The Checklist paradigm based non-commutative interval systems of Early Zadeh with their crispness and fuzziness

Five logic systems based on the Checklist paradigm by Bandler and Kohout investigated the systems of connectives that can be generated from the intervals of implication operator by means of group transformations. This paper further studies the relationships of their several fuzzy interval logic systems; in particular, the non-commutative system of Early Zadeh and its relationship with Kleene-Dienes and with the crispness/fuzziness of left/right proposition (i.e. a or b) by means of group transformation. The crispness and fuzziness of propositions play an important role in expressing the dependencies between the logic systems.