Non-Commutative Fuzzy Interval Logics with Approximation Semantics Based on the Checklist Paradigm and their Group Transformations

This paper continues investigation of systems of fuzzy interval logics based on the checklist paradigm semantics of Bandler and Kohout (1993). While the previous work was mainly concerned with the interval systems containing commutative AND and OR, this paper describes the system in which these connective types are non-commutative. While the commutative systems can be sufficiently characterized by an 8-element group of transformations, the non-commutative require the symmetric 16 element group S_{2times2times2times2}