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Weakly Divisible MV-Algebras and Product

✍ Scribed by Anatolij Dvurečenskij; Beloslav Riečan

Publisher
Elsevier Science
Year
1999
Tongue
English
Weight
686 KB
Volume
234
Category
Article
ISSN
0022-247X

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✦ Synopsis

We introduce weakly divisible MV-algebras and we show that every weakly divisible a-complete MV-algebra is isomorphic to the system of all continuous fuzzy functions defined on some compact Hausdorff space which generalizes a result of Di Nola and Sesse (in "Non Classical Logics and Their Application to Fuzzy Subsets," Kluwer Academic, Dordrecht, to appear). This enables us to define an associative and commutative product on weakly divisible a-complete MV-algebras with a multiplicative unity 1. As an application, we show that any system of observables on this MV-algebra admits a joint observable with respect to this

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