Non-commutative System of Fuzzy Interval Logic Generated by the Checklist Paradigm Measure m 3 Containing Early Zadeh Implication

Abstract

This paper continues investigation of systems of fuzzy interval logics based on the Checklist Paradigm semantics of Bandler and Kohout [1] [2]. While the early papers dealt with checklist paradigm based interval systems containing commutative AND and OR, this paper is the fifth in the series of papers in which we have been describing the systems in which these connective types are non-commutative. In the present paper we investigate non-commutative interval system generated from implication operators based on the Checklist Paradigm measure m 3 of Bandler and Kohout. This system includes the well-known Early Zadeh implication operator (PLY) which is not contrapositive. While the commutative systems can be sufficiently characterized by an 8-element group of transformations, the non-commutative systems require the 16 element group ${\mathcal S}_{2 \times 2 \times 2 \times 2}$.