Volume 15, 2003

University of Bialystok

Copyright (c) 2003 Association of Mizar Users

**Takashi Mitsuishi**- Miyagi University
**Grzegorz Bancerek**- Bialystok Technical University

- This article concerns a connection of fuzzy logic and lattice theory. Namely, the fuzzy sets form a Heyting lattice with union and intersection of fuzzy sets as meet and join operations. The lattice of fuzzy sets is defined as the product of interval posets. As the final result, we have characterized the composition of fuzzy relations in terms of lattice theory and proved its associativity.

This work has been partially supported by the Polish Academy of Sciences and the Japan Society for the Promotion of Science when the first author was visiting Bia{\l}ystok Technical University as postdoctoral fellow.

- Posets of Real Numbers
- Product of Heyting Lattices
- Lattice of Fuzzy Sets
- Associativity of Composition of Fuzzy Relations

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