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Issue:An embedding IF-sets to MV-algebras

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Title of paper: An embedding IF-sets to MV-algebras
Petra Mazureková
Faculty of Natural Sciences, Matej Bel University, Tajovského 40, SK-974 01 Banská Bystrica
Presented at: 3rd International Workshop on Intuitionistic Fuzzy Sets, 3 October 2007, Banská Bystrica, Slovakia.
Published in: Notes on Intuitionistic Fuzzy Sets, Volume 13, Number 4, pages 5—9
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Abstract: MV-algebras and IF-sets were studying in the past. On MV-algebras there is built a good theory of probability. It will be good make use this theory of probability in connection with IF-set. Therefore I essayed about embedding IF-set to MV-algebra. Then we can use known knowledges from MV-algebras. In my contribution I define fundamental notions, like MV-algebra, tribe and IF-set. There I declare and prove, that any IF-set can be embedded to an MV-algebra. This result generalized the previous result of [3], where it was proved only for tribes of all measurable functions.
Keywords: Intuitionistic fuzzy sets, Intuitionistic fuzzy partitions, Intuitionistic fuzzy dynamical systems, Intuitionistic fuzzy entropy
  1. Atanasov, K.: Intuitionistic Fuzzy Sets: Theory and Applications. Physica Verlang, New York 1999.
  2. Cignoli R., D'Ottaviano I.M.L., Mundici D.: Foundations of Many - Valued Reasoning. Kluwer, Dordrecht 2000.
  3. Riecan, B.: On IF-sets and MV-algebras,Proc. IPMU'2006 (accepted)

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