626 (2020); DOI: 10.1007/s00500-020-04964-y. 64. M. Albassam, Muhammad Aslam: Monitoring Non-Conforming Products Using Multiple Dependent State Sampling Under Indeterminacy-An Application to Juice Industry. IEEE Access, vol. 8, pp. 172379-172386, 2020; DOI: 10.1109/ACCESS.2020.3024569. 65. Ahmed Ibrahim Shawky , Muhammad Aslam, Khushnoor Khan: Multiple Dependent State Sampling-Based Chart Using Belief Statistic under Neutrosophic Statistics. Hindawi: Journal of Mathematics, Volume 2020, Article ID 7680286, 14 pages; DOI: 10.1155/2020/7680286. 66. Muhammad Aslam: Introducing Grubbs’s test for detecting outliers under neutrosophic statistics - An application to medical datas. Science Direct: Journal of King Saud University - Science, Volume 32, Issue 6, September 2020, 2696-2700; DOI: 10.1016/j.jksus.2020.06.003. 67. Muhammad Aslam: A New Sampling Plan Using Neutrosophic Process Loss Consideration. MDPI: Symmetry, 2018, 10 (5), 132; DOI: 10.3390/sym10050132. 68. Muhammad Aslam, Osama H. Arif: Testing of Grouped Product for the Weibull Distribution Using Neutrosophic Statistics. MDPI: Symmetry, 2018, 10 (9), 403; DOI: 10.3390/sym10090403. 69. Muhammad Aslam, Nasrullah Khan, Muhammad Zahir Khan: Monitoring the Variability in the Process Using Neutrosophic Statistical Interval Method. MDPI: Symmetry, 2018, 10 (11), 562; DOI: 10.3390/sym10110562. 70. Muhammad Zahir Khan, Muhammad Farid Khan, Muhammad Aslam, Abdur Razzaque Mughal: Design of Fuzzy Sampling Plan Using the Birnbaum-Saunders Distribution. MDPI: Mathematics, 2019, 7 (1), 9; DOI: 10.3390/math7010009. 71. Muhammad Aslam, Ali Hussein Al-Marshadi: Design of Sampling Plan Using Regression Estimator under Indeterminacy. MDPI: Symmetry, 2018, 10 (12), 754; DOI: 10.3390/sym10120754. 72. Muhammad Zahir Khan, Muhammad Farid Khan, Muhammad Aslam, Seyed Taghi Akhavan Niaki, Abdur Razzaque Mughal: A Fuzzy EWMA Attribute Control Chart to Monitor Process Mean. MDPI: Information, 2018, 9 (12), 312; DOI: 10.3390/info9120312. 73. Muhammad Aslam, Nasrullah Khan, Mohammed Albassam: Control Chart for Failure-Censored Reliability Tests under Uncertainty Environment. MDPI: Symmetry, 2018, 10 (12), 690; DOI: 10.3390/sym10120690. 74. Muhammad Aslam, Mohammed Albassam: Application of Neutrosophic Logic to Evaluate Correlation between Prostate Cancer Mortality and Dietary Fat Assumption. MDPI: Symmetry, 2019, 11 (3), 330; DOI: 10.3390/sym11030330. 75. Muhammad Aslam, Mansour Sattam Aldosari: Inspection Strategy under Indeterminacy Based on Neutrosophic Coefficient of Variation. MDPI: Symmetry, 2019, 11 (2), 193; DOI: 10.3390/sym11020193. 76. Muhammad Aslam: A Variable Acceptance Sampling Plan under Neutrosophic Statistical Interval Method. MDPI: Symmetry, 2019, 11 (1), 114; DOI: 10.3390/sym11010114. 77. Muhammad Aslam, Nasrullah Khan, Ali Hussein Al-Marshadi: Design of Variable Sampling Plan for Pareto Distribution Using Neutrosophic Statistical Interval Method. MDPI: Symmetry, 2019, 11 (1), 80; DOI: 10.3390/sym11010080. 78. Muhammad Aslam, Rashad A. R. Bantan, Nasrullah Khan: Design of S2N—NEWMA Control Chart for Monitoring Process having Indeterminate Production Data. MDPI: Processes, 2019, 7 (10), 742; DOI: 10.3390/pr7100742. 79. Muhammad Aslam, Ali Hussein Al-Marshadi, Nasrullah Khan: A New X-Bar Control Chart for Using Neutrosophic Exponentially Weighted Moving Average. MDPI: Mathematics, 2019, 7 (10), 957; DOI: 10.3390/math7100957. 80. Muhammad Aslam, P. Jeyadurga, Saminathan Balamurali, Ali Hussein Al-Marshadi: Time-Truncated Group Plan under a Weibull Distribution based on Neutrosophic Statistics. MDPI: Mathematics, 2019, 7 (10), 905; DOI: 10.3390/math710090557. 