# neutrosophic probability

## neutrosophic probability

(logic)
An extended form of probability based on Neutrosophy, in which a statement is held to be t true, i indeterminate, and f false, where t, i, f are real values from the ranges T, I, F, with no restriction on T, I, F or the sum n=t+i+f.

http://gallup.unm.edu/~smarandache/NeutProb.txt.

["Neutrosophy / Neutrosophic Probability, Set, and Logic", Florentin Smarandache, American Research Press, 1998].
References in periodicals archive ?
Neutrosophy, Neutrosophic Set, Neutrosophic Probability (third edition), American Research Press: Rehoboth, NM, USA, 1999.
[4.] Smarandache, F.: Neutrosophy, Neutrosophic Probability, Sets and Logic, Proquest Information & Learning, Ann Arbor, Michigan, USA, 105p,1998
Therefore, the neutrosophic logic, neutrosophic set, neutrosophic probability, neutrosophic statistics, neutrosophic measure, neutrosophic precalculus, neutrosophic calculus, and so forth were born in neutrosophy .
Also, he suggested an extension of the classical probability and imprecise probability to "neutrosophic probability".
Neutrosophy is the basis of neutrosophic logic, neutrosophic probability, neutrosophic set, and neutrosophic statistics.
A cloud is a neutrosophic set, because its borders are ambiguous, and each element (water drop) belongs with a neutrosophic probability to the set (e.g.
One uses the definitions of Neutrosophic probability and Neutrosophic set operations.
Further the Smarandache neutrosophic probability bivector will be a bicolumn vector which can take entries from [-1, 1] [union] [-I, I] whose sum can lie in the biinterval [-1, 1] [union] [-I, I].
Neutrosophy: neutrosophic probability, set and logic, American Research Press, Rehoboth, (1998).
Let X be a non- empty set and Abe any type of neutrosophic crisp set on a space X, then the neutrosophic probability is a mapping NP: X [right arrow] [[0,1].sup.3], NP(A) = <{P([A.sub.1]),P([A.sub.2]),P([A.sub.3])>, that is the probability of a neutrosophic crisp set that has the properly that--
Similar generalizations are done for n-Valued Refined Neutrosophic Set, and respectively n-Valued Refined Neutrosophic Probability.
He demonstrated that the neutrosophic probability of the true price of the derivative security being given by any theoretical pricing model is obtainable as NP (H [intersection] [M.sup.C]); where NP stands for neutrosophic probability, H = {p : p is the true price determined by the theoretical pricing model }, M = {p : p is the true option price determined by the prevailing market price } and the C superscript is the complement operator.

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