Klein Groups in Fuzzy Inference

We discuss the structural properties of Klein four-groups and the factor groups of Klein four-groups formed over particular collections of fuzzy propositions and their fuzzy normal forms. We consider three alternative collections of operators, namely, (i) max, min; (ii) probabilistic sum, product; (iii) bold union, bold intersection. We show that these structural properties (i) provide a base for some desirable results associated with human approximate reasoning, and (ii) improve the design of expert systems with considerable programming advantage.