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On effect algebras of fuzzy sets. (English) Zbl 1127.06003

Summary: We introduce the category IE of effect algebras of fuzzy sets and sequentially continuous effect homomorphisms and describe its fundamental properties. We show that IE and the category ID of D-posets of fuzzy sets are isomorphic, hence the constructions and properties of ID related to applications to probability theory are valid for the corresponding effect algebras. We describe basic properties of categorical coproducts in ID and dually of categorical products in the corresponding category MID of measurable spaces. We end with remarks on fuzzy probability notions.

MSC:

06A11 Algebraic aspects of posets
03E72 Theory of fuzzy sets, etc.
28E10 Fuzzy measure theory
54A20 Convergence in general topology (sequences, filters, limits, convergence spaces, nets, etc.)
54B30 Categorical methods in general topology
60A05 Axioms; other general questions in probability
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