tautological set

tautological set

(logic)
A notion introduced by Florentin Smarandache: An element x(T, I, F) belongs more than sure to the set M; here T, I, F are real subsets representing the truth, indeterminacy, and falsity percentages respectively, and sup(T)>100.

tautological set are used for universally true propositions where no parameter such as time, space, or subjectivity influences the truth value.

[Florentin Smarandache, "A Unifying Field in Logics. / Neutrosophy: Neutrosophic Probability, Set, and Logic", American Research Press, Rehoboth, 1999]
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The concept of neutrosophic set [1, 2, 3, 4] generalizes the Cantor set discovered by Smith [5] in 1874 and introduced by German mathematician Cantor [6] in 1883, fuzzy set introduced by Zadeh [7], interval valued fuzzy sets introduced independently by Zadeh [8], Grattan-Guiness [9], Jahn [10], Sambuc [11], L-fuzzy sets proposed by Goguen [12], intuitionistic fuzzy set proposed by Atanassov [13], interval valued intuitionistic fuzzy sets proposed by Atanassov and Gargov [14], vague sets proposed by Gau, and Buehrer [15], grey sets proposed by Deng [16], paraconsistent set proposed by Brady [17], faillibilist set [2], paradoxist set [2], pseudoparadoxist set [2], tautological set [2] based on the philosophical point of view.
to intuitionistic set (set incompletely known), paraconsistent set, dialetheist set, faillibilist set (each element has a percentage of indeterminacy), paradoxist set (an element may belong and may not belong in the same time to the set), pseudoparadoxist set, and tautological set respectively.
To handle the indeterminate information and inconsistent information which exist commonly in real situations, Smarandache [1] firstly presented a neutrosophic set from philosophical point of view, which is a powerful general formal framework and generalized the concept of the classic set, fuzzy set, interval-valued fuzzy set, intuitionistic fuzzy set, interval-valued intuitionistic fuzzy set, paraconsistent set, dialetheist set, paradoxist set, and tautological set [1, 2].