Solution of Fuzzy Relation Equations Using Duality of Operators

The two typical composite operations of fuzzy relation are the max-min and the min-max composite operations. It is known that the two operations can be completely dual. This paper pays attention to the nature that these two typical operations are completely dual and investigates the correlation between the max-min composite relation equation and the min-max composite relation equation. An important scheme of correlation is in the characteristic of solution sets derived from these two fuzzy relation equations. The paper explains that one of the composite fuzzy relation equations is solvable using the solution method of the other fuzzy relation equation. The above-mentioned duality plays an important role in this solution procedure. Since it is not necessary to build the solution method separately like before, calculation efficiency can be raised. Moreover, the solution for the relation ...