Suppose two intervals defined on real number axis: A = [a_l, a_r] and B = [b_l, b_r].
Are there any thorough discussions about how to order them?
There are many approaches in the literature, such as the one below. But each method seems to fit some specific conditions.
Ishibuchi, Hisao, and Hideo Tanaka. "Multiobjective programming in optimization of the interval objective function." European Journal of Operational Research 48.2 (1990): 219-225.
There acannot be a single approach as the problem is purely heuristcal.
I two intervals coincide, you simply DO NOT KNOW, which of the two values is larger (if any). You can only GUESS, which of them is MORE LIKELY to be larger.
And as you also, have no explicit likelihood function, you are doomed to use heuristics.
A good (at least IMHO) survey can be found in P. Sevastjanov, A. Tikhonenko ,"Direct interval extension of TOPSIS method", Lecture Notes in Computer Science, 2012, 7204, 404-512, but - probably - you already know enouch approaches.
More hints (on which one to use) are possible if you give us more info about the problem under solution.
Good luck!
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