Fuzzy Set operator unification and interpretation

Fuzzy Logic (FL) facilitates modeling of within-the-event uncertainty. The crisp logic models the ‘between the events’ uncertainty. Fuzzy techniques in the form of approximate reasoning aid decision making with powerful reasoning capabilities. The FL techniques have been used in varieties of applications: i) image analysis, detection of edges, feature extraction, classification, and clustering, ii) parameter estimation of unknown dynamic systems, iii) home appliances – washing machine, air conditioning systems, and iv) decision fusion, situation and threat assessment. In this report, we study FL concepts, fuzzy sets, several membership functions and their properties, FL operators, fuzzy proposition and attempt to bring out relationships, interconnectivities, contradistinctions between various operations/operators and unification. Illustrative example is presented to make the above concepts very clear.