Publication Date



Technical Report: UTEP-CS-20-72


In many applications of fuzzy logic, to estimate the degree of confidence in a statement A&B, we take the minimum min(a,b) of the expert's degrees of confidence in the two statements A and B. When a < b, then an increase in b does not change this estimate, while from the commonsense viewpoint, our degree of confidence in A&B should increase. To take this commonsense idea into account, Ildar Batyrshin and colleagues proposed to extend the original order in the interval [0,1] to a lexicographic order on a larger set. This idea works for expressions of the type A&B, so maybe we can extend it to more general expressions? In this paper, we show that such an extension, while theoretically possible, would violate another commonsense requirement -- associativity of the "and"-operation. A similar negative result is proven for lexicographic extensions of the maximum operation -- that estimates the expert's degree of confidence in a statement A\/B.