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# "A Unifying Field In Logics. / Neutrosophy: Neutrosophic Probability, Set, and Logic"

IP.com Disclosure Number: IPCOM000128850D
Original Publication Date: 1999-Sep-11
Included in the Prior Art Database: 2005-Sep-19
Document File: 2 page(s) / 14K

## Publishing Venue

Software Patent Institute

## Related People

Florentin Smarandache: AUTHOR [+3]

## Abstract

One designes software for the neutrosophic logic, which is a generalization of the fuzzy logic (besides other logics), and is used in neural networks, artificial intelligence, and quantum theory. Here there are the new five definitions introduced by the author.

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THIS DOCUMENT IS AN APPROXIMATE REPRESENTATION OF THE ORIGINAL.

"A Unifying Field In Logics. / Neutrosophy: Neutrosophic Probability, Set, and Logic",

by Florentin Smarandache,

American Research Press, 1999. One designes software for the neutrosophic logic, which is a generalization of the fuzzy logic (besides other logics), and is used in neural networks, artificial intelligence, and quantum theory. Here there are the new five definitions introduced by the author:

1) NEUTRSOPHY is a new branch of philosophy which studies the neutralities and their interactions with various ideational spectra. Spreading this attribute out one obtains:

2) NEUTROSOPHIC PROBABILITY: Let T, I, F be real subsets, with sup T = t_sup, inf T = t_inf, sup I = i_sup, inf I = i_inf, sup F = f_sup, inf F = f_inf, and n_sup=t_sup+i_sup+f_sup, n_inf=t_inf+i_inf+f_inf. The neutrosophic probability is a generalization of the classical probability in which the chance that an event A occurs is t% true- where t varies in the subset T, i% indeterminate - where i varies in the subset I, and f% false - where f varies in the subset F (with no restrictions on the real subsets T, I, F, neither on their superior sum n_sup, nor on their inferior sum n_inf). The sets T, I, F are not necessarily intervals, but may be any real subsets: discrete or continuous; single-element, finite, or (countably or uncountably) infinite; union or intersection of various subsets;formed of positive or negative numbers; etc. They may also overlap. One notes NP(A)=(T,I,F), a triple of sets. This representation is closer to the human mind reasoning than any other used logic. In the case when the truth- and falsity-components are complementary, i.e. no indeterminacy and their sum is 100, one falls to the classical probability. As, for example, tossing dice or coins, or drawing cards from a well-shuffled deck, or drawing balls from an urn.

3) NEUTROSOPHIC STATISTICS: Analysis of the events described by the neutrosophicprobability. This is also a generalization of the classical statistics.

4) NEUTROSOPHIC SET: Let T, I, F be real subsets, with sup T = t_sup, inf T = t_inf, sup I = i_sup, inf I = i_inf, sup F = f_sup, inf F = f_inf, and n_sup = t_sup + i_sup + f_sup, n_inf = t_inf + i_inf + f_inf. An element x(T,I,F) belongs to a set M in the following way: it is t% true in the set, i% indeterminate in the set, and f% false, where t varies in T, i varies in I, f varies in F (with no restrictions on the real subsets T, I, F, neither on their superior sum n_sup, nor on their inferior sum n_inf). One can s...