A fuzzy voting scheme for hardware and software fault tolerant systems

Voting algorithms are used to arbitrate between the results of redundant modules in fault-tolerant systems. Inexact majority and weighted average voters have been used in many applications, although both have problems associated with them. Inexact majority voters require an application-specific 'voter threshold' value to be specified, whereas weighted average voters are unable to produce a benign output when no agreement exists between the voter inputs. Neither voter type is able to cope with uncertainties associated with the voter inputs. This paper introduces a novel voting scheme based on fuzzy set theory. It softens the harsh behaviour of the inexact majority voter in the neighbourhood of the 'voter threshold', and handles uncertainty and some multiple error cases in the region defined by the fuzzy input variables. The voter assigns a fuzzy difference value to each pair of voter inputs based on their numerical distance. A set of fuzzy rules then determines a single fuzzy agreeability value for each individual input which describes how well it matches the other inputs. The agreeability of each voter input is then defuzzified to give a weighting value for that input which determines its contribution to the voter output. The weight values are then used in the weighted average algorithm for calculating the voter final output. The voter is experimentally evaluated from the point of view safety and availability, and compared with the inexact majority voter in a Triple Modular Redundant structured framework. The impact of changing some fuzzy variables on the performance of the voter is also investigated. We show that the fuzzy voter gives more correct outputs (higher availability) than the inexact majority voter with small and large errors, less incorrect outputs (higher safety) than the inexact majority voter in the presence of small errors, and less benign outputs than the inexact majority voter. The percentage of the benign outputs of the majority voter that are successfully handled by the fuzzy voter (resulting in correct outputs) is more than the percentage of those that are unsuccessfully resolved by the fuzzy voter (resulting in incorrect outputs). Our results suggest that the fuzzy voter is a viable alternative to a traditional inexact voter in cases where the benefits of a large increase in availability, and a considerable decrease in the number of benign outputs outweighs the cost of a small degradation in the safety performance of the system. The fuzzy voter is also a useful voting algorithm when arbitrating between the responses of dynamic channels of control systems incorporating uncertainties. This is the first reported use of a complete fuzzy voter in the context of fault tolerance.