Geodesic
Semisimple Algebras of Infinite Valued Logic and Bold Fuzzy Set Theory
Canadian journal of mathematics, Tome 38 (1986) no. 6, pp. 1356-1379

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In classical two-valued logic there is a three way relationship among formal systems, Boolean algebras and set theory. In the case of infinite-valued logic we have a similar relationship among formal systems, MV-algebras and what is called Bold fuzzy set theory. The relationship, in the latter case, between formal systems and MV-algebras has been known for many years while the relationship between MV-algebras and fuzzy set theory has hardly been studied. This is not surprising. MV-algebras were invented by C. C. Chang [1] in order to provide an algebraic proof of the completeness theorem of the infinitevalued logic of Lukasiewicz and Tarski. Having served this purpose (see [2]), the study of these algebras has been minimal, see for example [6], [7]. Fuzzy set theory was also being born around the same time and only in recent years has its connection with infinite-valued logic been made, see e.g. [3], [4], [5]. It seems appropriate then, to take a further look at the structure of MV-algebras and their relation to fuzzy set theory. 
Belluce, L. P. Semisimple Algebras of Infinite Valued Logic and Bold Fuzzy Set Theory. Canadian journal of mathematics, Tome 38 (1986) no. 6, pp. 1356-1379. doi: 10.4153/CJM-1986-069-0
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