MIN and MAX Operators for Trapezoidal Fuzzy Intervals PART I: Formalization and Application

This two part paper proposes a methodology for determining an extension of the MIN and MAX general analytical expression, initially developed for triangular fuzzy intervals (R. Boukezzoula et al., 2007) to trapezoidal ones when Zadehpsilas extension principle is considered. In order to determine the MIN and MAX analytical expressions, the first part exhibits the conventional interval relations and their extension in fuzzy case where trapezoidal fuzzy intervals are assumed. The formalization and justification of the so-built analytical expressions are detailed in part II of this paper. The potential use of these operators in the framework of uncertain aggregation operators and ranking fuzzy intervals is illustrated with an illustrative example.