zbMATH — the first resource for mathematics

Vector-valued fuzzy measures on fuzzy quantum posets. (English) Zbl 0781.28005
Summary: The notion of a Hilbert space-valued fuzzy measure on fuzzy quantum posets is studied. Some results about the relation among fuzzy measures, Hilbert space-valued fuzzy measures and fuzzy morphism are mentioned, too.
28E10 Fuzzy measure theory
28B05 Vector-valued set functions, measures and integrals
81P15 Quantum measurement theory, state operations, state preparations
06A99 Ordered sets
Full Text: EuDML
[1] DVUREČENSKIJ A.: Models of fuzzy quantum spaces. (Slovak) In: Proceedings PROBASTAT’89, MÚ SAV, Bratislava, 1989, pp. 96-96.
[2] DVUREČENSKIJ A.: On existence of probability measures on fuzzy measurable spaces. Fuzzy Sets and Systems 43 (1991), 173-181. · Zbl 0742.28009
[3] DVUREČENSKIJ A., PULMANNOVÁ S.: Random measures on a logic. Demonstrate Math. 14 (1989), 305-320.
[4] DVUREČENSKIJ A., PULMANNOVÁ S.: State on splitting subspaces and completeness of inner product spaces. Internat. J. Theoret. Phys. 27 (1988), 1059-1067. · Zbl 0661.46019
[5] HAMHALTER J., PTÁK P.: Hilbert Space Valued States on Quantum Logics. Preprint, ČVUT, Praha, 1989. · Zbl 0767.03034
[6] KRUSZYNSKI P.: Vector measures on orthocomplemented lattices. Math. Proc. A 91 (1988), 427-442. · Zbl 0819.46036
[7] LOEVE M.: Probability Theory. (Russian translation: Teorija rešetok), Izd. Inostr. Lit., Moskva, 1962. · Zbl 0108.14202
[8] LONG L. B.: Fuzzy quantum posets and their states. Acta Math. Univ. Comenian. 58-59 (1991), 231-238. · Zbl 0733.60007
[9] LONG L. B.: A new approach to representation of observables on fuzzy quantum posets. Appl. Math. 37 (1992), 357-368.
[10] PIASECKI K.: On some relation between fuzzy probability measure and fuzzy P-measure. BUSEFAL 23 (1985), 73-77. · Zbl 0588.60005
[11] PULMANNOVÁ S., DVUREČENSKIJ A.: Quantum logics, vector valued measures and representation. Ann. Inst. H. Poincaré Probab. Statist. 53 (1990), 83-95. · Zbl 0742.46030
[12] PTÁK P., PULMANNOVÁ S.: Quantum Logics. (Slovak), Veda, Bratislava, 1989.
[13] PYKACZ J.: Quantum logics and soft fuzzy probability spaces. BUSEFAL 32 (1987), 150-157. · Zbl 0662.03055
[14] RIEČAN B.: A new approach to some notions of statistical quantum mechanics. BUSEFAL 35 (1988), 4-6.
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.