Fixed points of involutive interval-valued negations

Different from involutive negations on [0, 1], the fixed points of an involutive interval-valued negation are uncountable. In this paper, all the fixed points of an involutive interval-valued negation are characterized. Also, it is proved that an involutive interval-valued negation is uniquely determined by its fixed points. Moreover, a constructive representation of involutive interval-valued negations is obtained. ► All the fixed points of an involutive interval-valued negation are characterized. ► The definitions of the imaginary fixed points and of the fixed point function are given. ► An involutive interval-valued negation is characterized by its fixed points. ► As an application of the fixed point function, a representative theorem of an involutive interval-valued negation is constructed.