81. Muhammad Aslam, Osama Hasan Arif: Classification of the State of Manufacturing Process under Indeterminacy. MDPI: Mathematics, 2019, 7 (9), 870; DOI: 10.3390/math7090870. 82. Muhammad Aslam, Mohammed Albassam: Inspection Plan Based on the Process Capability Index Using the Neutrosophic Statistical Method. MDPI: Mathematics, 2019, 7 (7), 631; DOI: 10.3390/math7070631. 83. Muhammad Aslam, Rashad A. R. Bantan, Nasrullah Khan: Monitoring the Process Based on Belief Statistic for Neutrosophic Gamma Distributed Product. MDPI: Processes, 2019, 7 (4), 209; DOI: 10.3390/pr7040209. 84. Muhammad Aslam: Product Acceptance Determination with Measurement Error Using the Neutrosophic Statistics. Hindawi: Advances in Fuzzy Systems, Volume 2019, Article ID 8953051, 8 pages; DOI: 10.1155/2019/8953051. 85. Muhammad Aslam, Rashad A. R. Bantan, Nasrullah Khan: Design of a New Attribute Control Chart Under Neutrosophic Statistics. Springer: International Journal of Fuzzy Systems, Volume 21, 433–440 (2019); DOI: 10.1007/s40815-018-0577-1. 86. Muhammad Aslam, Osama H. Arif: Test of Association in the Presence of Complex Environment. Hindawi: Complexity, Volume 2020, Article ID 2935435, 6 pages; DOI: 10.1155/2020/2935435. 87. Mohammed Albassam, Nasrullah Khan,Muhammad Aslam: The W/S Test for Data Having Neutrosophic Numbers: An Application to USA Village Population. Hindawi: Complexity, Volume 2020, Article ID 3690879, 8 pages; DOI: 10.1155/2020/3690879. 88. Muhammad Aslam, Osama H. Arif, Rehan Ahmad Khan Sherwani: New Diagnosis Test under the Neutrosophic Statistics: An Application to Diabetic Patients. Hindawi: BioMed Research International, Volume 2020, Article ID 2086185, 7 pages; DOI: 10.1155/2020/2086185. 88. Muhammad Aslam, Ali Hussein Al-Marshadi: Design of a Control Chart Based on COM-Poisson Distribution for the Uncertainty Environment. Hindawi: Complexity, Volume 2019, Article ID 8178067, 7 pages; DOI: 10.1155/2019/8178067. 89. Muhammad Aslam, Osama H. Arif: Multivariate Analysis under Indeterminacy: An Application to Chemical Content Data. Hindawi: Journal of Analytical Methods in Chemistry, Volume 2020, Article ID 1406028, 6 pages; DOI: 10.1155/2020/1406028. 90. Muhammad Aslam, Abdulmohsen Al-Shareef, Khushnoor Khan: Monitoring the temperature through moving average control under uncertainty environment. Nature: Sc. Rep., Volume 10, Article number: 12182 (2020). 91. Muhammad Aslam: Design of Sampling Plan for Exponential Distribution Under Neutrosophic Statistical Interval Method. IEEE Access, vol. 6, pp. 64153-64158, 2018; DOI: 10.1109/ACCESS.2018.2877923. 92. Muhammad Aslam: Control Chart for Variance Using Repetitive Sampling Under Neutrosophic Statistical Interval System. IEEE Access, vol. 7, pp. 25253-25262, 2019; DOI: 10.1109/ACCESS.2019.2899020. 93. Muhammad Aslam, M. Azam, M. Albassam: Sampling Plan Using Process Loss Index Using Multiple Dependent State Sampling Under Neutrosophic Statistics. IEEE Access, vol. 7, pp. 38568-38576, 2019; DOI: 10.1109/ACCESS.2019.2906408. 94. Naeem Jan, Muhammad Aslam, Kifayat Ullah, Tahir Mahmood, Jun Wang: An approach towards decision making and shortest path problems using the concepts of interval-valued Pythagorean fuzzy information. Wiley: International Journal of Intelligent Systems, Volume 34, Issue 10, October 2019, 2403-2428. 95. Muhammad Aslam: Attribute Control Chart Using the Repetitive Sampling Under Neutrosophic System. IEEE Access, vol. 7, 2019, 2163-3536; DOI: 10.1109/ACCESS.2019.2895162. 