Evolutionary Design of Fuzzy Systems Based on Multi-objective Optimization and Dempster-Shafer Schemes

The paper considers a novel intelligent approach to the design of fuzzy systems based on Multi-Objective Evolutionary Fuzzy Systems (MOEFSs) theory. The presented approach is based on the principle of Pareto optimality using evidence combination schemes of Dempster-Shafer. The evidence combination scheme is used in evolutionary operators of search algorithms during implementation of fitness assignment and solution selection. The paper proposes new representation forms for integral and vector criteria reflecting not only accuracy and complexity of multi-objective fuzzy systems, but also their interpretability characterizing readability of fuzzy-rule base and semantic consistency. The main advantage of the considered MOEFSs is that they satisfy to many criteria simultaneously, which include interpretability properties of fuzzy systems, such as compact description, readability, semantic consistency and description completeness. The novel technique of solution selection and combination based on fusion of fitness estimations from several individuals using Dempster-Shafer theory is proposed. Here, Dempster-Shafer theory allows to select those solutions from Pareto-optimal ones, which are most satisfactory in multi-objective design terms. Solution selection and combination based on probability theory of evidence combination increase objectivity of the best solution selection in evolutionary algorithms. The novel techniques of fitness ranging in evolutionary algorithms and expert preferences integration into MOEFSs design based on Dempster-Shafer modified network models are proposed. The comparison results of MOEFSs design using several evolutionary algorithms are shown in the example of railway task decision. These results prove that the proposed evolutionary design provides a better compromise between accuracy and interpretability in comparison with conventional algorithms.