Interpretation and Unification of Fuzzy Set Operators

Fuzzy logic provides a way to model the events or conditions that have inherent uncertainties, i.e. imprecisely defined. The approximate reasoning capability of Fuzzy logic [FL) aids in development decision support/expert system which can be used as a powerful tool for implication or inference. Fuzzy logic has been used in variety of applications such as: event detector in situation & threat assessment, image analysis (detection of edges, feature extraction, classification and clustering), parameter estimation, electronically stabilized camcorders, subway trains, auto, focus cameras, and air conditioners etc. In this paper, we study Fuzzy logic operators such as T-norm and S-norm, and show some interconnectivities/relations between T norms and S-norms, different implication functions/methods, and relations between Fuzzy logic operators and Fuzzy implications. The application of Fuzzy logic is demonstrated using one engineering example and a sensitivity study is carried out to evaluate the system performance w.r.t. different aggregation methods.