[in Japanese]

View full abstract

In this paper we consider two-person zero-sum games with fuzzy multiple payoff matrices. We assume that each player has a fuzzy goal for each of the payoffs. A degree of an attainment of the fuzzy goal is defined and the max-min strategy with respect to the attainment degree of the fuzzy goal is examined. If all of the membership functions both for the fuzzy payoffs and for the fuzzy goals are linear functions, the formulated mathematical programming problem which yields the max-min strategy can reduced to the linear programming problem by making use of Sakawa's method, the variable transformations and the relaxation procedure.

View full abstract

In this paper, we focus on large-scale linear programming problems with the block angular structure which have been solved by the Dantzig-Wolfe decomposition method. By considering the imprecise nature of human judgements, we assume that the decision maker may have a fuzzy goal for the objective function and fuzzy constrains for the coupling constraints. Having elicited the corresponding linear membership functions through the interaction with the decision maker, we adopt the convex fuzzy decision. Then if some simple conditions are satisfied, it is shown that the formulated problem can be reduced to a number of independent linear subproblems and the overall optimal solution is directly obtained just only solving the subproblems. Even if the conditions are violated, it is clarified that the overall optimal solution is obtained by applying the Dantzig-Wolfe decomposition method.

View full abstract

Decision-making in real problems is done in a fuzzy environment. Thus, Fuzzy-Bayes decision rules have been proposed to cope with a fuzzy state of nature. These decision rules are based on the probability of fuzzy events or the possibility measure of fuzzy events. Furthermore, a decision rule based on fuzzy utility functions are constructed. In this paper we discuss a decision rule on possibility distributions of fuzzy events. The object of our study is the decision problem, in which the decision maker obtains the one-peak symmetric possibility distribution of a state of nature and the one-peak symmetric membership function of fuzzy events, by his knowledge and his belief. We propose two decision rules. First, we propose a decision rule based on the concept of the ordering of fuzzy numbers. Second, avoiding the large fuzziness by using extension principle, we propose a simple rule based on the representation interval of the possibility of fuzzy events and the representation value of fuzzy utility function. Furthermore, we construct the setting rule for fuzzy utility as the representation value of fuzzy utility function.

View full abstract

The basic spirit of fuzzy modeling is to deal with vagueness, but from the aspect of application the emphasis is put on the treatment of nonlinearity. Its feature lies in modeling of an object as a system of understandable substructures. Especially, the model proposed by Takagi and Sugeno consists of a set of linear models with membership functions in which the nonlinearity of the system is embedded. In this paper we consider the fuzzy modeling from the viewpoint of finding local linear substructures of a system from given data. The proposal is a clustering technique called the hyperellipsoidal clustering method which takes account of a balance between continuity and linearity of the data distribution.

View full abstract

In this paper, the conventional fuzzy reasoning methods, where the fuzzy relations are defined by using conjunctive functions, are interpreted in view of uncertainty generation rules using necessity measures. The variables in conclusion parts of uncertainty generation rules are regarded as conjunctive variables which represent the possible ranges of disjunctive variables. A disjunctive variable takes only one value in a specified range, whereas a conjunctive variable takes one or more values. Considering the difference between disjunctive and conjunctive variables, a fuzzy reasoning method based on the uncertainty generation rules using necessity measures is formulated. Since the formulated fuzzy reasoning method is resemble to the conventional fuzzy reasoning method using conjunctive function in form, the relationships are discussed. The class of the conventional fuzzy reasoning method interpreted as fuzzy reasoning method under uncertainty generation rules is obtained together with mapping from implication functions to conjunctive functions and the inverse. These obtained mappings represent the correspondence between an implication function used in the necessity measure and a conjunctive function used in fuzzy relation. The properties of the mappings are investigated.

View full abstract

A diagnosis expert system using fuzzy relation can determine the causes of problems from the symptoms. Generally, the system estimates the causes from the symptoms by using the method to solve the inverse problem of fuzzy relational equation. By the way, in this method, if there is a symptom which is not observed, it is inferred that the causes relative to the symptom hardly has possibility from the point of view of solving inverse problem. However, all the symptoms relative to the causes are not always observed in all cases. Therefore, in order to calculate certainty factor of every causes corresponding to any condition of input of symptoms, the certainty factor of the causes is to represented by the index obtained from two different view points; all of symptoms should be observed for each cause, and only part of symptoms can be observed for each cause.

View full abstract

In this paper, we intend to construct an n-person cooperative fuzzy game in characteristic function form for effective formation of international concord. In particular, the fuzziness in evaluating the characteristic function for coalitions is considered, which is treated in terms of an admissible interval of the function for each coalition and represented as the membership function. The fuzzy game is formulated as the fuzzy linear programming problem with fuzzy constraints, which is converted to the parametric programming problem. With this device, all possible solutions of the game are obtained as nucleolus or augmented nucleolus according to the variation of the parameter. These solutions can be found as the crisp number and compared with each other for examining their policy implications.

