Abstract:

The aim of this paper is to discuss the approximate rea-
soning problems with interval-valued fuzzy environments based
on the fully implicational idea.First,this paper constructs a class
of interval-valued fuzzy implications by means of a type of impli-
cations and a parameter on the unit interval,then uses them to
establish fully implicational reasoning methods for interval-valued
fuzzy modus ponens(IFMP)and interval-valued fuzzy modus tol-
lens(IFMT)problems.At the same time the reversibility properties
of these methods are analyzed and the reversible conditions are
given.It is shown that the existing unified forms ofα-triple I(the
abbreviation of triple implications)methods for FMP and FMT can
be seen as the particular cases of our methods for IFMP and IFMT.