Fuzzy set representations of some quantum structures

✍ Scribed by Anatolij Dvurečenskij

• Publisher: Elsevier Science
• Year: 1999
• Tongue: English
• Weight: 803 KB
• Volume: 101
• Category: Article
• ISSN: 0165-0114
• DOI: 10.1016/s0165-0114(97)00050-x

✦ Synopsis

Quantum structures are algebraic structures like quantum logics (orthomodular posets and lattices), orthoalgebras, effect algebras (D-posets) which model event structures of quantum mechanics. The elements of orthomodular posets can be represented by question observables having their spectrum in {0, 1 }, so they are considered as two-valued physical quantities. We show that if such a structure possesses an order determining system of states (= probability measures), it can be represented by a system of fuzzy sets and conversely.