A bipolar-valued fuzzy set is an intersected interval-valued fuzzy set

Abstract

This paper shows that a bipolar-valued fuzzy set and a special interval-valued fuzzy set, whose cut-off point of left and right ends of the interval-valued membership is λ (0 < λ < 1), are identical from a mathematical point of view. All results on bipolar-valued fuzzy sets can be obtained by corresponding results of interval-valued fuzzy sets or fuzzy sets. This paper does not completely reject bipolar-valued fuzzy sets, but points the way for such research.