Bridging Computational Verbs and Fuzzy Membership Functions Using Computational Verb Collapses

Each noun in natural languages can have attribute values, which are in general adjectives, and action values, which are in general verbs. In the computational verb theory, a computational verb collapse can transform an action value into an attribute value while computational verb extension principles can transform an attribute value into action values. The transformations between attribute values and action values connect fuzzy membership functions to and from computational verb evolving functions. They also set up the relationship between fuzzy logic operations and operations to evolving functions of computational verbs. They help to recover dynamics from the ORing, ANDing and trimmed fuzzy sets. The connections of fuzzy rules and inferences to computational verb rules and inferences are studied based on these transformations. The precise results based on bell-shaped membership functions are presented together with illustrative examples shown in figures. Copyright c © 2006 Yang’s Scientific Research Institute, LLC. All rights reserved.