In the literature, works on interval ranking are found. Should we really compare intervals? We can rank real numbers. Length, breadth etc can be ranked, in terms of real numbers. Therefore, lengths of intervals can be ranked. What can be the physical significance of comparing 'intervals' directly?
Dr. Hemanta,
Comparing 'intervals' directly has no sense, and your doubt looks fine. But if you divide the rank in certain units by the media in the same units, then you may try to compare rankings in a better way. Is that the sense of your question? Regards, Emilio
Dear Professor Chaves,
Thank you for your assertion that ranking intervals directly makes no sense. Could you please explain the second part of your answer in detail?
For example, [1,2] may be said to be less than [5,6]. But is it meaningful to compare [3,9] and [5,7], say? How about comparing [5,9] and [3,7]?
Proff. Semanta. Let´ suppose that intervals [5,9] and [3,7] belong to same sample with same media U=6 measured in same units. Then first interval in medias is [5/6,9/6] and distance from U=1 media is 1-5/6=1/6 medias for first case and distance for second case is 9/6-1=3/6 medias. If we do it for [3,7] we obtain two distances from U=1: 1-3/6= 2/6 and 7/6-1=1/6.
This short analysis means that the relative position of media is different for both cases, even though the two intervals have equal rank. So equal rank by itself has no sense in comparing intervals because it depends of their relative position inside distribution, and there may be a huge number of intervals with equal rank and different positions inside the same distribution.
OK, that is my argument, there may be other ones to improve answers to your question. Thanks, Emilio
Subrata, in the example I worked, [5,9] and [3,7], there is a common overlapping interval: [5,7]. How do you compare them to answer the original question of Proff. Semanta, if there is not information of the original common sample? May you give an example of dataset to explore it?
Dear Professor Chavez,
Indeed, in the mathematics of fuzziness, ranking of intervals is a very popular topic. However, there are too many methods used to rank fuzzy intervals. Why should there be many methods? There should have been just one method! Therefore I asked whether ranking of intervals, fuzzy or otherwise, is proper.
Proff. Semanta thanks for your explanation. Fuzzy intervals is not my field. Emilio
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