an:06806611
Zbl 1387.03071
Chajda, Ivan; Paseka, Jan
Galois connections and tense operators on q-effect algebras
EN
Fuzzy Sets Syst. 298, 56-68 (2016).
0165-0114
2016
j
03G12 06A15 06C15 81P10
effect algebra; q-effect algebra; Galois q-connection; q-tense operators; Jauch-Piron q-state; q-representable q-effect algebra
It is known that tense operators on a Boolean algebra can be obtained by the canonical construction from a time frame and that this is not true for effect algebras in general. The authors [Soft Comput. 16, No. 10, 1733--1741 (2012; Zbl 1318.03059)] found special conditions that ensures this representation. They introduce a q-effect algebra (an effect algebra with two specific unary operations \(d\) and \(q\) derived from the theory of MV-algebras), q-tense operators (using a Galois connection preserving \(d\) and \(q\)) and q-states. The representation is constructed for q-tense operators on some q-effect algebras (such that every q-state is Jauch-Piron and the set of q-states is order reflecting).
Josef Tkadlec (Praha)
1318.03059