Publication Date




Published in the Proceedings of the Joint 9th World Congress of the International Fuzzy Systems Association and 20th International Conference of the North American Fuzzy Information Processing Society IFSA/NAFIPS 2001, Vancouver, Canada, July 25-28, 2001, pp. 1991-1996.


Traditionally, in logic, only unary and binary operations are used as basic ones - e.g., "not", "and", "or" - while the only ternary (and higher order) operations are the operations which come from a combination of unary and binary ones. For the classical logic, with the binary set of truth values {0,1}, the possibility to express an arbitrary operation in terms of unary and binary ones is well known: it follows, e.g., from the well known possibility to express an arbitrary operation in DNF form. A similar representation result for [0,1]-based logic was proven in our previous paper. In this paper, we expand this result to finite logics (more general than classical logic) and to multi-D analogues of the fuzzy logic - both motivated by interval-valued fuzzy logics.