Characterizing the Solvability of Bipolar Equations in the Unit Interval

Abstract

Bipolar equations are the base of bipolar fuzzy relation equations, a modified version of fuzzy relation equations involving a negation operator. This paper characterizes the solvability of bipolar equations defined with an adjoint pair in the unit interval from three different perspectives: the case of a bijective negation; the case of a continuous negation; and the case of an adjoint conjunctor with continuous and injective partial mappings. Ample examples illustrate the usefulness and simplicity of the corresponding characterizations.