The problem reduction method under uncertainty and decomposition of functions. (English) Zbl 0714.68101
Summary: The problem reduction method provides a useful tool for the design of expert systems. In the method, how to acquire and represent combination functions is an important issue. It is interesting to know whether or not the combination functions can be decomposed. If they do, a complex issue will be much simplified. We discuss the necessary and sufficient conditions under which functions of several variables can be represented by binary operations satisfying some conditions such as associativity and commutativity, especially by triangular norms or conorms.
MSC:
| 68T35 | Theory of languages and software systems (knowledge-based systems, expert systems, etc.) for artificial intelligence |
| 03B52 | Fuzzy logic; logic of vagueness |
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