Fuzzy transitive coupling is interconnecting two fuzzy subsystem models defined by fuzzy matrices A and B, and a common, transitive, fuzzy contextual relation to form a fuzzy system model defined by fuzzy matrix M. It is an integral part of fuzzy structural modeling. It may be difficult to find general solutions to this problem. In this paper, we show that this problem has particular solutions. We also consider transitive bordering corresponding to the special case B=1. Furthermore, we describe the effective application of the fuzzy transitive coupling to the embedding process for fuzzy structural modeling.

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This paper proposes Fuzzy Programmable Logic Arrays(PLA's)that can realize fuzzy logic functions on the basic research of fuzzy computer. The fuzzy logic functions can be represented by fuzzy logic formulas composed of fuzzy AND(・), OR(∨), NOT(〜)and variables.Considering to apply the fuzzy logic functions on the engineering use, some meaningful special classes of the fuzzy logic functions have been studied, e.g., P-type and C-type fuzzy logic functions. Therefore, this paper investigates the design of fuzzy PLA's realizing the above fuzzy logic functions. First, it proposes an AND-OR fuzzy PLA as an extension of a binary AND-OR PLA and shows that the column number requires 3^n+n-1. The analysis of the maximum number of the column in a PLA is interesting for the reason why if a PLA is used to implement a function, the cost is directly related to the column number. Therefore, in order to minimize the size of PLA's, a fuzzy PLA that is constructed by an AND-OR PLA, an OR-AND PLA and an output decoder is proposed. Although the PLA requires an output decoder, the column number is saved, that is, it requires 2^<n+1>. Thus, the column number is smaller than that of the former, and the efficiency of the latter increases as the variable number of the fuzzy logic function becomes larger.

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We proposed a clustering algorithm to create a balance between the continuity and the linearity of data distribution within clusters. The purpose of this clustering is to find linear substructures of the system under study in order to build a fuzzy implication inference model proposed by Takagi and Sugeno. The technical proposal in this paper is related to the integration of rules : selection of conditional variables, identification of membership functions, and evaluation of the obtained fuzzy model. A concrete example presented is a macro model that can predict water quality of small rivers in the Tokyo metropolitan area under certain scenarios of human activity.

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In this paper, we propose a new method, based on a non conventional approach, to determine exactly all the widest solution sets of a fuzzy relational equation. Fuzzy relational equations have received much attention from many researchers until now, however the proposed methods rarely enable to calculate the widest solution sets only. Indeed, it is often the case that some of the calculated solution sets are included in wider ones and then have to be removed from the list of solution sets. In this paper, we propose a rule-based method whose main advantage is to provide with exactly all the widest solution sets.

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The aim of the present paper is to show usefulness of a class of fuzzy graphs as a basis of hierarchical clustering. For this purpose classical results are reviewed and new results are proved using fuzzy graphs. Namely, the followings are discussed. 1. A formalization of hierarchical classifications is given and its relation with traditional description of methods in hierarchical clustering is discussed. 2. Meaning of the fuzzy graphs employed herein is explained in terms of a three dimensional description. 3. Equivalence between the Wishart method of mode analysis and connected components of fuzzy graphs with fuzzy grades on the vertices is proved. 4. Refinement relation between two methods of hierarchical clustering is defined and it is proved that this relation holds for the Ling method and the Wishart method and for the nearest neighbor method and the group average method(or the farthest neighbor method). 5. Significance of the results of equivalence and refinement in applications are discussed. The above 3,4,and 5 show new results, whereas 1 and 2 are reviews. To compile old results into the present form is necessary in order to describe new results in an appropriate way. In this sense, the review is an essential part of the present paper.

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The procedure of a statistical model selection is extended by introducing fuzziness into the optimization of a criterion. First, statistical properties of the proposed fuzzy model selection method are shown. Secondly, the fuzzy model selection is applied to the order determination of a time series model and to the estimation of unknown parameters of the normal distribution. The prediction of a time series using the fuzzy model selection is also discussed.

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Quantitative studies of attraction emotions in humans have been mainly concerned with geometric methods(multivariate-statistical analysis). However, these methods confine us to analyzing semantic structures and interpreting them semantically. We present an alternative approach in which these emotions are described by a fuzzy concept. The concept is represented as a fuzzy set whose universe of discourse is the collection of adjectives associated to emotions. Similarity to the concept(fuzzy set)represents the degree of attraction emotions. For illustration purposes we present an application of evaluating cat images. However, the method has applicability to the evaluation of a wide range of consumer products.

