Multiple Boolean algebras and their application to fuzzy sets (Q1065043)

The author introduces the new algebraic concept of \(p\)-Boolean algebra \((E,\circ_ 1,...,\circ_ p,u)\) for \(p\geq 2\), where \(\circ_ 1,...,\circ_ p\) forms a cycle of semilattice operations (each distributive with respect to the next one), and u: E,\(\circ_ m)\to (E,\circ_{m+1})\) is a \(p\)-cyclic bijection for \(m=1,2,...,p\) \((p+1\) is identified with 1). The family of fuzzy sets \(A: U\to \{0,1/n,2/n,...,n- 1/n,1\}\) can be considered as a function multiple Boolean algebra (with multiplicity \(p=n+1)\). The paper contains a list of open problems connected with this new concept.