Uncertainty Modeling


I have a data set with attributes {X1,X2,X3,X4,X5}
Each attribute has a value {1,2,3,4}
Each data set has a utility U
Run time object could be {1,1,2,3,1,4} with Utility 0.98
This run time object is considered as an input for a process in case that it has a utility of 0.
the process then produces another object say {1,3,1,4,2} with utility greater than zero.
Now here is my question , some times the input data set could contain unknown values like: {1,2,3,?,4}
I want to know how can I model this uncertainty in the input and how to know its effect on the utility of the input object ?
I was thinking of making 4 input objects to represent this input with uncertainty like:
A1= {1,2,3,1,4} , Utility(A1)
A2= {1,2,3,2,4} , Utility(A2)
A3= {1,2,3,3,4} , Utility(A3)
A4= {1,2,3,4,4} , Utility(A4)
to represent all possible objects with their utility, but do not know how to make this formally.
So I need to know if there is model to represent this knowing that I am interested in objects that make the utility equal zero or a predefined value.
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1) Is it that Medoos want to replace missing values?

2) Or is it that Medoos want to model how utility is influenced by x1,.., x5 so that it is an analysis of variance problem with utility as dependent variable and x1, …, x5 as the explanatory variables.

3) Or is it that Medoos want to model the relationships among the x1 through x5. Then we can think of a multivariate contingency model. If it had been just x1 and x2 it would have been a 4-by-4 table (because {1,2,3,4}). For three variables it would have been a 4-by-4-by-4-table. With 5 variables it is a 4^5 table. That can be modelled by log-linear-contingency models. (That’s a generalized linear model by the way so it can be modelled in that framework.)

Medoos mentions 5 x-variables but in the example gives 6 variable “ {1,1,2,3,1,4}” responses.

Or what is it he wants?

Post Scriptum:

I just saw Medoos new comment:

Please give yourself 2 min and read it again
Oh no Medoos, it is your problem. You want to have help. If you are not understood then it is your duty to explain. Not for someone else to “read it again”!
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