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So far, several fuzzy modeling methods such that parameters of the fuzzy model are tuned using gradient method have been proposed. But the problem in these methods is that the constraints on the shape parameters of the membership functions are not considered explicitly. To solve this problem, in this paper, we firstly formulate the original fuzzy modeling problem of class C^n as a parameter optimization problem with inequality constraints which guarantee that the order of vertex values of antecedent membership functions is always preserved. Nextly, the original constrained optimization problem is transformed to an unconstrained optimization problem using an interior penalty method. The explicit expression of the gradient of the augmented objective function and learning algorithm are derived. Furthemore, we propose a hybrid algorithm called free grid method, which consists of above self-tuning method and self-generating algorithm which generates new rules iteratively in the fuzzy partitioned input regions with the maximum mean inference error. Numerical examples are given which demonstrate that the proposed free grid method can achieve the specified model accuracy with less number of fuzzy rules than the similar gradient type tuning methods proposed so far. Moreover, we compare the function approximation ability of fuzzy model of class C^0,C^1,and C^2 using the free grid method.

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In conventional studies, many methods to generate fuzzy inference rules or neural networks which can compute the input-output relation of the given input-output data were proposed. However, all these methods deal with only numerical attributes which can be naturally expressed in number(e.g. weight, length, etc). In dealing with real world problems, not only numerical attributes but also symbolic attributes which can be naturally expressed by symbols should be handled. In this paper, we propose a new method which can generate appropriate inference rules even if both numerical attributes and symbolic attributes are included in the given input-output data.

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In this paper, we propose a practical complete decentralized control scheme that does not exchange information among its subsystems, using a hybrid controller which is composed of a feedback controller and a fuzzy controller for a interconnected system in which there are uncertainties caused by interactions among the subsystems. A feedback controller, which is based on conventional control theory, is designed to feedback the state of the subsytem using the mathmatical model applied for the local subsystem. On the other hand, the fuzzy controller, which is activated by a control error caused by uncertainties, generates the auxilary control input as its output to compensate the control error using fuzzy inference and the linguistic contol rule which is based on human control behavior. The fuzzy controller, which is proposed in this paper, determines its own control input which is cooperating with the feedback controller by including the output of the feedback controller as its fuzzy input variables. The linguistic control rules designed in this paper are very similar to human reasoning and thinking, therefore, it is easy to understand the application of these rules. And it makes possible to share a common rule set to execute inference in every subsystem because of its generality, and every subsystem only needs a small memory load. Furthermore, by using meta-rules as well as general rules, each subsystem has adaptability for input information and can determine the output adequately to match the changing situation. The hybrid controller proposed in this papar has been designed to support experimental trials to link the conventional control theory with the fuzzy control. And, this decentralized control scheme doesn't need any information to be exchanged, nor doesn't require redesign or adjustment when the new subsytems are joined. It is shown that the proposed hybrid controller gives a desirable control performance by the numerical simulations provided.

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Objective judgements of the freshness of raw oyster using fuzzy reasoning were carried out based on the three biochemical indicators such as gill respiratory(succinate dehydrogenase(SDH))activity, body fluid pH and body fluid ammonia concentration. After tuning treatment of fuzzy inference rules, more excellent correlation(correlation coefficient r=0.947)could be obtained between the sensory judgements of the experts of oyster farm and fuzzy estimations of the freshness compared with that obtained in our previous work(r=0.936). Moreover, availability of this fuzzy reasoning were examined using several types of membership functions and rules. As a result, estimated freshness were almost constant irrespective of membership functions used. In addition, estimations by fuzzy reasoning showed always better correlations between the expert sensory judgements and calculated judgements compared with the conventional mean-squre methods indicating that the availability of fuzzy reasoning could be confirmed.

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This paper constructs fuzzy systems based on trainable fuzzy if-then rules for rice taste analysis and examines the ability of fuzzy systems by computer simulations. The relation between six factors in the sensory test on rice taste is modelled by fuzzy systems with five input variables(flavor, appearance, taste, stickiness, toughness)and a single output variable(overall evaluation). Fuzzy if-then rules with non-fuzzy singletons in the consequent parts are employed in fuzzy systems. A learning rule based on a descent method is applied to the consequent part of each fuzzy if-then rule. By a random subsampling technique, the performance of fuzzy systems for test data and training data is compared with that of multi-layer neural networks. The usefulness of generated fuzzy if-then rules by learning is also examined.

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This paper presents a new method for describing behavior of fuzzy dynamical systems. The new method uses fuzzy rules of fuzzy systems and enables the description of the dynamical behavior using the language of the rules. New definitons of behavior of the fuzzy dynamical systems are also presented in this paper. Simulations using a simple nonlinear plant are done to demonstrate the feasibility of the new method.

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