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Full Length Article
Volume 12 , Issue1, PP: 9-12 , 2020


True-False Set is a particular case of the Refined Neutrosophic Set

Authors Names :   Florentin Smarandache   1     Said Broumi   2  

1  Affiliation :  Dept. Math and Sciences, University of New Mexico, Gallup, NM 87301, USA

    Email :  smarand@unm.edu

2  Affiliation :  Laboratory of Information Processing, Faculty of Science Ben M’Sik, University Hassan II, Casablanca, Morocco

    Email :  broumisaid78@gmail.com

Doi   :  10.5281/zenodo.4247831

Received: Octobre 30, 2020 Accepted: Novembre 05, 2020

Abstract :


Borzooei, Mohseni Takallo, and Jun recently proposed a new type of set, called True-False Set [1], and they claimed it is a generalization of Neutrosophic Set [2]. We prove that this assertion is untrue. Actually it’s the opposite, the True-False Set is a particular case of the Refined Neutrosophic Set..


Keywords :

Refined Neutrosophic Set , True-False Set , Neutrosophic Set , Indeterminacy.

References :

[1]  R. A Borzooei, M. Mohseni Taakallo, Y. B. Yun: True-False Sets, 2020 8th Iranian Joint Congress on Fuzzy and Intelligent Systems (FIS), September 204, 2020, Mashad, Iran, 5 pages.


[2]   F. Smarandache: Neutrosophy. Neutrosophic Probability, Set, and Logic. Rehoboth: American Research Press, 1998;  http://fs.unm.edu/eBook-Neutrosophics6.pdf  


[3]  F. Smarandache, Neutrosophic Overset, Neutrosophic Underset, and Neutrosophic Offset. Similarly for Neutrosophic Over-/Under-/Off- Logic, Probability, and Statistics, 168 p., Pons Editions, Bruxelles, Belgique, 2016; https://arxiv.org/ftp/arxiv/papers/1607/1607.00234.pdf,https://hal.archives-ouvertes.fr/hal-01340830

      [4]    F. Smarandache: n-Valued Refined Neutrosophic Logic and Its Applications to Physics. Progress in Physics, 143-146, Vol. 4, 2013; arXiv:1407.1041 [cs.AI] 2013; http://fs.unm.edu/RefinedNeutrosophicSet.pdf