Neutro-Intelligent Set is a particular case of the Refined Neutrosophic Set
1 Mathematics, Physical and Natural Sciences Division University of New Mexico, 705 Gurley Ave.
Gallup, NM 87301, USA ; smarand@unm.edu; victorchristianto@gmail.com
2 Regional Center for the Professions of Education and Training, Casablanca-Settat,Morocco; broumisaid78@gmail.com
3 Laboratory of Information Processing, Faculty of Science Ben M'Sik
University Hassan II, Casablanca, Moroccobroumisaid78@gmail.com
Abstract
In this short note we show that the newly introduced concept of Neutro-Intelligent Set (NIS) deserves attention in its applications to the human brain activity, and that NIS is a particular case of the Refined Neutrosophic Set.
Keywords: Neutrosophic Logic, Physical Neutrosophy, gravitation, physics constants
In order to simplify the notations, we use Latin descriptive letters, instead of Greek letters, to denote by T the truth (or membership), by I the indeterminacy, and by F the falsehood (or nonmembership).
Let U be a universe of discourse, and A be a non-empty neutrosophic subset of U, defined as follows:
, where for all x U one has
Sunny Raza Qureshi [1] has introduced the Neutral Degree ( ) of the Neutrosophic Set, defined as follows:
It was a nice idea to extend the neutrosophic set from 3 to 4 components, where for all x U, the original components remain totally independent from each other, while the fourth component is totally dependent of the first three components.
Then Sunny Raza Qureshi [1] introduced the Neutro-Intelligent Set (NIS) by adding the neutral Degree to each element, defined as follows:
Let U be a universe of discourse, and be a non-empty subset of U, defined as follows:
, where for all x U
, because:
T1 = 0.4, I1 = 0.2, F1 = 0.3, whence the neutral
T2 = 0.7, I2 = 0.2, F2 = 0.3, whence the neutral
In 2013 the neutrosophic theories were extended to the refined [n-valued] neutrosophic set, refined neutrosophic logic, and refined neutrosophic probability respectively [2], i.e. the truth value T was refined/split into types of sub-truths such as T1, T2, …, Tp, similarly indeterminacy I was refined/split into types of sub-indeterminacies I1, I2, …, Ir, and the falsehood F was refined/split into sub-falsehood F1, F2, …, Fs.
Let U be a universe of discourse, and be a non-empty subset of U, then the Refined Neutrosophic Set is defined as follows:
where p, r, s are positive integers, and at least one of them is ≥ 2,
also for all x U,
.
If one takes the particular case: p = 1, r = 2, s = 1, one gets T, I1, I2, F, with I1 = indeterminacy and I2 = neutrality, one gets the Neutro-Intelligent Set (NIS). The original part of the NIS is that I2 (neutrality) is taken as dependent from T, I, and F.
The author [1] has introduced a neutrosophic model of the human brain, the Multi-Phase/State Neutrosophic Set and aggregated it to its Neutro-Intelligent Set forming a Final Phase Neutrosophic Set, to analyze the human mind uncertainty, especially the sentimental and emotional activities.
Funding: “This research received no external funding”
Conflicts of Interest: “The authors declare no conflict of interest.”
References
[1] Sunny Raza Qureshi, New Dimensions in MCDM with Multi Phase Hyper Neutrosophic Sets, Master of Science In Mathematics, Supervisor Dr. Madiha Qayyum Senior Scientific Officer (OG-II), COMSATS University Islamabad, Lahore Campus, Pakistan, Spring 2021.
[2] Florentin Smarandache, n-Valued Refined Neutrosophic Logic and Its Applications in Physics, Progress in Physics, 143-146, Vol. 4, 2013;
https://arxiv.org/ftp/arxiv/papers/1407/1407.1041.pdf
http://fs.unm.edu/n-ValuedNeutrosophicLogic-PiP.pdf