Hajime Yamashita

Sociometry analysis applying fuzzy node fuzzy graph

Sociometry is a social structure measurement and evaluation method, which we can effectively analyze by applying fuzzy graph theory. We extend the fuzzy graph theory, and propose a fuzzy node fuzzy graph, and we transform it to a crisp node fuzzy graph using by T-norm. The authors explain a fuzzy node fuzzy graph, and propose new T-norm family quasi logical product. By using this new T-norm, we could reasonably transform the fuzzy node fuzzy graph to the crisp node fuzzy graph.

Learning structure analysis system applying fuzzy theory

The inexact phenomena such as the mental process and cognition would effectively be analyzed by using the fuzzy graph. In this paper, we would explain about the learning structure analysis system by applying fuzzy graph, present its practical case study and the effectiveness.

Fuzzy Clustering Level Analysis Using AIC Method for Large Size Samples

This paper investigates the fuzzy clustering level analysis using AIC (Akaikes information criterion) method for small size samples. Since AIC is obtained by the asymptotic normality for the maximal likelihood estimator, it is difficult to apply it to small size samples. Therefore, in the paper, we would show that the AIC method can be applied to large size samples which are constructed by a simulation with pseudo random numbers obeying several distributions.

Instruction and cognition analysis applying fuzzy graphs

Abstract The inexact phenomena concerning human behavior, mental processes, and cognition are reasonably represented as fuzzy graphs. In order to clarify the global features of such fuzzy information, we analyze them from the points of view similarity and connectivity. We recently developed an analytical method concerning the cognitive structure of a subject by applying fuzzy theory, which enables us to verify and / or modify instruction programs on the basis of test data. In order to carry out the data analysis accurately and quickly, a computer support system was developed and has been effectively utilized. In this paper, we discuss the theoretical explanations of the analysis system and illustrate its instruction effectiveness through case studies in mathematics.

Decision Analysis of Fuzzy Partition Tree Applying AIC and Fuzzy Decision

We often use fuzzy graph to analyze inexact information such as sociogram structure ([1] and [2]). Concerning the hierarchical cluster analysis of a fuzzy graph ([3], [4] and [5] ), the number of clusters may have to be decided in the actual cluster analysis. In other word, we woud like to decide the optimal level with a partition tree. Concerning this problem, while AIC method in statistical analysis has been designed by us ([6] and [10]), we will now propose a fuzzy decision method which is based on the evaluation function paying attention to the size and number of clusters at each level.

Exchange Probability and Convergence Characteristics of Genes in Inversion in GA

The genes exchange method in inversion is categorized into three types. The exchange probability of genes in those types has different tendency. Also ex change probabilities of genes in loci depend on locations of those except mode 3. In model, genes exchange probability in center area is larger than that in the ends. In mode 2, genes exchange probability in center area is smaller than that in the ends. In mode 3, exchange probability of genes does not depend on the location of those loci. Calculated results of gene exchange probability have good agreement with that simulated.

Fuzzy graph analysis for sociometry on latticed display

The fuzzy graph will make it possible to quantitatively analyze fuzzy information such as expression of human relations and mental processes. To clarify the main feature of a fuzzy graph, we would represent it as an approximate graph and extract its characteristics such as similarity and connectivity structures. Therefore we must proceed to analyze many kinds of information concerning the structure of a fuzzy graph, such as drawing and displaying comprehensively fuzzy graphs in the process. We have developed a computer-aided method for analyzing fuzzy graphs through human interaction. This method can quickly and comprehensively draw a graph arranged on a circular, a partition tree, cluster representative graph corresponding to a cluster and a specified shape of approximate n-valued fuzzy graph. However, it can not draw automatically a graph with nodes on the lattice intersection. So, we would rearrange the nodes on the lattice intersection for any fuzzy graph through user interface. This display is convenient for traditionally analyzing fuzzy graphs. We propose an analysis method using the lattice type of fuzzy graph display. Here, it plays an important role in this system. In this paper, we describe the analysis method and user interface of this system, and their application to sociometry analysis.