In this paper, two fuzzy classification functions of fuzzy c-means for data with tolerance are proposed. First, two clustering algorithms for data with tolerance are introduced. One is based on the standard method and the other is on the entropy-based one. Second, the fuzzy classification function for fuzzy c-means without tolerance is discussed as the solution of a certain optimization problem. Third, two optimization problems are shown so that the solutions are the fuzzy classification function values for fuzzy c-means algorithms with respect to data with tolerance, respectively. Fourth, Karush-Kuhn-Tucker conditions of two objective functions are considered, and two iterative algorithms are proposed for the optimization problems, respectively. Through some numerical examples, the proposed algorithms are discussed.

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Clustering by Self-Organizing Map (SOM) can extract clusters of arbitrary distribution shapes based on the distance between the code-vectors (representative points of the input data). Hence, this is one of the “distance-based” clustering approaches. On the other hand, there are “distribution-based” clustering approaches that consider the distribution of input data when extracting clusters appropriately. For example, x-means method adopts Bayesian Information Criterion (BIC) into k-means method. Information criteria are also easily introduced into the clustering method by SOM. In this paper, we propose a clustering method by SOM and information criteria. In this method, initial cluster-candidates are derived by SOM, and then these candidates are merged appropriately based on information criterion such as BIC or AIC (Akaike Information Criterion). Through the clustering experiments for the artificial datasets and UCI Machine Learning Repository's datasets, we confirm that our proposed method can extract clusters more accurately and stably than the SOM-only method. Furthermore, we show that AIC is suitable for the proposed method compared to BIC and that our method also can estimate the number of clusters in dataset.

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A fuzzy neighborhood model to analyze text data is proposed. This method can represent a sequencial structure in a set of texts, while traditional methods like the vector space model cannot as it simply counts the number of words in a text. Moreover fuzzy neighborhood model is a generalization of the vector space model and fuzzy equivalence relations. An advantage of this model is that it provides a positive definite kernel for data analysis. Accordingly we apply the present model to text analysis using kernel c-means clustering and kernel principal component analysis. Two examples of analysis of newspaper articles and medical incident reports are shown.

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This paper develops an analyzing method for a time series of cityscape evaluations so as to take account of interactions between views in the previous time period and the current period. Two evaluation models are provided, one of which includes interaction terms, and the other of which is an additive model having no interaction terms. These models are represented in the state-spaces by the auto-regression process to estimate evaluation values by the Kalman filtering. The necessity of considering interactions is examined by comparing the accuracy of their estimations when these models are applied to a cityscape evaluation problem. Also, it is checked whether observed results meet the application condition for the additive model. These examinations give an affirmative answer to the question about the necessity of considering interactions. In addition, a brief but instructive comment is made on color sequences suitable to façades in a cityscape.

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Choquet-integral-based comprehensive evaluation method are proposed. Fuzzy measures are derived from a fuzzy rule table that formulation is the same as the simplified fuzzy reasoning's. To be applied in social science, global evaluation methods are required some strict properties such as monotonicity. Unlike the fuzzy reasoning models, the models have monotonicity if the fuzzy rule table is monotonicity. Unlike the ordinal Choquet integral models, this model allows to switch the evaluation attitude -complementary or substitute- depending on input value situations. This model can represent the cumulative prospect theory and Choquet integral with respect to bi-capacities. Lastly, we show an application for performance evaluation such as balanced scorecards.

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This paper discusses a generalization of the domain on which ordinary coalitional games are defined to a larger class, and introduces a new solution concept on the class. The generalization possesses some existing games, multi-choice games, bi-capacities and so on, on lattices. Therefore, we can apply the new solution concept to games on lattices.

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The paper studies and proposes the requirements that a conditioning rule of Evidence theory should satisfy, and a new conditioning rule satisfying them. It also proposes a generalized conditioning rule that abandons one of the requirements. The proposed requirements are i) focal elements of a conditional basic belief assignment are limited to subsets of a set representing the condition, ii) conditional bba must be defined except the case where the condition set is empty and iii) bba conditioned by the universal set equals bba without any condition. The first requirement represents that the given condition is completely reliable, the second is derived from the interpretation that Evidence theory deals with beliefs in human minds, not uncertainty related to frequency, and the third is the result from the fact that the universal set contains all possible elements. The paper proposes a conditioning rule satisfying the above three requirements. Then, it generalizes the rule with abandoning the first requirement by introducing a degree of reliability. The generalized rule is equivalent to the one satisfying the three requirements when the degree is one, and to the original bba without any condition when the degree is zero. When the degree is between zero and one, the rule interpolates both the ends linearly. Numerical examples show the difference between the proposed rule and well-known conventional conditioning rules. They show that only the proposed one satisfies all the three requirements. In addition, they also show that instability that a little difference between two prior beliefs may produce a large difference between the posterior beliefs, which is observed in the case of conditioning with normalization such as Dempster' rule, is solved with the proposed conditioning rule.

