neutrosophic

neutrosophic

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The neutrosophic set developed by Smarandache [7, 8, 9] is a formal framework which generalizes the concept of the classic set, fuzzy set [14], interval valued fuzzy set, intuitionistic fuzzy set [1], interval valued intuitionistic fuzzy set and paraconsistent set etc.
Neutrosophic logic is a powerful tool to deal with incomplete, indeterminate, and inconsistent information, which is the main reason for widespread concerns of researchers.
Smarandache [8] introduced the notion of neutrosophic sets (NSs) as a generalization of the fuzzy sets [14], intuitionistic fuzzy sets [12], interval valued fuzzy set [11] and interval-valued intuitionistic fuzzy sets [13] theories.
Therefore, the neutrosophic logic, neutrosophic set, neutrosophic probability, neutrosophic statistics, neutrosophic measure, neutrosophic precalculus, neutrosophic calculus, and so forth were born in neutrosophy [15].
More general is the Neutrosophic Logic [Smarandache, 1995], where the truth (T) and the falsity (F) and the indeterminacy (1) can be any numbers in [0, 1], then 0 [less than or equal to] T + I + F [less than or equal to] 3.
One first presents the evolution of sets from fuzzy set to neutrosophic set.
Neutrosophic set is a powerful general formal framework which generalizes the concept of the classic set, fuzzy set [12], Vague set [11] etc.
We first define the notion of Smarandache pseudo neutrosophic bisemigroup.
Some neutrosophic algebraic structures and neutroscophic N-algebraic structures.
Smarandache [[13], [14] introduced the concepts of neutrosophy and neutrosophic set.
To express indeterminate and inconsistent information which exists in real world, Smarandache [9] originally proposed the concept of the neutrosophic set from a philosophical point of view.
To overcome this, Smarandache [4], in 1998, introduced neutrosophic sets as an extension of classical sets, fuzzy sets, and intuitionistic fuzzy sets.