MIN and MAX operators for trapezoidal fuzzy intervals

The purpose of this paper is to determine an extension of the MIN and MAX general analytical expression for triangular fuzzy intervals to trapezoidal ones when Zadeh's extension principle is considered.

In order to determine the MIN and MAX analytical expressions, the paper exhibits the conventional interval relations and their extension in fuzzy case where trapezoidal fuzzy intervals are assumed. The formalization and the justification of the so‐built analytical expressions are then detailed where mathematical mappings are proposed. The potential use of these operators in the framework of uncertain aggregation operators and ranking fuzzy intervals is shown with illustrative examples.

It is discovered that the MIN and MAX operations for fuzzy intervals can be formulated by a general analytical form.

The proposed methodology can be directly applied for ranking fuzzy intervals and implementing a large class of uncertain aggregation operators, especially for two‐additive Choquet integral.

The originality of the proposed technique resides in exploiting the interval relations between supports and kernels to express a general and compact analytical MIN and MAX expressions for fuzzy intervals.