When the data is observed by human, there are cases that the data is not always exact or it is difficult to observe the data exactly. In these cases, if we are able to observe the data including vagueness of observers, then its observation becomes easy. Then, in this paper, on the assumption that the observations include human vagueness, we treat the fuzzy interval data including unclear border of intervals. And, we give the processing method of the regression analysis by least square method using fuzzy interval data. But, it is difficult to treat the fuzzy interval data exactly. So, in this paper, we execute the regression analysis apploximately using the representative value of fuzzy interval data which is treated easily. And, the usefulness of our method is illustrated using computer simulation.
People often rely on their feelings in choosing and deciding their behavior in everyday life. Analytic Hierarchy Process (AHP) is one of the most popular tools for supporting human decision making, and several fuzzy extensions of AHP have been proposed. The present study investigated both psychological effects of fuzzy ratings in fuzzy AHP and effective presentation forms for the results from fuzzy AHP. The results confirmed that fuzzy ratings in fuzzy AHP could incorporate the fuzziness of a person's feelings in his/her decision making. The results also revealed that exaggerating the priority of only one specific alternative with respect to some characteristic could help a decision maker make his/her decision, especially when a decision maker was being puzzled about his/her choice. Moreover, the possibility of interactive support system for human decision making by fuzzy AHP was discussed.
A GA^d (Genetic Algorithm with Degeneration) is an algorithm that employs a genetic algorithm and introduces the idea of genetic damage. In GA^d, the information of a damaged rate is added to each gene, the genes that have lower effectiveness are inactivated using genetic damage, degeneration is realized and unnecessary model parameters or rules are reduced. It is difficult to select proper degeneration speed when GA^d is used for structural learning of fuzzy rules, because the proper speed depends on each system to be approximated. If the degeneration speed is low, estimation error becomes sufficient but the reduction of rules is not enough. If the degeneration speed is high, the reduction of rules is satisfactory but estimation error becomes rather big. To solve this problem, we propose to divide the process of structural learning into 3 steps: the first step to lower the rule parameter values, the second step to delete the parameters actively, and the final step to minimize the estimation error. It is shown that the improved Gad is an efficient algorithm for the structural learning of RBF (Radial Basis Function)-fuzzy rules by applying it to the learning of some function identification problems.
Widely chaos model is employed to forecast a value in short term future using such time-series data that its regularity is hardly found. The chaotic short-term forecasting method is based on Takens Embedding Theorem which enables us to reconstruct an attractor in multi-dimensional space using such data that seem to be random. Even if data has no random nature but deterministic and geometrical nature, it is also hard to forecast their future values based on the chaos method if the data cannot be reconstruct in sufficiently low dimensional space. This paper proposes the method to embed another reference data related closely to the original focal data. The method can enable us to abstract the chaotic portion out of the focal data and increase the forecasting precision. In the chaotic forecasting method based on Euclidean distance, the fuzzy reasoning is employed in order to deal with vague information included in the focal data. These two methods are evaluated by simulation examination on the comparison with a conventional method. The simulation result shows its effectiveness by applying the method to forecasting the future value of Nikkei Mean Value of Tokyo Stock Market. It should be noted that fuzzy membership functions used in premises of rules in fuzzy reasoning are automatically and optimally tuned by genetic algorithm and that the forecasting model is rebuild easily.
In the case where observed data are put in the analysis based on a regression model, the latent system of observed data is too complicated to be analyzed by the regression model. The same situations happen when the structures of the latent system are changed. In such a case an analyzer used to separate each of samples accordingly to the different structures and apply each of regression models to a group of the samples. In other words, when the given samples come out of several different systems, we should separate samples into several groups according to each of the latent systems and apply a regression model to each of samples. Without such a process we cannot obtain proper results from the given samples. Nevertheless, it is hard to separate samples according to each latent system in the case of multivariate data. Hitherto, there are many researches to investigate the structure under obtained data and analyze such data. J. C. Bezdek proposes Switching Regression Model based on Fuzzy Clustering Model to formulate a forecasting model. The model proposed by Bezdek is to separate mixed samples coming from plural latent systems and apply each regression model to the group of samples coming from each system. That is a Fuzzy c-Regression Model. In this paper, in order to deal with the possibility of a system, we employ a fuzzy regression model to build a Fuzzy Switching Regression Model. The fuzzy switching regression model is explained to analyze wholesale price indices in Japan.
This paper proposes an agent-based rule extraction method from mixed database. In the database, some heterogeneous structures are often included together. In addition, some symbolic attributes and some numerical attributes are often stored together in the databases. The proposed agent has a role for collecting data objects and detecting a local rule, based on a similarity and identified sets. The interaction between the agents focuses on squabbling about objects. % considering attributes. The agent identifies an if-then rule based on the collected data. The consequence of the obtained rule is changed by the agent, depending on the condition.
In general, observed data sets are statistically processed and summarized. If it is possible to observe both the positive (P) and negative (N) phases independently, it will become possible to calculate the degree of contradictions for the i-th paired data (P_i,N_i) by using the Hyper Logic Space (HLS) model. In conventional measurement methods, only the positive phase is observed. However, the negative phase can also be estimated if the simple principle introduced here is used. The algorithms proposed here can calculate the degree of contradictions among more than two data pairs.
FCR-methods (Fuzzy-set Concurrent Rating Methods) are integration methods of the true value (α) and the false value (β) without the constraint α + β = 1. The property α + β ≠ 1 corresponds to the non-additively of fuzzy measures and we research the properties of FCR methods using fuzzy measure theory's view. Some FCR methods correspond to one of the λ fuzzy measure identification method and we propose the inverse φ_s transformation method which corresponds to the λ fuzzy measure identification method using φ_s transformation. Next, we research the properties of FCR methods such as monotonicity, continuity, duality and so on. Lastly, we propose the inverse FCR-method which calculates the α and β value from the integrated value of FCR-method and the Contradiction-Indifference index.
A fuzzy node fuzzy graph is an extension of a fuzzy graph and it has been applied to many fields, e.g. social structure analysis, instruction structure analysis and so on. Since the fuzzy node fuzzy graph is usually too complicated to analyze, we transform it into a crisp node fuzzy graph using T-Norm. Further, to simplify the crisp node fuzzy graph, we construct its approximate graph. As an application of the approximate graph we treat Sociometry analysis.