Fuzzy set, Ignorance, Inconsistency, Missing membership degrees, Non-existence

In real-world applications, mathematical models must often deal with values that are missing or undefined. The aim of this paper is to provide a survey on types and reasons for such non-availability. It motivates the need to handle different reasons for missingness in a different, but appropriate way. In particular, non-existence, ignorance, and inconsistency are studied. The paper also presents a novel way of how to compute with different types of missing values at the same time.