Modeling architectures for VLSI Implementations of Fuzzy Logic Systems

Fig. 3 Total silicon area versus number of inputs (n), with number of fuzzy sets constant List of Symbols n Number of inputs p Number of fuzzy sets A f Device area for fuzzifier circuit A m Device area for multiplier circuit A tad Total active device area A ts Total silicon area A s Device area for a summer circuit A ic Device area of intersection block A ti Total area for interconnect λ scaleable metric which is used to describe the dimensions of the tracks and contacts. [Werntges93] Werntges, HW " Partitions of unity improve neural function approximation " , Number of Inputs n Silicon Area (arb. units, log scale) A tad-A ti fuzzy set to the appropriate intersection block. The number of transmission nodes is equal to the number of distinct fuzzy sets (np). The intersection block determines the firing degree of each rule in the system. In this work the product operator was used for intersection and as a result this block essentially consists of a number (n-1) of two variable multipliers. The firing degree of each rule is then passed to the corresponding implication block for each rule. This implication circuit is a two variable multiplier, as this work employs the zero-order Sugeno fuzzy model. Finally the outputs of the implication blocks are summed to provide the crisp result. This stage has been simplified (by not performing the division) by assuming the fuzzy partitioning strategy has a partition of unity [Werntges93]. The full paper will present a detailed mathematical description of the derived model. In this abstract only the results of this model are presented, thus providing an approximation of the total silicon area in terms of the total active device area and the total interconnect area. The total active device area A tad can be approximated in terms of both the area number of circuits in the fuzzy reasoning system as given by: A tad = nA f + np n A m + A s where the variables are defined in the list of symbols at the end of this abstract. Similarly the total interconnect area depends on the size and number of tracks. The tracks between the transmission nodes and the intersection circuits account for the majority of the interconnect requirement in this fuzzy reasoning system, as illustrated in Fig. 1. The developed model offers two methods of determining the area required …