Abstract
The idea of consensus is introduced to construct a fuzzy set system. The two different approaches to the fuzzy set theory — the falling shadow and the fuzzy set system based on consensus — are shown to be closely related, and the latter gives another analysis of those three types of set operations that were investigated by the former, and proves them to be subject to the combinations of concerning representative consensus sets. A notion of homomorphism is defined and applied to two fuzzy set systems to clarify similarity between them. This notion shows itself very useful in the study of fuzzy set systems.
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