96. Muhammad Aslam, R. A. R. Bantan, N. Khan: Design of a Control Chart for Gamma Distributed Variables Under the Indeterminate Environment. IEEE Access, vol. 7, pp. 8858-8864, 2019; DOI: 10.1109/ACCESS.2019.2891005. 97. Muhammad Aslam, Muhammad Ali Raza: Design of New Sampling Plans for Multiple Manufacturing Lines Under Uncertainty. Springer: International Journal of Fuzzy Systems, volume 21, 978–992 (2019); DOI: 10.1007/s40815-018-0560-x. 98. Muhammad Aslam: A New Failure-Censored Reliability Test Using Neutrosophic Statistical Interval Method. Springer: International Journal of Fuzzy Systems, volume 21, 1214–1220 (2019); DOI: 10.1007/s40815-018-0588-y. 99. Muhammad Aslam: Neutrosophic analysis of variance: application to university students. Springer: Complex & Intelligent Systems, volume 5, 403–407 (2019); DOI: 10.1007/s40815-018-0588-y. 100. Muhammad Aslam, Mohammed Albassam: Presenting post hoc multiple comparison tests under neutrosophic statistics. Elsevier: Journal of King Saud University - Science, Volume 32, Issue 6, September 2020, 2728-2732; DOI: 10.1016/j.jksus.2020.06.008. 101. Muhammad Aslam, Mansour Sattam Aldosari: Analyzing alloy melting points data using a new Mann-Whitney test under indeterminacy. Elsevier: Journal of King Saud University - Science, Volume 32, Issue 6, September 2020, 2831-2834; DOI: 10.1016/j.jksus.2020.07.005. 102. Muhammad Aslam: On detecting outliers in complex data using Dixon’s test under neutrosophic statistics. Elsevier: Journal of King Saud University - Science, Volume 32, Issue 3, April 2020, 2005-2008; DOI: 10.1016/j.jksus.2020.02.003. 103. Muhammad Aslam: A new attribute sampling plan using neutrosophic statistical interval method. Springer: Complex & Intelligent Systems, 5, 365–370 (2019); DOI: 10.1007/s40747-018-0088-6. 104. Muhammad Aslam, Saminathan Balamurali, Jeyadurga Periyasamypandian, Ali Hussein Al-Marshadi: Plan for Food Inspection for Inflated-Pareto Data Under Uncertainty Environment. IEEE Access, vol. 7, 164186-164193, 2019; DOI: 10.1109/ACCESS.2019.2951019. 105. Muhammad Aslam, R. A. R. Bantan, N. Khan: Design of X-Bar Control Chart Using Multiple Dependent State Sampling Under Indeterminacy Environment. IEEE Access, vol. 7, pp. 152233-152242, 2019; DOI: 10.1109/ACCESS.2019.2947598. 106. Muhammad Aslam: Introducing Kolmogorov-Smirnov Tests under Uncertainty: An Application to Radioactive Data. American Chemical Society: ACS Omega 2020, 5, 1, 914-917; DOI: 10.1021/acsomega.9b03940. 107. Muhammad Aslam: Design of the Bartlett and Hartley tests for homogeneity of variances under indeterminacy environment. Taylor&Francis: Journal of Taibah University for Science, Volume 14, 2020, Issue 1; DOI: 10.1080/16583655.2019.1700675. 108. Muhammad Aslam, Muhammad Ali Raza, Liaquat Ahmad: Acceptance sampling plans for two-stage process for multiple manufacturing lines under neutrosophic statistics. IOS Press: Journal of Intelligent & Fuzzy Systems, vol. 37, no. 6, pp. 7839-7850, 2019; DOI: 10.3233/JIFS-182849. 109. Muhammad Kashif, Hafiza Nida, Muhammad Imran Khan, Muhammad Aslam: Decomposition of Matrix under Neutrosophic Environment. University of New Mexico: Neutrosophic Sets and Systems, vol. 30, 143-148, 2019. 110. Muhammad Aslam, Nasrullah Khan: A new variable control chart using neutrosophic interval method-an application to automobile industry. University of New Mexico: Journal of Intelligent & Fuzzy Systems, vol. 36, no. 3, pp. 2615-2623, 2019; DOI: 10.3233/JIFS-181767. 