Masatoshi Kitaoka

On the Generalization of Grey Relational Analysis

In this paper we developed new grey relational analysis by expanding a range of treatable value. The classical GRA procedure deals with almost whitened values, reference vectors (or sequences), inspected vectors and grey relational grades. The classical GRA is called White-In-White-Out (WIWO) GRA in this paper. We developed two kinds of GRA algorithm based on the topological-based GRA, after defined several new operations of the interval grey number. On the one hand, GRA which provides the grey relational grade a whitened value finally is named Grey-In-White-Out (GIWO) GRA. On the other hand, GRA which provides the grey relational grade the interval grey number is named Grey-In-Grey-Out (GIGO) GRA. Both new GRA procedures deal with the reference vector and inspected vectors as the interval grey number. Three examples are given in this paper; the properties of the grey relational grade given by the proposals are discussed.

Circular Data Analysis of Periodic Time Series Data Using Grey Theory

Circular data can be expressed as circular diagram for time series data. This study presents the computational procedure, which made circular diagram for the data with periodicity. The method for displaying circular diagram using spline function and GM(1,1) model of the Grey Theory is developed to analyze the periodic data. In addition, the method for displaying the fluctuation of the periodic data from least squares method, GM(1,1) model and periodic spline function is shown.

Multivariate analysis model for machine-part cell formation problem in group technology

The principal objective of this article is to formulate a multivariate analysis model to generate optimal machine cells and part families in GT problems. The algorithm is carried out in three stages. The double centering matrix for similarity of machines and parts is used as similarity coefficient matrix. A quantification method is applied to find the eigenvalues and eigenvectors on the double centering matrix. Cluster analysis is applied to make part families and machines groups while minimizing the distance of eigenvectors. A numerical example for the design of cell structures is provided.

Decision rule extraction and reduction based on grey lattice classification

This paper proposes a decision rule of extraction and reduction that is based on grey lattice classification. This proposal method comes from joining between rough set theory and grey theory as an approximation algorithm. Grey lattice operations are defined by combining interval grey number in grey theory with interval lattice operations in interval algebra. By defining the equivalents in interval grey number, given data space is correspondent to equivalents of rough set. This proposal method classifies each data set into 3-patterns from given training samples, as existing possibility class, newly made possibility class and existing necessity class. As given examples which require only necessity class, decision rule is simplified by a reduction procedure.

A Realization Algorithm of Grey Structural Modeling with MATLAB

Grey structural modeling (GSM in short) is a new approach of system modeling methods succeeding to ISM and FSM. GSM has two procedures: estimating a hierarchy of given elements, estimating paths among given elements. The former procedure is constructed from complex equations. In this paper we developed one realization algorithm of the GSM procedure. The main problem we should solve is how to group given elements into several classes and to decide their hierarchy. We are possible to group analyzing an error matrix which is obtained from the localized grey relational grade, and we are also possible to decide their hierarchy according to the localized grey relational grade. We used the topological-based grey relational analysis. These procedures are shown as a pseudo language with several figures, and are realized by MATLAB. Several examples applied with the developed program are shown in this paper

A K-means Clustering Approach Based on Grey Theory

A lot of clustering algorithms based on grey system theory, especially based on the grey relational matrix, have been already reported, which finds out a centroid of each class by moving given objects as vectors. We developed new clustering procedure called grey K-means, which is able to handle the number of required clusters such as the hard K-means or the fuzzy c-means. Assume that the number of found clusters by the proposal is between 1 and the number of classified instances, a required threshold value is exist in [0,1]. We defined a value range of the threshold as the interval grey number, and the range is specified automatically until obtaining the required clusters. In addition a new clustering method which analyzes the grey relational matrix closely instead of moving vectors is suggested. Several well-known data sets in the classification problem are applied, and we discuss their performances and the optimal threshold value.

Implementation of a case-based production scheduling system in C language

Abstract This paper presents the application of Case-Based Reasoning to the production scheduling problem in a corrugated card-board factory, its main task is to find a promising sequence for jobs processing, a prototype of the scheduling system is implemented in C language. In this system, a schedule case is represented in the form of ordered tree and each job is represented in the format of attribute-value pairs. When jobs to be sequenced are given, a previous case which is the best matching with the problem is recalled from the case-base, the sequence of given jobs can be decided assigning the jobs to the nodes of the ordered tree of the recalled case. Several real world scheduling problems in the factory have been solved and the system behaved as correctly as the human experts did. It was showed that the Case-Based Reasoning approach is well suited to solve production scheduling problems.

Numerous date in hierarchy for knowledge concentrated in decision tree

Abstract In the modern society, the more the amount of information is increased, the more the amount of information is to be received. This paper introduces a method to make numerous data in hierarchy for concentrated knowledge. In order to make knowledge concentrated in a simple form. There are many methods to come up this purpose. A method called interpretive structural modeling (ISM) can be used to decide the factors with affect the subject, and know how strong the factors affect to the object. Decision tree can be represented the knowledge briefly by information theory, it use the data elevated by ISM. Analytic hierarchy process (AHP) is used to show the order of the results. Knowledge concentrated method can be achieved in integration these methods for knowledge acquisition. We proposed a new method for knowledge concentration. Concentrated knowledge is compound with the tree main methods. This method is easily applied to the knowledge base in expert system. Here is shown a suggestion for metal making technology knowledge.

A Research on Grey Model by Grey Interval Analysis

Grey Model (GM) based on grey system theory has already been established as a prediction model in 1982. At present, it has been applied to many fields. However, in the traditional GM, the calculation methods of derivative value d(superscript n) x/dt(superscript n) and background value z are obtained by the analysis of observed white value. Therefore, it influenced the calculation of coefficient â and the prediction accuracy of the traditional GM is unsatisfied. Especially, the prediction accuracy falls in case of the multi-variable or multi-dimensional greatly. In this paper, a new calculation method of derivative value d(superscript n) x/dt(superscript n) and background value z is proposed according to cubic spline function and Taylor approximation method and it is analyzed by grey interval analysis. We obtain the new calculation method of coefficient â by the proposal GM, and this new model is defined as T-3spGM. We present two specific examples; the prediction accuracy of proposal model is verified. As the results, we report that the prediction accuracy of the proposal new model was raised greatly.

Inventory Management for Irregular Shipment of Goods in Distribution Centre

The shipping amount of commodity goods (Foods, confectionery, dairy products, such as public cosmetic pharmaceutical products) changes irregularly at the distribution center dealing with the general consumer goods. Because the shipment time and the amount of the shipment are irregular, the demand forecast becomes very difficult. For this, the inventory control becomes difficult, too. It cannot be applied to the shipment of the commodity by the conventional inventory control methods. This paper proposes the method for inventory control by cumulative flow curve method. It proposed the method of deciding the order quantity of the inventory control by the cumulative flow curve. Here, it proposes three methods. 1) Power method,2) Polynomial method and 3)Revised Holts linear method that forecasts data with trends that is a kind of exponential smoothing method. This paper compares the economics of the conventional method, which is managed by the experienced and three new proposed methods. And, the effectiveness of the proposal method is verified from the numerical calculations.