Neutrosophic Complement

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București la Pitești. Șansa de a câștiga (t) să zicem că este 60%, șansa de meci egal (i) de 30%, și șansa de a pierde (f) de 10%. Revenind la economie și prețuri, ar mai trebui adăugate și gradele (procentele) de nedeterminare (i) și de neapartenență (f) ale prețurilor. Numărul prezentat în articol este număr fuzzy triunghiular, dar putem să-l extindem la număr neutrosofic triunghiular dacă adăugăm același lucru pentru funcția de nedeterminare (i) și pentru cea de neapartenență (f). Cum să interpretăm deci conceptul "fuzzy tendential neutrosophic"? Cred că prin faptul că avem un grad de apartenență (deci fuzzy), dar mai există șansa unui grad de nedeterminare (deci neutrosofic) datorită impreciziei și neprevăzutului care există în fluctuațiile de market.

Neutrosophic Complement

To John Mordeson Now, if the complement c(.) is involutive in fuzzy set and intuitionistic fuzzy set, i.e. c(c(a)) = a for all a in [0, 1], the complement in general is not involutive in neutrosophic set.

In neutrosophic set there are several classes of definitions (designs) of neutrosophic complement, such as: c(T,I,F) = (F, I, T),

which is involutive; c(T,I,F) = (1-T, I, 1-F), which is also involutive; but c(T,I,F) = (F, (T + I + F)/3, T) is not involutive since c(c(T,I,F)) is different from (T,I,F) due to the indeterminacy which is not the same [although T and F are complementary]; similarly

c(T,I,F) = (1 - T, (T + I + F)/3, 1 - F) is not involutive since c(c(T,I,F)) is different from (T,I,F) due again to the indeterminacy which is not the same [although T and F are complementary]; also, the optimistic complement defined as: c(T,I,F) = (1 - T, (T + I + F)/3, |1 – F – I|) is not involutive, nor T and F are complementary; similarly the pessimist complement defined as: c(T,I,F) = (|1 – T – I|, (T + I + F)/2, 1 - F) is not involutive, nor T and F are complementary. T,I,F are more flexible in neutrosophic set, that they are in intuitionistic fuzzy set. The case T+I+F = 1 does not coincide with the intuitionistic fuzzy set (IFS), since when applying the IFS operators these operators are not applied to the indeterminacy I,

while in neutrosophic set (NS) the neutrosophic operators are also applied to the indeterminacy I. For example: In IFS one has the intersection (∧IF ): (0.1, 0.2, 0.7) ∧IF (0.4, 0.5, 0.1) = (0.1,0.7) ∧IF (0.4,0.1) = (min{0.1,0.4}, max{0.7,0.1}) = (0.1,0.7) = (0.1,0.2,0.7) since it is understood that the difference to 1 is hesitancy (indeterminacy).

In NS one has the intersection: (0.1, 0.2, 0.7) ∧N (0.4, 0.5, 0.1) = (min{0.1, 0.4}, max{0.2, 0.5}, max{0.7, 0.1}) = (0.1,0.5,0.7) whose sum of components is not 1 any longer, so the neutrosophic operators take in general the case

T+I+T=1 outside of the intuitionistic fuzzy set limits, i.e. the result in general is T+I+F < 1 or T+I+F > 1. Hence we obtained two different results even in the case

T+I+F=1 with respect to IFS and NS. In fuzzy theory and intuitionistic fuzzy theory, if T is big, then F has to be small in order to counterbalance the sum of them to be 1. For example, if T = 0.90, then F ≤ 0.10. So, T and F are complementary in fuzzy theories. But in neutrosophic theory, if T is big, then F can be anything (i.e. small, medium, or big), because their sum does not have to be 1.