111. N Khan, L Ahmad, M Azam, M Aslam, F Smarandache, Control Chart for Monitoring Variation Using Multiple Dependent State Sampling Under Neutrosophic Statistics, in the book Neutrosophic Operational Research (eds. F. Smarandache, M. Abdel-Basset), Springer, pp 55-70, 10 September 2021, https://link.springer.com/chapter/10.1007/978-3-030-57197-9_4. 112. Rehan Ahmad Khan Sherwani, Muhammad Aslam, Muhammad Ali, Raza Muhammad, Farooq Muhammad, Abid Muhammad Tahir, Neutrosophic Normal Probability Distribution—A Spine of Parametric Neutrosophic Statistical Tests: Properties and Applications, in the book Neutrosophic Operational Research (eds. F. Smarandache, M. Abdel-Basset), Springer, pp 153-169, 10 September 2021, https://link.springer.com/chapter/10.1007/978-3-030-57197-9_8. 113. Rehan Ahmad Khan Sherwani, Muhammad Aslam, Huma Shakeel, Kamran Abbas, Farrukh Jamal, Neutrosophic Statistics for Grouped Data: Theory and Applications, in the book Neutrosophic Operational Research (eds. F. Smarandache, M. Abdel-Basset), Springer, pp 263-289, 10 September 2021, https://link.springer.com/chapter/10.1007/978-3-030-57197-9_14.
114. Arif, O.H., Aslam, M. A new sudden death chart for the Weibull distribution
under complexity. Complex Intell. Syst. 7, 2093–2101 (2021),
118. Florentin Smarandache, Foundation of Appurtenance and Inclusion Equations for Constructing the Operations of Neutrosophic Numbers Needed in Neutrosophic Statistics (revised). Prospects for Applied Mathematics and Data Analysis (PAMDA), Vol. 03, No. 01, PP. 29-48, 2023, https://fs.unm.edu/NS/AppurtenanceInclusionEquations-revisited.pdf 119. Saadia Masood, Bareera Ibrar, Javid Shabbir, Ali Shokri & Zabihullah Movaheedi, Estimating neutrosophic finite median employing robust measures of the auxiliary variable, https://fs.unm.edu/NS/NeutrosophicFiniteMedian.pdf, Scientific Reports, (2024) 14:10255.
S1. History of Neutrosophic Set, Logic, Probability and Statistics and their Applications, Mathematics and Statistics Departments, King Abdulaziz University, Jeddah, Saudi Arabia, 19 December 2019.
S2.
Neutrosophic
Set and Logic / Interval Neutrosophic Set and Logic / Neutrosophic Probability
and Neutrosophic Statistics / Neutrosophic Precalculus and Calculus / Symbolic
Neutrosophic Theory / Open Challenges of Neutrosophic Set,
lecture series, by F. Smarandache, Nguyen Tat Thanh University, Ho Chi Minh
City, Vietnam, 31st May - 3th June 2016.
S3.
Neutrosophic
Set and Logic / Interval Neutrosophic Set and Logic / Neutrosophic Probability
and Neutrosophic Statistics / Neutrosophic Precalculus and Calculus / Symbolic
Neutrosophic Theory / Open Challenges of Neutrosophic Set, by
F. Smarandache, Ho Chi Minh City University of Technology (HUTECH), Ho Chi Minh
City, Vietnam, 30th May 2016.
S4.
Neutrosophic
Set and Logic / Interval Neutrosophic Set and Logic / Neutrosophic Probability
and Neutrosophic Statistics / Neutrosophic Precalculus and Calculus / Symbolic
Neutrosophic Theory / Open Challenges of Neutrosophic Set,
lecture series, by F. Smarandache, Vietnam national University, Vietnam
Institute for Advanced Study in Mathematics, Hanoi, Vietnam, lecture series, 14th May
– 26th May 2016. S5. Foundations of Neutrosophic Logic, Set, Probability and Statistics and their Applications in Science. n-Valued Refined Neutrosophic Set, Logic, Probability and Statistics, by F. Smarandache, Universidad Complutense de Madrid, Facultad de Ciencia Matematicas, Departamento de Geometria y Topologia, Instituto Matematico Interdisciplinar (IMI), Madrid, Spain, 9th July 2014.
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