View full abstract

To express decision making schemes of human beings, the authors have proposed a model based on fuzzy inference. This model fuzzily divides input spaces, which mean the evaluated values for the attributes of the objects, and the total evaluated values are realized with a linear function of the input variables in each sub-space. This paper presents a new decision making model with two more linear functions of the input variables in each sub-space. One of the two linear functions identifies the upper side of the total evaluated values and the other identifies the lower side of the total evaluation. This model can represent the variations of evaluations of human beings to the same objects. The upper side of the model corresponds to the positive evaluation and the lower does the negative one. The differences of the evaluations are represented with the coefficients of the evaluated values for the attributes. A new configuration of fuzzy neural network(FNN) which realizes this model is also presented in this paper. To identify the upper and lower sides, the modified back propagation algorithm proposed by Ishibuchi and Tanaka was used. Experiments were done using the data of impressions to facial expressions and those of the second handed motorcycles too show the feasibility of the new model. The results coincided well with the senses of the subjects. And the model could represent individual characteristics in decision making.

View full abstract

This paper formulates a fuzzy flow shop scheduling problem where the due-date of each job is given as a fuzzy set. The objective function of the problem is to maximize the minimum grade of satisfaction to fuzzy due-dates. A simulated annealing algorithm is applied to this problem. By computer simulations on randomly generated test problems, it is shown that the simulated annealing algorithm with an appropriate choice of a cooling schedule is superior to a local search algorithm. A simple method for modifying the objective function is proposed in order to improve the performance of the simulated annealing algorithm. It is shown by computer simulations on the test problems that the proposed method significantly improves the performance. A modified simulated annealing algorithm by the authors is also applied to the test problems and its robust performance with respect to the choice of a cooling schedule is demonstrated.

View full abstract

Representation of fuzzy set processing on computer systems is an important matter as a basis for the construction of intelligent systems based on fuzzy set theory. Fuzzy sets can be represented in various kinds of data structure and the integration of them is difficult. In this paper, the feasibility of fuzzy set manipulation based on object-oriented paradigm is studied, with the idea that object-orientation has the power of data abstraction and integrating various data structures. The fuzzy set manipulation system FOPS, which was developed as an prototype system, integrates two basic fuzzy set representaions AFS (arrayed fuzzy set) and PFS (paired fuzzy set), and realizes easy manipulation of fuzzy sets by treating fuzzy sets as numbers. It was shown that data abstraction ability and polymorphism in object-orientation are effective for fuzzy set manipulation. Details of internal data structures and evaluation of the developed system are also discussed.

View full abstract

In fuzzy expert systems which support conventional fuzzy reasonings, human interface capabilities, for example, found in rule editors using multiwindows, can be of a comparatively high level. However, such conventional fuzzy expert systems suffer from problems including difficulty with linking user's programs with the shell because rules run on the shell, and slow inference speeds because the shell systems are generally of a scale so large that real-time control is impossible. For these reasons, authors are developing an fuzzy shell FRASH (Fuzzy Realtime Advanced SHell) for a real-time intelligent control system that is expressible in a user's program. This paper mainly describes basic configurations and functions of expression in the FRASH. This shell possesses the following several features : 1) high-speed inference engines in the library format, 2) an online-tuning function for all data related to inferences, 3) an offline editor and an inference display function both using multiwindows, 4) fuzzy frame structures defined by fuzzy slot values, and 5) a fuzzy algorithm compiler using macro codes. We performed simple simulations to inspect the basic function of FRASH. By the simulation, it was proved that the fuzzy reasoning function is fast enough for use in real-time machine control. The fuzzy frame and the fuzzy algorithm functions are useful to complex problems such as macro decision making.

View full abstract

This paper proposes a new fuzzy auto-tuning algorithm for PID controllers with model classification. In the first stage of the tuning the plant is roughly classified based on a result of a plant identification. Then the PID gains are tuned using a fuzzy rule set prepared for the class. The advantage of the proposed tuning algorithm is summarized as follows : (1) The tuning is robust to disturbance, since the PID gains are modified by investigating the output of a plant which is in operation. (2) The proposed algorithm is effective over a wider range of plants than the conventional fuzzy auto-tuning algorithms. (3) Since identification results are used only for classifying plants, tuning performance is less degraded by identification errors than the identification-design method. Both simulation and experimental results for plants with various dead times and first-order-lags show that the proposed algorithm is effective over a wide range of plants.

View full abstract

Shell structures are used for roofs of gymnasiums and exhibition halls, and the structures are subjected to seismic and wind forces which are dynamic. Therefore it is very important to analyze the vibration of the shells to design the structures safely. However this vibration analysis method is negative. This paper presents a method to reduce the displacements and stresses of shells applying the control of fuzzy theory which is called fuzzy control and adjusting the ratios of dampers.

View full abstract