Zadeh introduced fuzzy theory during the 1960s. It has since been embraced by many researchers, particularly the Japanese, who have spent considerable effort on controllers and expert systems based on fuzzy logic. Fuzzy logic has also been warmly embraced by neural network researchers (see Kosko [1]).
Fuzzy logic circuits have been implemented in, among other technologies, current mode logic form, which is usually referred to as emitter-coupled logic (ECL) [2,3]. The authors devote their attention to multiple-input maximum and minimum current mode logic circuits. Both these circuits are necessary for implementing real-time fuzzy controllers and fuzzy inference engines (processors) that rely on such maximum and minimum functions. Yamakawa et al. had previously formulated maximum fuzzy logic circuits in terms of simultaneous rounded-difference equations [2] (multiple-input minimum circuits can be readily derived from these by applying De Morgan’s theorem). Such circuits are, however, restricted to two simultaneous inputs. Multiple-input max/min circuits can be constructed using these components as building blocks in binary tree form.
The authors use this approach as the starting point for their NMOS current mirror, positive feedback design. After providing a mathematical proof for the multiple-input extension, they summarize first the DC characteristics of a three-input implementation using MOS transistor arrays, and second the transient performance of this implementation as derived from a Spice2 simulation. In considering the downscaling of these MOS transistors (from a fabrication perspective), they suggest that the resulting decrease in parasitic capacitance should increase operational speed. Moreover, analog fuzzy circuitry may be more feasible than digital because it is less susceptible to the increase in threshold voltage resulting from downscaling. Finally, the number of transistors of the proposed max circuit is shown to increase as O(n2) where n is the number of inputs. In the two-input binary tree realization, transistors increase as O(log n). Furthermore, errors do not accumulate, which increases the overall accuracy. The effect of transistor mismatching within the multidrain current mirrors is not discussed, however.
One annoying aspect of this paper, which was largely beyond the authors’ control, is the time it has taken to be published. The manuscript was first submitted in September 1987 (which means the work was probably conducted during 1986), revised in August 1988, and eventually published almost two years later. This publishing bottleneck has been a lamentable feature of IEEE Transactions on Computers for some time now, even after the page allocation was increased. Readers of Computing Reviews are being informed of research that is almost five years out of date. No offense to the authors, but the field of fuzzy logic has advanced during the intervening years (see Gupta and Yamakawa [4]).
