Content-addressable memory implementations for the three key operations of fuzzy logic

Abstract

Today, most fuzzy logic operations are performed via soft- ware 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, digi- tized fuzzy logic operations can be written as a minimized sum-of- product term format, which can then be implemented based on program- mable logic arrays. We address a fundamental issue of the computational complexity of this method. We derive the minimum num- ber of the Boolean sum-of-product terms for some key fuzzy logic opera- tions, such as Union, Intersection, and Complement operators. Our deri- vations 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. © 1999 Society of Photo- Optical Instrumentation Engineers. (S0091-3286(99)00303-7)