Refinement of refinement

Refinement of refinement

Yanhui Guo We can define the data point’s T, I and F on each feature vector. For example, for data point F1=(f11; f12),

F2=(f21;f22)... We can use neutrosophic c-mean on (f11,f21,…,fn1) to have T11,T12, T13, T21, T22, T23, …., and I1,

I2,…, F1, F2, ... In this way, we can have a matrix with T,

I and F using an iteration way which is a general way and work for any data. Florentin Smarandache Yes, it is possible to do a neutrosophic refinement of first level of T, I, F into T1, T2, ..., I1, I2, ..., F1, F2, ...; and then a refinement of the refinement [refinement of second level], T1 to T11, T12, ...; T2 to T21, T22, ... ; and similarly for I1, I2, ... to be refined, and for F1, F2, ... to be refined. We can go further, if needed into the application, to do refinement of third level (T11 refined into T111, T112, ...; T12 refined into T121, T122, ...; and similarly for I11, I12,...; F11,

F12, ...). So, in general refinement of level n ≥ 1 as needed in each application. Such refinement, and refinement of refinement, then refinement of refinement of refinement, and so on, were not done in fuzzy and intutionistic fuzzy theories.

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Now, other things which were not done in fuzzy and intuitionistic fuzzy theories: neutrosophic overset (when

T, I, F can be > 1) and neutrosophic underset (when T, I,

F can be < 0). They occur in our everyday life. For example, if a full-time worker works 40 hours per week, then his membership is T(40) = 40/40 = 1 (we suppose that the norm is 40 h/week). But some people work overtime, for example John works 42 hours, hence T(42) = 42/40 > 1. Another person, George works no hour, so T(0) = 0/40 = 0, while Richard works no hour and in addition he intentionally starts a fire to destroy the company, therefore his membership has to be less than zero (because he is worst than George). *

Thus, you might use the neutrosophic over-/under-/off-set for describing the outlayer data points (too small data points, or too big data points). These were never used before, but they are accepted by the mainstream, since my below book was accepted in the arXiv.org: https://arxiv.org/ftp/arxiv/papers/1607/1607.00234.pdf You are an expert in image processing, so I bring you some idea of how the neutrosophics might help.

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For example, you may assign membership degrees less than zero to too small outlayers, and membership degrees greater than 1 to very big outlayers... *

Yanhui Guo One quick question, what is the advantage of refinement of refinement? It increases the complexity. Florentin Smarandache Indeed, it increases the complexity. But, if in some application you might need such complexity (I mean, you might need a more detailed result), it would be okay. The computers become faster and faster. Yanhui Guo For the second thinking, if we set the range from [0, 40] to [-100, 100], can we solve the underperformance and overperformance problems? Florentin Smarandache You may in general enlarge [0, 40] to [0-a, 40+b], where "a" and "b" are positive numbers. How much should "a" and "b" be? It depends on each application and its expert. In your case, if somebody gets the degree of membership between [-100, 0) then it is underperformance, but if the degree of membership is between (40, 100] then it is overperfromance (as you said).

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