In interval arithmetic, for an interval I= [a, b] we define -I = [-b, -a]. But, it does not satisfy the arithmetic formula like I + J -I = I and more specifically, I - I != [0,0]. It creates a whole lot of problems.
A question comes to mind as how authentic this arithmetic is? Can we call this as something other than arithmetic? Will it be simply another algebraic system which satisfies certain properties?
In this case, when intervals are reduced to singleton sets or numbers by making the end points meet, will it be same as normal arithmetic of numbers?
Can some some source material be linked for reference!
Dear Professor,
In above information "it does not satisfy the arithmetic formula like I + J -I = I". I think you mean "I + J - I = J" ?
Regards,
Wiwat Wanicharpichat
Dear Professor,
I found your paper entitled: "A New Approach to Manage Security Against
Neigborhood Attacks in Social Networks" and the article " Preserving Privacy in Social Networks Against Neighborhood Attacks" very interesting. I red them several times but I have some questions and I would be grateful if you can help me to understand
1. In your example of «Anonymizing two neighborhoods", please how
we compare two neighborhood with different number of components? when we
have two components with single vertex can we connect them ? if we make
this we will have one component? can we do this? for example in the
example of "Ada" and "Bob" you are connected between two components of the
neighborhood of "Ada"?
2. In the step of 'adding an edge', sometimes we can have a neighborhood
with two neighborhood components with a single vertex, can we add an edge
between these two components as shown in your example of Bob with Ada???
3. You have chosen as utility measure “the aggregation queries”, why you
specifically have chosen, is it possible to use structural Properties of
the social graph in addition to aggregation queries, for example seek to
preserve the property APL by adding noise nodes to the original graph in
addition to adding links as your algorithm do ?
I know that you are busy but your answers will help me in my work.
Best regards
You mean general addition of subsets. Take for example the theorem of Lagrange telling that every natural number is the sum of four squares of natural numbers. Let S be the set of squares of natural numbers. Then you can write this:
S + S + S + S = N
where S + S + S + S means the set of all the sums a+b+c+d where a, b, c, d in S.
If for two sets A and B, A + B means the set of all sums a+b with a in A and b in B, then you have such descriptions as above. This is useful for the additive number theory.
It is also useful to write R = Z + (0,1) because this fact help us to define the integer part and the fractional part of a real number.
If the sets are intervals, it is still useful and interesting to see that [0,1) + (0,1] = [0, 2) for example.
But you cannot pretend from this definition something that it does not provide.
I + J - I = I looks like nothing. If you meant in fact I + J - I = J, this looks like a kind of FORMAL addition rule. One can define a formal addition over every set of objects. The question is of course to which goal?
Dear Prof.Mihai,
The typographical error was rectified by me. You are right. Also, you can check the definition of a sub-interval. [a,b] is a subset of [c. d] if and only if a< c and b
It is difficult for me to understand what you are trying to convey. Think it carefully before answering. In general interval arithmetic, where these fuzzy enters? It has nothing to do with fuzzy or not.
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