When we solve a fuzzy transportation problem, in some cases we have negatives in the trapezoidal fuzzy numbers as an allocation amount or the minimum cost. It is actually happen because of arithmetic of fuzzy numbers. But in a transportation problem we consider the amount as non negative. It is also true that the equivalence of the defuzzified values of fuzzy number is positive. So if we encounter the questions that why is negative value in the trapezoidal cost. How should I handling this questions?
I think you have answered the question yourself: the fuzzy numbers introduce an element that is incompatible with the transportation problem. (There is a requirement of non-negative flows [Xij >= 0] so the flows cannot add to a negative number.)
A better way to approach this problem is to ensure that the constraints reflect the uncertainty you wish to model AND stay within an allowable range. For example, you could have max(0, Si-delta)
if in your problem the costs must be positive, then A-B = max (O, A-B), saying the max of zero trapezoidal numbers zero and A - B.
If the quantities can be negative, no problem, it will be necessary to interpret the calculated cost which is negative like a penalty :
algebraically negatively obviously
sorry, I forgot that your number (-1,3,5,7) is not a negative number.
it is positive and negative at the same time (but it is more positive than negative). it is the interest of the fuzzy theory.
it is necessary to calculate the surface of the intersection of (-1,0,0,0) with (-1,3,5,7) .., after normalization it will give the degree of membership to (-infinite, 0) and also calculate the degree of belonging to (0, + infinite) ..
focus on arithmetic of fuzzy numbers!
and so in your algorithms do the reasoning / calculating on the positive quantities (with membership to be positive/negativ) ... Eureka ... it will be a fuzzy number of Type 2 ...
This is a new result that you can post :)
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