[in Japanese]

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[in Japanese]

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[in Japanese]

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[in Japanese]

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An approximate reasoning on multiple fuzzy rules has two main methods. One is FATI (First Aggregation Then Inference) and the other is FITA (First Inference Then Aggregation), It is generally known that FATI shows a more specific inference result, in other words, a less vague inference result than FITA. However, FITA is better than FATI from the viewpoint of easiness and the efficiency of computing because FITA makes parallel computing possible. In this paper, we set up the approximate reasoning environment that has sup-t-norm composition, Godel implication, min aggregation, and multiple fuzzy rules with normally partitioned L-R type fuzzy numbers, and then we study the conditions of equivalence of FATI and FITA. Under these conditions, the approximate reasoning method based on FITA can give a less vague inference result.

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In this paper, the author proposes a newly developed concept of fuzzy random vectors(FRVCs), which have intrinsically both properties of fuzziness and randomness and they are considered to be obtained as vague perceptions of ordinary non-fuzzy random vectors. Firstly, fuzzy vectors are introduced by using the set representation approach of fuzzy sets. Secondly, using the proposed fuzzy vectors and the theory of correspondences, FRVCs are defined as the families of measurable correspondences. Some of measurability properties of proposed FRVCs are also investigated. Adopting the multiple-valued logic known as the extension principle of fuzzy sets, the expectations of FRVCs are finally introduced.

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The recognition of hand written characters requires to apply an algorithm which Lakes into consideration of the individual differences. Considering the difference, the author proposes a new method for recognizing hand written Hangul character in terms of consideration of the structure. Hangul characters are basically made of 6 patterns by position. The characters are classified into 6 structure patterns based on the peripheral distributions. The characters are recognized by taking pattern matching with the references in the classified pattern. In the experiment, 95% of 884 characters hand written by 15 persons were recognized correctly by this method.

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This paper presents interactive fuzzy programming for two-level linear fractional programming problems. In our interactive method, after determining the fuzzy goals of the decision makers at both levels, a satisfactory solution is derived efficiently by updating the satisfactory degree of the decision maker at the upper level with considerations of overall satisfactory balance between both levels. An illustrative numerical example is provided to demonstrate the feasibility of the proposed method.

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"SIRMs Dynamically Connected Fuzzy Inference Model" is proposed for plural input fuzzy control. For each input item, a single input rule module (SIRM) is constructed, and a dynamic importance degree is introduced, The dynamic importance degree is defined as the sum of a base value and a dynamic value. The base value is used to insure the role of the corresponding input item at steady state, and the dynamic value is allowed to change in real time with control situations. The output of the model is obtained by summarizing the products of the dynamic importance degree and the fuzzy inference result of each SIRM. Then, constant value control plants are taken into consideration, and the design method of the model is given in detail. In this case, each dynamic value can be determined based on the local information of the corresponding input item. Furthermore, the proposed model is applied to typical first-order delay plants with a lag time and second-order delay plants with a lag time. The simulation results show that the reaching time can be shortened by more than 10% without overshoot or vibration compared with the SIRMs connected fuzzy inference model.

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This paper proposes an efficient usage of the fuzzy c-Means clustering algorithm to obtain optimum solutions of the k-Means hard clustering problem with reasonable certainty. The k-Means clustering problem is formLllated as a mixed integer programming problem. Based on the studies about the stability of solution in a multi-linear form of the energy function of the Hopfield neural network, it is shown that by estimating a local minimum solution in the hypercube of solution space, the coefficients of energy function and a threshold value for deciding 0-1 integer valued solution can be properly estimated. The fuzzy c-Means problem is solved by the affine scaling interior point method for linear programming problems and the Lagrangian multiplier method for maximizing entropy fuzzy clustering. It is shown by numerical simulations that both of the methods outperform the conventional A-Means algorithm in the quality of solutions found.

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This paper considers the inverse problem of nonlinear systems described by the Takagi-Sugeno fuzzy models. The solution to this problem is not unique generally because the correspondence from output to input is one-to-many in a fuzzy model. It is required to develop an algorithm that derives all possible combinations of inputs, together with the confidence of their combinations, The paper proposes an algorithm to solve inverse problems, where the genetic algorithm and the fractional programming are used for the first and the second stages, respectively. However, the fractional programming does not work well when the degrees of confidence of all rules are small. The paper also discusses this problem in the context of future prediction.

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This paper proposes a new method of fuzzy c-means using the entropy function as a regularizing term in the objective function of the fuzzy c-means. An entropy maximization method has already been proposed but introduction of the concept of regularization makes the method of the entropy function more useful, since the use of regularization implies that the entropy method can be discussed within the alternative optimization of the general fuzzy c-means algorithm. Consequently, variations of the standard fuzzy c-means such as the fuzzy c-varieties can be transformed into corresponding methods using the regularization by the entropy. Thus, a method of fuzzy c-varieties by the entropy can be developed. The standard method of fuzzy c-means generates a set of fuzzy prototype classification functions by which the membership of a new observation to each cluster is calculated. This means that the entropy method generates a set of new fuzzy classification functions. Theoretical properties of the classification functions by these two methods are investigated, and the way in which the classification functions and the Voronoi diagram in the computational geometry are related is disclosed. A numerical example is given to compare the clustering results and the classification functions.

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This paper develops a stable fuzzy control scheme for a general class of nonlinear systems. Using the concept of local design and global interpolation, the developed scheme starts by probing the operating region of an unknown nonlinear system to determine a set of local points. Simple linear controllers are designed around these local points. The global control is then formed by interpolating these local controllers through a fuzzy modeling algorithm. One of the important features is that the fuzzy modeling algorithm used is adaptive in nature. which refines repeatedly the initial set of local points and interpolate to form a sequence of updated global controllers until the performance of the control system is satisfactory. The second feature is that such an adaptive design process can be shown to deliver a stable fuzzy controller. The analysis has been carried out to derive the conditions under which the stability of the overall control system are maintained. It appears that with the appropriate choices of learning parameters, there will be a guaranteed stability of the close-loop system. The third feature of the proposed scheme is that almost nothing is assumed about the dynamics of the nonlinear system to be controlled during the construction of the controller, This is unlike many of the nonlinear control techniques which require a detailed process model h order to design the control system. An illustrative example is also included to show the control system performance for the pH control, which is a typical nonlinear control problem.

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Fuzzy value is a special type of Fuzzy sets on the closed interval [0.1] which is a generalization of triangular type Fuzzy sets. In this note we define. between two Fuzzy values A, B, a distance D(A, B) which is also a Fuzzy value and called a FuZZy distance. Topological properties with respect to the Fuzzy distance will be investigated in further papers.

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The fuzzy structural Modeling (FSM) method, which is a technique to arrange elements in a hierarchy by applying the fuzzy theory to the data obtained from paired comparisons, has been developed. In order to elucidate the structure of the usability for operating systems. we proposed to use the FSM method. In two questionnaire surveys, the subjects were asked to compare two items, which describe the problems in operating the operating systems, according to the importance for the usability. The results from the FSM method showed that Microsoft Windows for personal computers and UNIX for work-stations had different structures of the usability. These results indicated that the FSM method would provide useful information for the usability of computer systems.

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