Since the theory of fuzzy set was proposed in 1965 by Dr.Zadeh, the number of researches about the fuzziness implied in the natural language, as well as, its application in many fields has been reported. In this paper, we propose a solution method for fuzzy relation inequality R o A=B^*, an extension of fuzzy relation equation R o A=B with a very promising field of application. In addition, aiming to show an effective solution method of fuzzy relation inequality as a decision support in a fuzzy environment, we present an example of its application as a decision support to an examination for service.

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To identify the control actions of an experienced operator as fuzzy inference rules is one of the methods to design fuzzy controllers. But, it is very difficult to determine the shape of membership functions and fuzzy partitions. Recently, some useful methods have been proposed, such as the methods using the structures or learning methods of neural networks, or identifying the parameters defining the shape of membership functions by some kinds of optimization methods. But, in these methods, the number of rules have to be fixed before identifying the parameters of the membership functions. In this paper, we propose a new method to obtain fuzzy inference rules by generating new rules iteratively. New rules are generated in the region with the highest inference error, divided by the membership functions of antecedent part. Parameters of the membership functions are adjusted by applying the steepest descent method. So, the proposed method can automatically determine the number of rules necessary to identify the input-output relationship of the objective system. In order to prove the effectiveness of the proposed mothod, some numerical examples and an application to a mobile robot to avoid obstacles are reported.

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I n many of previous fuzzy inference methods, it has been necessary for an organization of the multi-input/output system to investigate a set of inference rules directly in the multidimentional input space. This fact is considered to make the construction of the system more complexly and difficult. An ordinal structure model of the fuzzy reasoning proposed in this paper is defined as a partially ordered set in which each proposition is arranged in order according to some human's sense of relative priority or importance of each rule. This paper presents some characteristics of this model and restricted conditions on the consequence. Furthermore, a few applications of the model to design fuzzy controller in multidimentional system are investigated.

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There are several methods of vibration control of structures. In this paper, damping ratios of dampers of multi-degree-of-freedom-system structures which are modeled from rigid frame structure (Rahmen structure), are controlled using fuzzy theory. As some examples, responses of three-degree-of-freedom-systems subjected to external forces are shown.

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A Choquet integral system (CI-system for short) is a system whose input is an n-dimentional vector f = (f (1), f (2), ..., f (n)), which can be regarded as a function on {1,2,…, n}, and whose output is the Choquet integral of the function f over {1,2,…, n}. This paper gives a necessary and sufficient condition for a CI-system to be hierarchically decomposed into several sub-CI-systems ; a necessary and sufficient condition for a subset Y⊂{1,2,…, n} to constitute a sub-CI-system is either that Y is a semi-atom or that {Y, Y^c} is an inter-additive partition.

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Fusion of fuzzy theory and neural networks have been actively studied. A research on neural networks which incorporate the fuzzy inference into the networks is one of the main topics of the fusion technology. This paper calls the networks doing fuzzy inference Fuzzy Neural Networks (FNNs). Learning capability of the FNN realizes auto-tuning of membership functions and auto-identification of fuzzy rules. The authors have proposed a FNN which has a special structure for easy apprehension of acquired fuzzy rules. The fuzzy measure proposed by Sugeno can represent human measure which is used for evaluation of complex objects. But the meaning of the fuzzy measure is the mean value of the human measure. The fuzzy measure is insufficient for modeling of the evaluating schemes of human beings. This paper proposes a new application of a new FNN modified from the FNN previously proposed. The new FNN identifies nonlinear human measures. The FNN divides the input space of evaluated values of each attribute into fuzzy sub-spaces and identifies approximate linear equation in each sub-space. Experiments are done to show the feasibility of the fuzzy modeling by the new FNN.

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