[in Japanese]

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[in Japanese]

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This paper deals with an exponential possibility distirbution and its application to discriminant analysis. First, possibility analysis based on exponential possibility distributions is discussed with possibility and necessity measures in contrast with statistical analysis. Second, the identification method for obtaining the possibility distribution from the given data is formulated. Then, using two possibility distributions, the possibility discriminant rule is obtained. Third, given two possibility distributions, the possibility disciriminant analysis is formulated by the possibility or the necessity measure. This problem of disciminant analysis can be described as finding a feature vector that minimizes the possibility or the necessity measure. This problem can be reduced to an eigenvalue problem. An unknown input can be classified by the possibility discriminant rule. Furthermore, this discriminant analysis is extented to the case where several unknown inputs are given. In this case, more clear classification might be obtained than one unknown input because of more information. Last, numerical examples are shown to illustrate our proposed methods.

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Since a fuzzy linear regression model was proposed in 1987,its possibilistic models are employed to analyze data. From view points of fuzzy linear regression, data are understood to express the possibilities of a latent system and the fuzzy linear regression is aimed to model them. On the other hand, when data have error or data are very irregular, the obtained model unnaturally has too wide possibility ranges. In this paper we propose a fuzzy linear regression for data with error to minimize the total error between the model and data, and also to build as clear and lucid a model as possible. The effectiveness of the proposed model is shown using numerical examples.

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This article is intended to present a 0-1 knapsack problem with multiple constraints under fuzzy environment, which all coefficients in the problem are represented as fuzzy numbers. We propose an approximate algorithm for solving the problem without transforming it into a crisp problem, keeping coefficients as fuzzy numbers in the process of the calculation. In the interpretation of the constraints, the degree satisfying the inequality relation between fuzzy numbers is defined on the basis of the agreement index. This degree is related to the areas of the membership functions of the fuzzy numbers in both sides of the constraint, so it takes into account the shapes of fuzzy numbers. The proposed algorithm is compared with the algorithm based on possibility theory, and the properties and differences of the solutions are shown.

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We expand the definition of Ishibuchi and Tanaka's order relation between intervals by means of the left and right limits, center, and width of an interval, and propose the new definition by introducing two kind of parameters, that is, one is the degree between partial and total order relation, the other is the degree of a decision maker's preference for the expectation and the pessimistic value. A variety of setting of the parameters enable him to control the number of maximal/minimal intervals and to reflect his preference in the order relation between intervals. We try to apply this definition to the shortest path problem which is one of the simple and basic network problems and has a wide range of applications. Let each arc in the network be transportation time or cost instead of distance. However, the time and cost fluctuate depending on traffic conditions, payload and so on. Therefore, each arc has better be represented as interval composed a pair of optimistic and pessimistic values. In order to solve the interval version of the problem, we expand the Dijkstra's algorithm, and propose a new algorithm for obtaining some incomparable interval lengths along the routes. When too many routes exist for the decision maker to select the best one, he can reduce the number of routes by altering of the parameters. Finally, A large scale example based on the proposed algorithm is shown and the effectiveness is demonstrated.

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We have fuzzy mathematical programming and stochastic programming which are used in making a plan under uncertainty. Stochastic programming has a merit of dealing with dependency among coefficients that is not dealt with by fuzzy mathematical programming. One of the popu-lar methods of stochastic programming is probabilistic constrained programming problems(PCPP). Generally speaking, if probabilistic distribution is continuous, PCPP are nonlinear programming problems. But if probabilistic distribution is discrete, PCPP are mixed 0-1 integer programming problems. In this paper, considering a merit of technique to solve, we express discrete distribution as scenarios. PCPP optimize objective functions after setting probability level. But it may be difficult for decision maker to set probability level uniquely and to catch a relation between objective functions and probability level. In this paper we propose a method of dealing with flexibly a relation between objective functions and probability level using fuzzy goal and interactive method.

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In this paper, we propose a fuzzy programming method for the solution of multiobjective linear continuous optimal control problems. When a system of differential equations is linear, the state variables of the system at any fixed time are described by definite integrals, whose integrand is linear in the control functions. Upon use of a suitable numerical integration formula, each of the definite integrals is approximately replaced by a weighted sum of a finite number of variables, we can formulate approximate linear multiobjective programming problems. Then by considering the vague nature of human judgements, we assume that the decision maker may have fuzzy goals for the objective functions. Having elicited the corresponding linear membership functions through the interaction with the decision maker, if we adopt the fuzzy decision for combining them, it is shown that the formulated problem can be reduced to a linear programming problem and the satisficing solution for the decision maker can be obtained through the simplex method of linear programming. An illustrative numerical example is worked out to indicate the efficiency of the proposed method.

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We propose a fuzzy algorithm with matrix representation for controlling actual systems, e.g.an.ove-rhead crane. Both the very slight swing and the very short running time during travel process are required for safe and quick operation of an overhead crane. The simple fuzzy algorithm with matrix representation, however, seems not to be very effective for reducing the swing and shortening the running time. We use the fuzzy adaptation algorithm with matrix representation for controlling an overhead crane. The fuzzy adaptation algorithm with matrix representation provides with adequate parameters of the control system based on the load mass, rope length and travel distance. This method is verified to be very effective in control of a scale model of an overhead crane.

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Automatic control of bulldozer is not easy, because (1)the operational techniques requires skillfulness, (2)the goal and environment of operation is various and (3)there is no sensor as excellent as human. We develop here a partially automatic control system for bulldozer where operator and controller cooperate together. That is, operator is in charge of recognition of circumstances and special manual operation if necessary. On the other hand, controller operates in normal condition and releases human from the simple but serious jobs. Fuzzy controller is most suitable for this kind of man-machine system. We first develop a simulation model of bulldozer under some assumptions. We obtain some principles of control from both simulation study and analysis of human operation. Next, these principles are substituted by a conventional PID controller. This controller acts well if we suppose that some special sensors are applicable and also the goal and the circumsutances of operation are fixed. However, these suppositions aren't practical. Then we study fuzzy control rules which cover all cases expected in real operation. Since the results of simulation study for this fuzzy controller are very good, we design a real fuzzy control system which is carried by a real bulldozer. This system is tested in the field with some different topography and its results are almost equivalent to those of skilled operator.

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For applying fuzzy inference method to multi-input systems, the followings are required : (1)Explosion of the number of fuzzy rules is suppressed; (2)Computaion time for the fuzzy modeling is made short; (3)Fuzzy modeling with insufficient data is made possible; (4)Obtained fuzzy rules are clear and comprehensible. This paper presents a constructing method of fuzzy inference networks for multi-input systems. The new method can satisfy the above requirement. The new method is applied to knowledge acquisition of avoiding rules for a ship and the feasibility of the new method is shown.

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