Neutrosophic Logic was created by Florentin Smarandache (1995) and is an extension / combination of the fuzzy logic, intuitionistic logic, paraconsistent logic, and the three-valued logics that use an indeterminate value.
Definition of Neutrosophic Logic:
Let T, I, F be standard or non-standard real subsets of the non-standard unit interval ]-0, 1+[,
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.
Of course, -0 <= n_inf <= n_sup <= 3+.
A logic in which each proposition is estimated to have the percentage of truth in a subset T,
the percentage of indeterminacy in a subset I, and the percentage of falsity in a subset F,
where T, I, F are defined above, is called Neutrosophic Logic.
The sets T, I, F are not necessarily intervals, but may be any real sub-unitary subsets: discrete or continuous; single-element, finite, or (countable or uncountable) infinite; union or intersection of various subsets; etc.
They may also overlap. The real subsets could represent the relative errors in determining t, i, f (in the case when the subsets T, I, F are reduced to points).
Statically T, I, F are subsets. But dynamically, looking therefore from another perspective, the components T, I, F are at each instance dependant on many parameters, and therefore they can be considered set-valued vector functions or even operators.
T, I, and F are called neutrosophic components, representing the truth, indeterminacy, and falsehood values respectively referring to neutrosophy, neutrosophic logic, neutrosophic set, neutrosophic probability, neutrosophic statistics.
This representation is closer to the reasoning of the human mind. It characterizes / catches the imprecision of knowledge or linguistic inexactitude perceived by various observers (that’s why T, I, F are subsets - not necessarily single-elements), uncertainty due to incomplete knowledge or acquisition errors or stochasticity (that’s why the subset I exists),
and vagueness due to lack of clear contours or limits (that’s why T, I, F are subsets and I exists; in particular for the appurtenance to the neutrosophic sets).
The advantage of using neutrosophic logic is that this logic distinguishes between relative truth, that is a truth in one or a few worlds only, noted by NL(relative truth)=1, and absolute truth, that is a truth in all possible worlds, noted by NL(absolute truth)=1+. And similarly, neutrosophic logic distinguishes between relative falsehood, noted by 0, and absolute falsehood, noted by –0.
In neutrosophic logic the sum of components is not necessarily 1 as in classical and fuzzy logic, but any number between –0 and 3+, and this allows the neutrosophic logic to be able to deal with paradoxes, propositions which are true and false in the same time: thus NL(paradox)=(1, I, 1); fuzzy logic can not do this because in fuzzy logic the sum of components has to be 1.