I don't want to trivialize this article, but I feel like the whole thing can be reduced to the statement "define 'smaller'". Instead it reads like a "this is w

I don't want to trivialize this article, but I feel like the whole thing can be reduced to the statement "define 'smaller'". Instead it reads like a "this is what 'smaller' means for intervals" at which point I just want to comment "why?" and add a "[citation needed]" tag. It all depends on what your interval represents, or how you can agree that it should be treated. Does it relate to confidence intervals? Does it summarise a distribution? Should it relate to stochastic dominance? Should it represent conflicting evidence between true and false? Should it be treated as a fuzzy membership function? All these interpretations would lead to different, equally valid interpretations for the term 'smaller'.