A characterization for residuated implications on J [0, 1]. Application to the L-fuzzy concept theory.

Abstract

In this paper, a new characterization for the interval-valued residuated fuzzy implication operators is presented, with which it is possible to use them in a simple and efficient way, since the calculation of the values of an interval-valued implication applicated to two intervals is reduced to the study of a fuzzy implication applicated to the extremes of these intervals. This result is very important in order to extract knowledge from an L-fuzzy context with incomplete information. Finally, some examples of interval-valued residuated fuzzy implications built by this constructive method and some properties are shown.