Two statistics, termed rFGC(revised Fuzzy Grouping Criterion)and rFGC^*, to get fuzzy clusters suited for data in the fuzzy c-means method are presented. These are revisions of FGC by making use of the ratio of the attainable within-clusters variance to the total variance even if the population has no clusters. The rFGC is a statistic to estimate the number of clusters and the rFGC^* is one to estimate the degree of fuzziness of clusters. The performance of two statistics was examined by a simulation study in several dimensional normal population. The rFGC could detect no clusters, though the pseudo-F and FGC failed. The rFGC, pseudo-F and FGC could estimate the true number of clusters if data had well separated clusters. The rFGC had a 'conservative' property, though the pseudo-F and FGC had an'overfitting' property. The goodness of the degree of fuzziness was assessed by the mean squared error(MSE)of estimated cluster centers. The non-fuzzy clustering gave relatively large MSEs if population had overlapping clusters. The fuzzy clustering with fixed m=2 gave relatively large MSEs if population had well separated clusters or if data dimension was large. Wherase, the clustering by rFGC^* gave relatively small MSEs in all cases. It is found objectively that the fuzzy clustering with an appropriate degree-of fuzziness, which can be obtained by rFGC^*, is better than both the non-fuzzy one and the fuzzy one with fixed m=2 from the viewpoint of MSE.

Soft-computing applications for music are increasing in recent years. They are regarded as suitable solutions for musical information processing. In this paper, an application for a multi-modal conducting simulator is mentioned. It recognizes human conducting and behaves like an orchestra in real-time. Even for the same conducting intention, both the gesture characteristics and the time-domain structure vary depending on the conductor, and on the connection between previous or latter parts. Soft-computing is applied for recognition to cope with both these variance and to detect conductor's intention. The beat recognition process is built on the model of actual musicians' recognition processes. The right-hand conducting gesture is captured by accelerometers and recognized with HMM(Hidden Markov Models). Based on interviews with conductors and orchestra players, musical score information and performance information are also applied to the recognition on the fuzzy model. The watching point and breath of a user is detected with a eye tracker and a breath sensor, respectively. To shape the musical performance in real-time, the system recognizes important and universal conducting elements conforming to the grammar of conducting : i.e., beginning and ending of a piece, Einsatz(cue for a player or a part, an important direction by a conductor)with eye, beat timing including Agogik(rubato, changes in tempo), the beat number in a measure, fermata(to lengthen notes or rests arbitrarily, to pause), Dynamik(dynamics), some aspects of articulation(i.e.espressivo-staccato), and breathing. The system simulates orchestra response to correct breathing and Einsatz by a user. It also simulates sounding delay and autonomy of actual orchestra. When the autonomous degree is 100%, the system ignores the conducting input and plays with tempo on music data. When the autonomous degree is 0%, the system is glued to the conducting. In this case, when the conducting gesture stops, the system stops replay simultaneously and waits until the next beat input.

In this paper, we focus on mixed 0-1 programming problems and propose an approximate solution method by combined use of the Benders' patitioning procedures and genetic algorithms. After overviewing the Benders' patitioning procedures, we examine how to apply genetic algorithms to the subproblems with 0-1 variables. Then we propose a coding method for applying genetic algorithms to the subproblems and a new decoding method for satisfying the constraints. Through computational experiments, the feasibility and efficiency of the proposed method are examined and compared with the branch and bound method for mixed 0-1 programming problems with respect to CPU time and perfomance.

In this paper, we consider the stabilization of sampled-data fuzzy systems. We first consider sampled-data fuzzy models and the design of stabilizing state feedback controllers and asymptotically convergent observers. We shall show that if there exist a stabilizing state feedback controller and an observer, then the output feedback controller based on them always stabilizes the sampled-data fuzzy model. Finally we design an output feedback controller of a mass-spring system to illustrate our design procedures.

In this paper, we consider two-level programming problems in which there are one decision maker(the leader)at the upper level and two or more decision makers(the followers)at the lower level and decision variables of the leader and the followers are 0-1 variables. We assume that there is coordination among the followers while between the leader and the group of all the followers, there is no motivation to cooperate each other, and fuzzy goals for objective functions of the leader and followers are introduced in order to take fuzziness of their judgements into consideration. The leader maximizes the degree of satisfaction(the value of the membership function)and the followers choose in concert so as to maximize a minimum among their degrees of satisfaction. A computational method, which is based on the genetic algorithms, for obtaining a solution to the above mentioned problem is developed. To demonstrate the feasibility and efficiency of the proposed algorithm, computational experiments are carried out.

In this paper we consider a production model in which multiple decision makers pool resources to produce finished goods. Such a production model, which is assumed to be linear, can be formulated as a mathematical programming problem with fuzzy parameters from the viewpoint of experts' imprecise or fuzzy understanding of the nature of parameters in a problem-formulation process. It is shown that a cooperative game with values of coalitions represented by fuzzy numbers arises from the linear production programming problem with fuzzy parameters, and such a game is referred to as a fuzzy linear production programming game. The values of coalitions in the game can be obtained by employing a parametric approach to solving the linear production programming problem with fuzzy parameters. We employ the α-core, which is the extended core in fuzzy cooperative games, as a solution concept. It is proven that the α-core of the game is not empty, and a computational method is developed.

In this paper we deal with two-level mixed zero-one programming problems with zero-one upper level decision variables and continuous lower level decision variables. After the decision maker(DM)at the upper level chooses a strategy, the DM at the lower level chooses a strategy with full knowledge of the strategy of the DM at upper level in the two-level programming model. Such strategies are called Stackelberg solutions when the two DMs are in a noncooperative situation. We develop computational methods through genetic algorithms for obtaining the Stackelberg solutions. To demonstrate the feasibility and efficiency of the proposed methods, computational experiments are carried out and comparisons between the methods based on the branch-and-bound techniques and the proposed methods are presented.