What If We Use Different And -Operations in the Same Expert System

In expert systems, we often face a problem of estimating the expert\u27s degree of confidence in a composite statement A & B based on the known expert\u27s degrees of confidence a = d(A) and b = d(B) in individual statements A and B. The corresponding estimate f&(a,b) is sometimes called an and -operation. Traditional fuzzy logic assumes that the same and -operation is applied to all pairs of statements. In this case, it is reasonable to justify that the and -operation be associative; such and -operations are known as t-norms. In practice, however, in different areas, different and -operations provide a good description of expert reasoning. As a result, when we combine expert knowledge from different areas into a single expert system, it is reasonable to use different and -operations to combine different statements. In this case, associativity is no longer a natural requirement. We show, however, that in such situations, under some reasonable conditions, associativity of each and -operation can still be deduced. Thus, in this case, we can still use associative t-norms