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Takagi-Sugeno fuzzy system can describe a wide class of nonlinear systems, and is widely used in many engineering fields. Recently, system analysis and control design for nonlinear systems based fuzzy system approach have been active. This paper is concerned with robust observer for sampled-data fuzzy systems. The system is usually modelled as a continuous-time fuzzy system, while the observation is taken at discrete instants. First it is shown that the error system which stems from an original fuzzy system and a sampled-data observer becomes a time-delay systems. Sufficient conditions for the error system to be asymptotically stable are given in terms of linear matrix inequalities (LMIs). We derive such conditions via descriptor system representation under the assumption that sampling-time is not greater than some prescribed number. Based on the conditions, we propose an observer design for a fuzzy system and then extend to a robust observer for the same class of systems. Numerical examples are given to illustrate our sampled-data observer.

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This paper proposes a novel keyword discrimination method by focusing on information flows on weblogs. Our approach assumes that the process of the term diffusion among bloggers is determined by the influence of the terms and the bloggers. We make a matrix whose elements indicate the number of bloggers to whom a blogger conveyed a term, and get the first left and right singular vectors as the influence of the terms and the bloggers. The highly influential terms are the keywords. As a result, we can extract not only bursty terms but also terms mentioned constantly as keywords.

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The paper discusses generalization of conditioning in Evidence theory proposed recently, and proposes a new generalized conditioning with an uncertain belief. It also shows that a conventional method of evidential reasoning could be interpreted by the proposed generalized conditioning. A conditioning rule proposed recently by Kimala et al. satisfies the following three requirements: a) focal elements of conditional basic belief assignment are limited to subsets of the given condition, b) conditional bba must be defined for any condition except for the empty set, and c) conditional bba with condition of the universal set equals to bba with no condition. All those requirements are natural and appropriate with understanding that Evidence theory deals with subjective uncertainty of humans, though there are no conditioning rules satisfying all of the three requirements. They also proposed a generalized conditioning that loosens a requirement a) by introducing reliability of the condition. The paper generalizes further Kimala et al.'s generalized conditioning. The proposed generalized conditioning uses a belief represented by a bba as the condition. Ichihashi et al. and Dubois et al. have already proposed similar conditioning rules. However, since they are extensions of Bayesian conditioning and Jeffrey's rule, they cannot satisfy the requirement b). The conditioning proposed in the paper satisfy both b) and c), though a) is lost because of the generalization. The paper also discusses the relation between a conventional evidential reasoning and conditioning rules. The evidential reasoning is understood as an extension of Bayesian reasoning. In the paper we show that it could be interpreted as a combination of evidence in Transferable Belief Model proposed by Smets et al., as well as the proposed generalized conditioning rule with an uncertain belief.

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In general, the state feedback control gain can be obtained by solving certain linear matrix inequalities (LMIs) when using the Takagi-Sugeno (T-S) fuzzy model to develop a control system. In this paper, the reconstruction error between the real system to be controlled and its T-S fuzzy model, which consists of parameter uncertainties and external disturbance, is considered. As a result, we arrive at an adaptive controller that has two parts: one is obtained by solving certain LMIs (fixed part) and another one is acquired by an adaptive law (variable part). The proposed controller can guarantee the control state to converge and uniformly bounded while maintaining all the signals involved stable. Also, the convergence and boundedness in terms of relaxing the LMIs conservatism are discussed. An inverted pendulum is provided to demonstrate the effectiveness of the proposed adaptive fuzzy controller.

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Skill science begins to attract much research attention recently. One of the most important issue in skill science is to discover rules of cooperative motion. In this problem, such relations as “if state B occurs in one sequence, state A will occur within a few minutes in another sequence” should be learned by analyzing time series data from sensors. However, in the actual applications, we often have to deal with time series data without knowing what the internal states are. For these cases, conventional correlation-based methods for time series analysis do not work well since they lack the capability of handling complicated structures such as the relations between time intervals. Based on the background, we propose a procedure to discover temporal relational patterns inductively after converting time series data into a set of state transition sequences. This paper proposes a new framework for analyzing time series multivariate data with non-stationary feature which are often observed in such data as EMG of human performance of skillful motion. Firstly, we determine a sequence of stationary stochastic models of a given time series datum for each component of multivariate measurement data. Secondly, we cluster the stochastic models and allocate a symbol to each cluster, resulting in a set of symbol sequences corresponding to each measurement. Thirdly we convert each symbol sequence into a sequence of time-interval-symbols (TIS) by associating each symbol with the start and end timestamps of the interval. Finally, we extract temporal relational rules (TRR) of TIS sequences using Inductive Logic Programming. Then, we can expect that the extracted rules represent some of the important features of the given multivariate time series data. In our experiments, we applied our proposed framework to the EMG of the skillful motion of playing Chellos, and showed that useful skill knowledge can be obtained.

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