Abstract
The aim of this paper is to discuss the approximate reasoning 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 implications 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 tollens (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 of α-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.
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