Fully implicational methods for approximate reasoning based on interval-valued fuzzy sets

摘要

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 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.