Fuzzy inference systems; fuzzy interpolation; solvability of systems of fuzzy relational equations; defuzzification; resulting function; continuity; monotonicity

We focus on fuzzy relational inference systems. Investigating such systems leads to natural mathematical problems (properties). Among them, we may find fuzzy interpolation (preserving the modus ponens property) or continuity and monotonicity of a resulting function that is obtained if we use a defuzzification. All these properties were investigated separately. Natural question is, whether conditions for preserving one of such properties do not contradict conditions for the other properties. This paper is a combination of a survey paper, position paper and a research paper that tries to overroof the whole area by collecting the most relevant results concerning every single property and to answer the most natural questions.