MIN and MAX operators for trapezoidal fuzzy intervals Part II: Analytical expressions proof

This part paper aims at the proof and the justification of the general MIN and MAX analytical expressions, determined according to the Zadeh extension principle and used in the Part I of this paper. The so-proposed MIN and MAX operators are different from the standard fuzzy intersection and union. Indeed, according to fuzzy extension principle, MIN and MAX are the lattice operations to be used for ordering fuzzy intervals. These analytical expressions can be used in aggregation operators and ranking fuzzy intervals (see the Part I of this paper).