733 425
Full Length Article
International Journal of Neutrosophic Science
Volume 15 , Issue 2, PP: 89-97 , 2021 | Cite this article as | XML |PDF


Indeterminacy in Neutrosophic Theories and their Applications

Authors Names :   Florentin Smarandache   1 *  

1  Affiliation :  Mathematics, Physics and Natural Sciences Division,The University of New Mexico, 705 Gurley Ave., Gallup, NM 87301, USA

    Email :  smarand@unm.edu

Doi   :   https://doi.org/10.54216/IJNS.150203

Received:March15, 2021, Accepted: July 28, 2021

Abstract :

       Indeterminacy makes the main distinction between fuzzy / intuitionistic fuzzy (and other extensions of fuzzy) set / logic vs. neutrosophic set / logic, and between classical probability and neutrosophic probability. Also, between classical statistics vs. neutrosophic and plithogenic statistics, between classical algebraic structures vs. neutrosophic algebrais structures, between crisp numbers vs. neutrosophic  numbers. We present a broad definition of indeterminacy, various types of indeterminacies, and many practical applications. 

Keywords :

Indeterminacy , Neutrality , <neutA> , Neutrosophic Triplets , Types of Indeterminacies , Numerical Indeterminacy , Literal Indeterminacy , Neutrosophic Number , Quadruple Neutrosophic Number , Refined Indeterminacy , Subindeterminacies , Null Indeterminacy , Over-/Under-/Off-Indeterminacy , TransIndeterminacies

References :

[1] F. Smarandache, Neutrosophy. Neutrosophic Probability, Set, and Logic, ProQuest Information & Learning, Ann Arbor, Michigan, USA, 105 p., 1998; http://fs.unm.edu/eBook-Neutrosophics6.pdf

[2] F. Smarandache, Neutrosophic Quadruple Numbers, Refined Neutrosophic Quadruple Numbers, Absorbance Law, and the Multiplication of Neutrosophic Quadruple Numbers, Ch. 7, pp. 186-193, Chapters in his book: Symbolic Neutrosophic Logic, Europa Nova, Brussels, 194 p., 2015; http://fs.unm.edu/SymbolicNeutrosophicTheory.pdf

[3] F. Smarandache, n-Valued Refined Neutrosophic Logic and Its Applications in Physics, Progress in Physics, 143-146, Vol. 4, 2013; http://fs.unm.edu/n-ValuedNeutrosophicLogic-PiP.pdf

[4] F. Smarandache, Introduction to Neutrosophic Measure, Neutrosophic Integral, and Neutrosophic Probability, Sitech & Educational, Craiova, Columbus, 140 p., 2013; https://arxiv.org/ftp/arxiv/papers/1311/1311.7139.pdf

[5] F. Smarandache: Introduction to Neutrosophic Statistics, Sitech & Education Publishing, 2014, 124 p.; http://fs.unm.edu/NeutrosophicStatistics.pdf

[6] J. Kaplan, Neutrosophic Statistics is a generalization of Classical Statistics, Open Library, San Francisco, USA, https://archive.org/details/neutrosophic-statistics?tab=about  

[7] W. B. Vasantha Kandasamy, F. Smarandache, Fuzzy Cognitive Maps and Neutrosophic Cognitive Maps, Xiquan, Phoenix, 211 p., 2003, http://fs.unm.edu/NCMs.pdf

[8] F. Smarandache, Neutrosophic Precalculus and Neutrosophic Calculus, EdituraNova, Belgium, 2015, http://fs.unm.edu/NeutrosophicPrecalculusCalculus.pdf

[9] F. Smarandache, Neutrosophic Overset, Neutrosophic Underset, and Neutrosophic Offset. Similarly for Neutrosophic Over-/Under-/Off- Logic, Probability, and Statistics, 168 p., Pons Editions, Brussels, Belgium, 2016, http://fs.unm.edu/NeutrosophicOversetUndersetOffset.pdf,   on Cornell University’s website: https://arxiv.org/ftp/arxiv/papers/1607/1607.00234.pdf and in France at the HAL international scientific database: https://hal.archives-ouvertes.fr/hal-01340830

[10] N. Martin, Priya. R, F. Smarandache: Decision Making on Teachers’ adaptation to Cybergogy in Saturated Interval-valued Refined Neutrosophic overset /underset /offset Environment, International Journal of Neutrosophic Science (IJNS), Volume 12, Issue 2, pp. 58-70, 2020; DOI: 10.5281/zenodo.4268284

[11] Tiago S. dos Reis, Walter Gomide, James A.D.W. Anderson, Construction of Transreal Numbers and Algebraic Transfields, IAENG International Journal of Applied Mathematics, 46:1, IJAM_46_1_03, Advance Online Publication: 15 February 2016.

[12] F. Smarandache, Matter, Antimatter, and Unmatter, CERN - The European Organization for Nuclear Research, Geneva, Switzerland, 01 Jun 1980, http://cdsweb.cern.ch/record/798551

[13] F. Smarandache, Neutrosophic Set is a Generalization of Intuitionistic Fuzzy Set, Inconsistent Intuitionistic Fuzzy Set (Picture Fuzzy Set, Ternary Fuzzy Set), Pythagorean Fuzzy Set (Atanassov’s Intuitionistic Fuzzy Set of second type), q-Rung Orthopair Fuzzy Set, Spherical Fuzzy Set, and n-HyperSpherical Fuzzy Set, while Neutrosophication is a Generalization of Regret Theory, Grey System Theory, and Three-Ways Decision, Journal of New Theory 29  pp. 01-35,2019; also in arXiv, Cornell University, New York City, NY, USA, pp. 1-50, 17-29 November 2019, https://arxiv.org/ftp/arxiv/papers/1911/1911.07333.pdf; and in The University of New Mexico, Albuquerque, USA, Digital Repository, https://digitalrepository.unm.edu/math_fsp/21.


Cite this Article as :
Florentin Smarandache, Indeterminacy in Neutrosophic Theories and their Applications, International Journal of Neutrosophic Science, Vol. 15 , No. 2 , (2021) : 89-97 (Doi   :  https://doi.org/10.54216/IJNS.150203)