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This paper indicates that most of fuzzy translating rules for a fuzzy conditional proposition “If x is A then y is B” with A and B being fuzzy concepts can lead to very reasonable consequences which fit our intuition with respect to several criteria such as modus ponens and modus tollens. Moreover, it is shown that a syllogism holds for most of the methods under the new compositions, though they do not always satisfy the syllogism under the max‐min composition.

Triangular norms have been around since the early 1940s and have been used in the context of statistical metric space. A number of examples of existing t‐norms are given which are known to provide good models of fuzzy set‐theoretic intersections. Pictorial representations of t‐norms that have been made with the aid of a computer are presented and the relationship between t‐norms and parametrised t‐norms is discussed in this context. Several new examples of t‐norms are proposed using triangular functions.