Fault-tolerant software voters based on fuzzy equivalence relations

Redundancy based fault-tolerant software strategies frequently use some form of voting to decide which of the answers their functionally equivalent versions produce is "correct." When voting involves comparisons of floating-point outputs, it is necessary to use a tolerance value in order to declare two outputs equal. Comparing more than two floating-point outputs for equivalence is potentially problematic since, in general, floating-point comparisons based on fixed tolerance may not form an equivalence relation, i.e., the comparisons may not be transitive. The more versions are involved, the more acute this problem becomes. This paper discusses an approach that in some situations alleviates this problem by forming a fuzzy equivalence relation (that preserves transitivity). We applied the method to different voting techniques such as Consensus Voting and Maximum Likelihood Voting. Our analyses, based on simulations, show that voting that uses fuzzy equivalence relations performs better than "classical" voting provided some criteria are met.