The convexity of the set of all fuzzy implications: a systematic way of deriving potential fuzzy implications

The pseudo-strict monotonicity property, a very important property that most of the fuzzy logic connectives fail to have, has been derived from its part of right in the realm of fuzzy logic research. It is extensively discussed and proposed as a compulsory requirement that any inference rule should fulfil. The concept of the convexity principle of the set of all fuzzy implications is proposed as a theoretical and practical framework for generating other potential fuzzy implications and for predicting the properties they exhibit.