Adjoint Pairs on Interval-Valued Fuzzy Sets

In this paper the authors present the definition of interval operator associated to two general increasing operators, on the set of subintervals of [0,1], and how its residuated implication must be defined, if the initial operator have adjoint implications. These results are necessary in several frameworks where mechanisms for reasoning under uncertainty are needed, such as decision and risk analysis, engineering design, and scheduling. We will show three framework where the interval values are used and, hence, where the results presented here can be useful.