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Developing Takagi-Sugeno fuzzy models by evolutionary algorithms mainly requires three factors: an encoding scheme, an evaluation method, and appropriate evolutionary operations. At the same time, these three factors should be designed so that they can consider three important aspects of fuzzy modeling: modeling accuracy, compactness, and interpretability. This paper proposes a new evolutionary algorithm that fulfills such requirements and solves fuzzy modeling problems. Two major ideas proposed in this paper lie in a new encoding scheme and a new fitness function, respectively. The proposed encoding scheme consists of three chromosomes, one of which uses unique chained possibilistic representation of rule structure. The proposed encoding scheme can achieve simultaneous optimization of parameters of antecedent membership functions and rule structures with the new fitness function developed in this paper. The proposed fitness function consists of five functions that consider three evaluation criteria in fuzzy modeling problems. The proposed fitness function guides evolutionary search direction so that the proposed algorithm can find more accurate compact fuzzy models with interpretable antecedent membership functions. Several evolutionary operators that are appropriate for the proposed encoding scheme are carefully designed. Simulation results on three modeling problems show that the proposed encoding scheme and the proposed fitness functions are effective in finding accurate, compact, and interpretable Takagi-Sugeno fuzzy models. From the simulation results, it is shown that the proposed algorithm can successfully find fuzzy models that approximate the given unknown function accurately with a compact number of fuzzy rules and membership functions. At the same time, the fuzzy models use interpretable antecedent membership functions, which are helpful in understanding the underlying behavior of the obtained fuzzy models.

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The steepest descent search algorithm is modified in conjunction with chaos to solve the optimization problem of an unstructured search space. The problem is that given only the gradient information of the quality function at the present configuration, X(t), we must find the value of a configuration vector that minimizes the quality function. The proposed algorithm starts basically from the steepest descent search technique but at the prescribed points, i.e., local minimum points, the chaotic jump is performed by the dynamics of a chaotic neuron. Chaotic motions are mainly caused because the Gaussian function has a hysteresis as a refractoriness. An adaptation mechanism to adjust the size of the chaotic jump is also given. In order to enhance the probability of finding the global minimum, a parallel search strategy is developed. The validity of the proposed method is verified in simulation examples of the function minimization problem and the motion planning problem of a mobile robot.