Fuzzy Rules, Graded Properties, IF--THEN Rules, Extensionality, Functionality, Partiality, Fuzzy Relations.

We propose two basic ways of merging various partial fuzzy rule-bases containing knowledge related to the same process or dependency in general. The knowledge that is not at the disposal is considered undefined and encoded using some dummy value. For simplicity, we use only one code for undefined membership value, and we handle the undefined membership values using operations of variable-domain fuzzy set theory, i.e., the theory that allows fuzzy sets to have undefined membership values. Moreover, we study one of the essential properties in fuzzy modeling--a graded property of functionality. We provide estimations for degrees of the functionality of input models and merged models of partial fuzzy rule-bases.