Variable-domain fuzzy sets - Part I: Representation

Abstract Despite the fact that fuzzy sets can generally have different domains, standard definitions of fuzzy set operations assume a common reference set for all their operands. The usual way to satisfy this precondition is to assign zero membership to elements outside the domain of each operand. In Part I of this two-part paper we point out several issues with this method and argue that keeping track of the original domains is necessary to ensure the intended behavior of numerous fuzzy set operations. We discuss several ways of representing fuzzy sets with variable domains, preparing the grounds for the apparatus of variable-domain fuzzy set theory described in Part II of the paper.

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