Complexity Reduction of Mamdani Fuzzy Systems through Multi-valued Logic Minimization

In this paper, we propose an approach to complexity reduction of Mamdani-type Fuzzy Rule-Based Systems (FRBSs) based on removing logical redundancies. We first generate an FRBS from data by applying a simplified version of the well-known Wang and Mendel method. Then, we represent the FRBS as a multi-valued logic relation. Finally, we apply MVSIS, a tool for circuit minimization and simulation, to minimize the relation and consequently to reduce complexity of the associated FRBS. Unlike similar previous approaches proposed in the literature, the use of MVSIS let us deal with nondeterminism, that is, let us manage rules with the same antecedent but different consequents. To allow nondeterminism guarantees to achieve a higher (or at least not worse) complexity reduction than the one achievable from removing nondeterminism as soon as it appears. We apply our approach to six popular benchmarks. Results show a considerable complexity reduction associated only sporadically with consistent accuracy degradation. Moreover, quite surprisingly, the complexity reduction often comes together with an improvement in the classification accuracy.