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Hesitancy as sub-part of Indeterminacy
(where * means unknown)
is good. Surely, this idea of complete indeterminacy (i.e. the value *) is interesting. The neutrosophic theories have the capabilities to be extended in many directions.
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Hesitancy as sub-part of Indeterminacy
To Harish Garg The hesitation degree in Intuitionistic Fuzzy Set is just the
Indeterminacy "I" degree in Neutrosophic Set. Actually, Indeterminacy "I" is more than hesitancy in general. When one considers the components T, I, F (or sources that provide them) are totally dependent (as in IFS), i.e.
T + I + F = 1, then I = 1- T- F, i.e. your "I" = hesitancy from IFS. If T, I, F are partially dependent and partially independent, i.e. T + I + F > 1, then indeterminacy "I" is including your hesitancy, and even more, i.e.
Indeterminacy is split in many types of subindeterminacies in function of the problem to solve, so hesitancy can be considered a subpart of the indeterminacy. In neutrosophic logic you can also refine T, I, F and go by sub-components.
For example, you can only refine "I", that you're interested in, for example as:
I1 = contradiction, I2 = vagueness, I3 = hesitancy etc. *
To W.B. Vasantha Kandasamy If we divide, let's say: (2+2I)/(1+I) = x + yI. We need to find x and y as real numbers. Then:
(1+I)(x+yI) 2+2I (identical) or x + (y+x+y)I 2+2I, whence x = 2 and y = 0, therefore alike in classical algebra: (2+2I)/(1+I) = 2. Yet, if we compute I/I = x+yI, we get: I I(x+yI), or I (x+y)I, whence x+y = 1, therefore I/I = (-a+1) + aI, where "a" is any real number, therefore we have infinitely many results for I/I. It is curious that (a+bI)/(dI) has no solution if a 0. And (a+bI)/(c+dI) has one solution only if ac 0. What do you think? Can we divide by a+bI or not ?