In this paper, we propose a multicriteria decision making (MCDM) method by using a genetic algorithm (GA). The system consists of three phases. In the first phase, a rough set of Pareto optimal solutions is obtained using Kohonen's self organizing map (SOM). In the second phase, the decision maker (DM) selects his preferred sclutions among the obtained set, where the mechanism of GA is used with the DM's preference assisted by radial basis function network (RBFN). In the third phase, the DM can explore the solution space further for the final decision. 0-7803-2559-1/9 § $4.00 0 1995 IEEE

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Abstract. For a vector optimization problem that depends on a parameter vector, the sensitivity analysis of perturbation, proper perturbation, and weak perturbation maps is dealt with. Each of the perturbation maps is defined as a set-valued map which associates to each parameter value the set of all minimal, properly minimal, and weakly minimal points of the perturbed feasible set in the objective space with respect to a fixed ordering cone. Using contingent cones in a finite-dimensional Euclidean space, we investigate the relationship between the contingent derivatives of the three types of perturbation maps and three types of minimal point sets for the contingent derivative of the feasible-set map in the objective space. These results provide quantitative informations on the behavior of the perturbation maps.

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This paper provides some results concerning sensitivity analysis in parametrized Ž convex vector optimization. We consider three types of perturbation maps i.e., . perturbation map, proper perturbation map, and weak perturbation map accord-Ž ing to three kinds of solution concepts i.e., minimality, proper minimality, and . weak minimality with respect to a fixed ordering cone for a vector optimization problem. As for general vector optimization, authors have already established the behavior of the above three types of perturbation maps by using the concept of contingent derivatives for set-valued maps in finite dimensional Euclidean spaces. In this paper we concentrate on convex vector optimization and provide quantitative properties of the perturbation maps under some convexity assumptions. Namely, we investigate the relationships between the contingent derivatives of the perturbation maps and those of the feasible set map in the objective space.

We develop a robust fixed-lag smoother for linear discrete-time systems having outliers both in the process and the observation noises. By modifying the system equation to a linear regression model, a robust Kalman filter and a robust fixed-lag smoother are derived using an M -estimate, Then the robust smoother is constructed using a robust Kalman filter and two robust sub-srnoothers; the outliers in the observation noise are detected by filtering, and those in the system noise are detected by smoothing. Monte Carlo simulations are also presented to show the effectiveness of the proposed algorithms.

In this study we consider the classification (supervised learning) problem in [0 1] n that utilizes fuzzy sets as pattern classes. Each class is described by one or more fuzzy hyperbox defined by their corresponding minimum-and maximum vertices and the hyperbox membership function. Two types of hyperboxes are created: inclusion hyperboxes that contain input patterns belonging to the same class, and exclusion hyperboxes that contain patterns belonging to two or more classes, thus representing contentious areas of the pattern space. With these two types of hyperboxes each class fuzzy set is represented as a union of inclusion hyperboxes of the same class minus a union of exclusion hyperboxes. The subtraction of sets provides for efficient representation of complex topologies of pattern classes without resorting to a large number of small hyperboxes to describe each class. The proposed fuzzy hyperbox classification is compared to the original Min-Max Neural Network and the Gene ral Fuzzy Min-Max Neural Network and the origins of the improved performance of the proposed classification are identified. These are verified on a standard data set from the Machine Learning Repository.

The author has been developing a navigation system for safety for mobile robots, mobility scooters and pedestrians by using depth sensors which can capture range data of image size. If the geometrical relation between the sensor and the space is completely known, each point of the captured range data can be classified into three groups: upper than the ground, on the ground, and lower than the ground. However, it is essential to be able to deal with the unpredictable change of the posture of the sensor due to the movement of the attached body. The author already developed a real-time estimation scheme of the posture including pitch angle, roll angle, and height from the observed data in the framework of optimization. In this paper, the author proposes an estimation scheme based on the state space model and apply Extended Kalman filter for the same application problem. We will compare the algorithms by experimental results and will show the usefulness of the proposed algorithm.