Abstract
In this paper, we define EI algebra and EII algebra, which are infinite distributive molecular lattices. We also define the AFS.structure, which is a special system of Graver and Watkins (1977). With these classical mathematical objects, we establish a totally new system of fuzzy sets and systems. We have a new concept of fuzzy sets. It is more acceptable to the classical mathematical opinions. We can directly make use of many classical mathematical results. The most important is that the system can be operated by computers.
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