States on soft fuzzy algebras - finite and countable additivity

Rok, strany: 1992, 125 - 134

We bring a summary of recent results on states on soft fuzzy algebras (s. f. algebras) and point out some of their explicit consequences. We are mainly interested in the characterization of state spaces, the enlargements of s.f. algebras related to states, extensions of states, etc. A special attention is paid to the comparison of results for finitely additive states and for countable additive states. The basic technical tool for our investigation is a Boolean representation of s.f. algebras, which, we believe, might shed light on many questions of fuzzy logics, too (see [G. Cattaneo, M. L. Dallachiara, R. Guintini: Empirical semantics for fuzzy-intuitionistic quantum logic, to appear], [G. Cattaneo, M. L. Dallachiara, R. Guintini: Fuzzy intuitionistic quantum logics, to appear], [C. A. Drossos, M. Shakhatreh: Boolean methods in $F$-quantum spaces, Tatra Mountains Math. Publ. 1 (1992)], [A. Dvurečenskij: On a representation of observables in fuzzy measurable spaces, J. Math. Anal. Appl., to appear], [M. Navara: Algebraic approach to fuzzy quantum spaces, to appear], [J. Pykacz: Fuzzy set ideas in quantum logics, in: Proc. Conf. Quantum Logics, Gdańnsk, Poland, 1990].

ISO 690:

Navara, M., Pták, P. 1992. States on soft fuzzy algebras - finite and countable additivity. In Tatra Mountains Mathematical Publications, vol. 1, no.1, pp. 125-134. 1210-3195.

APA:

Navara, M., Pták, P. (1992). States on soft fuzzy algebras - finite and countable additivity. Tatra Mountains Mathematical Publications, 1(1), 125-134. 1210-3195.