Fuzzy decision making based on variable weights

Variable weights analysis and its applications in fuzzy systems and especially in fuzzy decision making are researched in detail in this paper. After the background of variable weights is summarized, an empirical variable weights formula is discussed. Based on the empirical formula, the principles of variable weights are explored, and an axiomatic definition on variable weights is given. Then, an important idea, balance function about variable weights, is defined, and its structure is considered. And some kinds of variable weights are also introduced, which should often be used in many real cases. Especially, Weber-Fechnerʹs law with respect to variable weights is pointed out.