Using relative individual scores among alternatives, in this paper, we propose a set function that shows the feature of an alternative. In a weighted sum model such as the Analytic Hierarchy Process (AHP), a set function value is constructed from the weights of the model. The set function value for the alternative is calculated by averaging the values of the set function representation of randomly generated weights when the alternative has the highest comprehensive score. By interpreting the functions, we can understand the feature of an alternative. We conclude the paper by discussing the relation of the set functions with fuzzy measures.
The t-norms are significant operations useful for fuzzy theory. The domains of t-norms are usually the closed interval [ 0, 1 ] or general lattices L . Specific sets except [ 0, 1 ] are rarely used as domains of t-norms. In this article, two-dimensional t-norms defined on the closed unit square [ 0, 1 ] times [ 0, 1 ] and multi-dimensional t-norms are studied. Some examples of them are shown. Moreover the generating functions of them are studied.
This paper discusses a new method using “distance-adjusted covariates” in group decision making. We introduce a distance of opinions between two evaluators in the group, and define it by a distance between two vectors of covariates. The proposed method determines the scale of covariates (grade point) for each evaluator so that the distance of opinions will be adjusted which makes the influence on the group plan rather equal. Then the method introduces “VDI (Variety Dispersion Index)” that is an index for the equality degree on the influence for the group plan. If a VDI is small, it indicates that the influence on the group plan be equal. The simulation result shows that this method is also useful as a tool to analyze the group behavior by using grade points and VDI. The grade points and VDI can classify into four patterns groups, and show feature of each groups.
This paper presents a new method to improve generalization abilities for Support Vector Machines (SVM) based on topological data mapping used in Counter Propagation Networks (CPN). The proposal method produces new training data to be expanded or compressed while retaining topological data structure using competitive and neighbor algorithms on CPN. The number of new training data is controlled by the changing of units on a mapping layer of CPN. Using topological data mapping, interrupting data is created to sparse data regions and redundant data is removed from overlapping data regions. Especially, the characteristic of removing redundant data is connected to reduce the number of Support Vectors (SV) that treated for soft-margins. We applied our method to two classification datasets and a face dataset under illumination changes. The classification results indicate the basic characteristics of our method to be changed decision boundaries. The face recognition results show that our method provides not only improved generalization abilities, but also to be able to display spatial distributions of SV on a category map.
The ink drop spread (IDS) method is a modeling technique based on the idea of soft computing. This method divides a multi-input-single-output (MISO) modeling target system into multiple single-input-single-output (SISO) systems, which correspond to each input-output pair and are divided into small SISO systems. In order to make multiple images for each SISO system, the IDS method plots the input-output data of the target system on the two-dimensional planes like the wave pattern generated when the ink is dropped into the water. For each data point, an ink drop is dropped onto the two-dimensional plane so that the density of the ink is lower at the point more distant from the data point. By plotting all the data points in this way, the cumulative density of ink is higher at the point where more ink drops overlap, and as a result, a characteristic ink pattern appears on the plane. The IDS method extracts the features of the target system from these ink patterns, and integrates them into fuzzy inference to model the target system. It is important for the IDS method to decide an appropriate partitions of each input for accurately modeling the target system. Therefore, some methods have been proposed to decide partitions. However, there are some problems with these methods. For examle, they cannot decide both the positions and number of partitions simultaneously and require a long processing time to decide partitions. In this article, we propose a new partition method for the IDS method using the information exploited from images. The proposed method extracts the information useful for deciding appropriate partitions from the images generated on the two-dimensional plane, decides partitions using that information, and adjusts the generated partitions. In this article, we compare our method with the existing partition methods such as equal divide method and Genetic IDS and show that our method can generate better partitions with less search steps. Furthermore, through comparing our method with other modeling methods such as Feedforward Neural Network and Support Vector Machine, we demonstrate that our IDS method is more effective in approximating complex functions and solving binary classification problems.
This study investigates change of learning ability of English as a Foreign Language (EFL) by using scaffolding in EFL vocabulary learning system. We developed an EFL vocabulary learning system (S1) for Japanese students. It has an innovative scaffolding function that helps the learner guess the meaning of target English words in example sentences. This function is called “Hint Translation” and presents Japanese translation of example sentence expect for target English words upon user request. The experiment was conducted to compare how effectively learners were able to learn English words in S1 and a comparison system (S2). Both S1 and S2 were used by five lower and intermediate learners each for two weeks. In the result of experiment, we found that the intermediate learners in S1 group learned more vocabulary than S2 group. Moreover, we found that intermediate learners in S1 group phased out their use of Hint Translation and progressed in their English ability to guess the meanings of English words in example sentences without scaffolding. On the other hand, the lower learners in S1 group depended on using Hint Translation and did not learn English words.
This paper analyzes turn-taking structure in multiparty conversation based on the attitudes toward participant role expressed by nonverbal expressions. In previous studies turn-taking events have been mainly analyzed focusing on physical modalities such as utterances and gaze-directions. Unlike those studies we focus on expressions of internal statuses or attitudes toward participant roles (want to be a speaker / want to be a hearer) expressed by each participant at turn-takings. First, participant attitudes are subjectively evaluated by third party evaluators, then, are analyzed quantitatively and qualitatively. The results shows that participant attitudes such as “want to be a speaker” and “want to be a hearer” act as important cues for choosing next speaker and hearer. It suggests that the attitudes contribute to smooth turn-takings and cooperative conversations.