Optical EngineeringContent-addressable-memory for the three key operations of fuzzy logic
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Today, most fuzzy logic operations are performed via software means, which is inevitably slow. While searching for long term hardware solutions to realize analog fuzzy logic operations, the use of the well-developed Boolean logic hardware with analog to digital (A/D) and digital to analog (D/A) converters to implement the digitized fuzzy logic could provide an efficient solution. Similar to Boolean logic, digitized fuzzy logic operations can be written as a minimized sum-of- productterm format, which can then be implemented based on programmable logic arrays. We address a fundamental issue of the computational complexity of this method. We derive the minimum number of the Boolean sum-of-product terms for some key fuzzy logic operations, such as Union, Intersection, and Complement operators. Our derivations provide ways to estimate the general computational complexity or memory capacity of using binary circuits, electronic or optoelectronic, to implement the digitized analog logic operations.