Guo-Dong Li

A grey-based decision-making approach to the supplier selection problem

Supplier selection is a multiple-attribute decision-making (MADM) problem. Since the decision makers (DMs) such as preferences on alternatives or on the attributes of suppliers are often uncertain, supplier selection becomes more difficult. Grey theory is one of the methods used to study uncertainty, being superior in the mathematical analysis of systems with uncertain information. In this paper, we propose a new grey-based approach to deal with the supplier selection problem. The work procedure is as follows: firstly, the weights and ratings of attributes for all alternatives are described by linguistic variables that can be expressed in grey numbers. Secondly, using a grey possibility degree, the ranking order of all alternatives is determined. Finally, an example of a selection problem of supplier was used to illustrate the proposed approach.

A grey-based rough approximation model for interval data processing

A new rough set model for interval data named grey-rough set is proposed in this paper. Information system in the real world are quite complicated. Most of information tables record not only categorical data but also numerical data including a range of interval data. The grey lattice operation in grey system theory is one of the operations for interval data that modifies endpoints non-arithmetically, and which is useful for interval data processing. The grey-rough approximation is based on an interval coincidence relation and an interval inclusion relation instead of an equivalence relation and an indiscernibility relation in Pawlaks model. Numerical examples and four fields of practical examples, decision-making, information retrieval, knowledge discovery and kansei engineering are shown. The advantages of the proposal include: extending a treatable value compared with classical rough set for non-deterministic information systems, providing a maximum solution and minimum solution both in upper and lower approximations, and not only providing mathematical support to SQL but also functions for further extension in the future.

On the combination of rough set theory and grey theory based on grey lattice operations

A new rough set named grey-rough set based on the grey lattice operation in grey system theory is proposed in this paper. Information systems records not only categorical data but also numerical data including a range of interval. In order to handle interval data in such information systems, we describe two sorts of new rough approximation after introduced grey lattice operations: a special grey-rough set based on the equivalence relation of interval coincidence, and a general grey-rough set based on the meet operation and the inclusion relation instead of the equivalence relation. The special grey-rough set is applicable to categorical data and numerical discrete data like the traditional rough set. The general grey-rough set is applicable to numerical interval data, which means that the proposal is an advanced method for non-deterministic information systems. The proposal is illustrated with several examples.

A grey-based rough set approach to suppliers selection problem

The suppliers selection problem is one of the most important components in supply chain management. In recent years, rough set theory has emerged as a powerful tool for suppliers selection problem. In this paper, we proposed a grey-based rough set approach to resolve suppliers selection problem. The work is motivated by the following observations: First, in the decision table of rough set theory, attribute values must be known precisely. Generally, decision makers’ judgments on attribute often cannot be estimated by the exact numerical value. Second, in rough set theory, the alternatives of ideal suppliers are decided by lower approximation, so the ranks of each ideal supplier is equal. Therefore it is difficult to select the best ideal supplier. The work procedure is shown as follows briefly: First, the attribute values of rough set decision table for all alternatives are decided by linguistic variables that can be expressed in grey number. Second, ideal suppliers are decided by the lower approximation of grey-based rough set theory. Third, the best ideal supplier is decided by grey relational analysis based on grey number. Finally, an example of selection problem of suppliers was used to illustrate the proposed approach.

Reviewing crisp, fuzzy, grey and rough mathematical models

The aim of this paper is to investigate advantages of grey system theory. A lot of vague concepts like fuzzy sets, grey systems or rough sets has been proposed in the past. However, the unique concept of grey system theory, for example, it is useful under lack of data situation, is still unclear because a few articles discuss and deal with in real application. In this paper firstly numbers, membership functions, operations, crisp conversions and data pre-processing methods of each vague concept are summarized to review with several illustrations. Secondly the uniqueness of grey concept is discussed. It is found that the grey lattice operation and the nominal-the- better of grey generating are unique methods unlike fuzzy- based models or rough-based models. The unique concepts of grey system theory are interval data analysis and target-based data analysis, which should add to the existing ones. Given data sets are analyzed strategically in grey system theory from these concepts.

A Grey-Rough Set Approach for Interval Data Reduction of Attributes

Reduction in rough set theory is useful to compact given attributes of large-scale decision tables in data mining. In this paper a new method called grey-rough reduction is proposed for decision tables containing non-interval data and interval data complexly called grey-decision tables. First of all, a grey-rough approximation is introduced after summarized grey numbers, their operations and functions. Two sorts of reduction based on grey-rough sets, a basic approach and advanced approach are proposed with several illustrative examples. Three experiments, compatibility with the classical model, an application of the basic approach to decision-making and influence of the parameter in the advanced approach are shown. The advantages of the proposal are (1) it is compatible with the classical reduction model for non-interval data, (2) it is useful for complex decision tables and (3) it provides a possible reduction of attributes with a parameter by the advanced approach.

Prediction of relative dynamic elasticity modulus by extending a grey system theory

The relative dynamic elasticity modulus is an important evaluation criterion in frost resistance testing of concrete. Generally, in order to validate the decay rules of concrete durability, the measurement of relative dynamic elasticity modulus needs a large number of testing data over time. Therefore, it is often difficult to carry out this test and sometimes it is even not feasible due to cost consideration. In addition, the dynamic relationship between the relative dynamic elasticity modulus and freeze–thaw cycle is very intensive, but so far there is no definite explicit or implicit function to describe it. However, the relative dynamic elasticity modulus of a concrete material can be measured indirectly with the grey prediction model based on a grey system theory that only requires a limited number of discrete data to estimate the behaviour of a dynamic system with uncertain and incomplete information. In this paper, we developed an indirect measurement model of concrete relative dynamic elasticity modulus with the number of freeze–thaw cycles as a leading indicator on the basis of an improved grey prediction model. The improved grey prediction model is established with the Taylor approximation method. We validated the effectiveness of the proposed model by using the relative dynamic elasticity modulus of the concrete material and corresponding experimental data concerning the number of freeze–thaw cycles.

A hybrid grey-based dynamic model for international airlines amount increase prediction

In this paper, we propose a hybrid grey-based dynamic model, then it is applied to the prediction problem of international airlines amount increase in China. The work is motivated by the following observations: First, a system of international airlines is an uncertain dynamic system, and the effects of other systems on the system being monitored are also unclear. Thus it is difficult for us to predict next annual airlines amount from the system. Second, grey system theory is one of the methods that used to study uncertainty, and it is superior in mathematical analysis of systems with uncertain information. The system of international airlines can be viewed a grey dynamic system, therefore grey dynamic model GM(1,1) which is a single variable first order differential prediction model based on grey system theory can be used to solve the prediction problem. Third, since the development trend of international airlines amount is affected by variant random factors, it is difficult to obtain high predicted accuracy by single grey dynamic model. The work procedure is shown as follows briefly: First, the Markov-chain is integrated into GM(1,1) to enhance the predicted accuracy. Second, we present Taylor approximation method based on grey interval analysis for obtaining high accuracy furthermore. Finally, the statistics data of international airlines amount from 1985 to 2003 in China is used to verify the effectiveness of proposed model.

A Kansei Evaluation Modeling for Product Design Support

In this paper, a multiple attribute decision making (MADM) approach which combine rough set with grey relational analysis (GRA) from grey system theory is proposed to establish a product design selection decision modeling considering kansei information. The proposed approach takes advantage of mathematical analysis power of grey system theory and at the same time take advantage of data mining and knowledge discovery power of rough set theory. It is suitable to the decision making under a more uncertain environment. A case of product design evaluation considering kansei information was used to validate the proposed approach.