Search results

1 – 10 of over 8000
Article
Publication date: 1 August 2006

Zhi‐geng Fang, Si‐feng Liu, Aiqing Ruan and Xuewei Zhang

A study is made of the payoff matrix which is made up of grey interval number because of asymmetry information, player's finite knowledge and bounded rationality and all sorts of…

Abstract

Purpose

A study is made of the payoff matrix which is made up of grey interval number because of asymmetry information, player's finite knowledge and bounded rationality and all sorts of stochastic and non‐stochastic factors.

Design/methodology/approach

On the base of concept of equipollent, superior and inferior potential degree, the paper designs determinant rules of interval grey number potential relations, opens out player's decision‐making laws in the conditions of finite knowledge and logos. And it designs the grey game decision‐making rules which player choices maximum potential degree of grey game value (the most favorableness situation) under the cases of that there are all likely to be minimum potential degree of grey game value (the most disadvantage situation), which is a reliable way for both sides to accept.

Findings

The paper recognizes and defines overrated and underrated risk of potential optimal pure strategy in the grey game, designs arithmetic for determining player's overrated and underrated risk under the situation of potential optimal pure strategy.

Practical implications

The presents system meets the requirement of judging pure strategy solutions in the grey potential situation.

Originality/value

This paper builds up the system of judgment for grey potential.

Details

Kybernetes, vol. 35 no. 7/8
Type: Research Article
ISSN: 0368-492X

Keywords

Article
Publication date: 28 January 2014

Qiao-Xing Li, Sifeng Liu and Nai-Ang Wang

This paper attempts to establish the general formula for computing the inverse of grey matrix, and the results are applied to solve grey linear programming. The inverse of a grey

Abstract

Purpose

This paper attempts to establish the general formula for computing the inverse of grey matrix, and the results are applied to solve grey linear programming. The inverse of a grey matrix and grey linear programming plays an important role in establishing a grey computational system.

Design/methodology/approach

Starting from the fact that missing information often appears in complex systems, and therefore that true values of elements are uncertain when the authors construct a matrix, as well as calculate its inverse. However, the authors can get their ranges, which are called the number-covered sets, by using grey computational rules. How to get the matrix-covered set of inverse grey matrix became a typical approach. In this paper, grey linear programming was explained in detail, for the point of grey meaning and the methodology to calculate the inverse grey matrix can successfully solve grey linear programming.

Findings

The results show that the ranges of grey value of inverse grey matrix and grey linear programming can be obtained by using the computational rules.

Practical implications

Because the matrix and the linear programming have been widely used in many fields such as system controlling, economic analysis and social management, and the missing information is a general phenomenon for complex systems, grey matrix and grey linear programming may have great potential application in real world. The methodology realizes the feasibility to control the complex system under uncertain situations.

Originality/value

The paper successfully obtained the ranges of uncertain inverse matrix and linear programming by using grey system theory, when the elements of matrix and the coefficients of linear programming are intervals and the results enrich the contents of grey mathematics.

Details

Grey Systems: Theory and Application, vol. 4 no. 1
Type: Research Article
ISSN: 2043-9377

Keywords

Article
Publication date: 2 November 2015

Shervin Zakeri and Mohammad Ali Keramati

Supplier selection is a complex multiple criteria decision (MCDM) problem which directly depends on decision makers’ choice. Some decisions are getting involved with linguistic…

Abstract

Purpose

Supplier selection is a complex multiple criteria decision (MCDM) problem which directly depends on decision makers’ choice. Some decisions are getting involved with linguistic variables and they are not mathematically operable. To solve a typical decision problem through MCDM techniques, a number or a numerical interval should be defined. The purpose of this paper is to focus on that numerical interval and in a case of supplier selection, the aim is to close the decisions to the real number that the decision maker mentions and this number is in a numerical interval.

Design/methodology/approach

The proposed method deals with grey relational analysis (GRA) and develops it by applying triangular fuzzy numbers. The grey numbers have two defined bounds; the proposed method defines two fuzzy bounds for each grey attribute. In the proposed method, the fuzzy membership function has been employed for each bounds of grey attribute to make them to fuzzy bounds with two undefined bounds. Also to make comparison, with employing of TOPSIS technique, both of the grey fuzzy combination decision matrix and the original grey decision matrix are obtained.

Findings

The results indicate that, except to the ideal solutions, the grey relation coefficient for each alternative is too close to each other. Indeed, they are too close to zero. Applying the proposed method in problem of supplier selection shows the difference between two selected supplier in proposed method and the original grey method.

Originality/value

As mentioned heretofore this paper aims to make decision makers’s decision more accurate and actually there is no other researches which used this combination method.

Details

Grey Systems: Theory and Application, vol. 5 no. 3
Type: Research Article
ISSN: 2043-9377

Keywords

Article
Publication date: 7 August 2017

Ke Zhang, Qiupin Zhong and Yuan Zuo

The purpose of this paper is to overcome the shortcomings of existing multivariate grey incidence models that cannot analyze the similarity of behavior matrixes.

Abstract

Purpose

The purpose of this paper is to overcome the shortcomings of existing multivariate grey incidence models that cannot analyze the similarity of behavior matrixes.

Design/methodology/approach

First, the feasibility of using gradient to measure the similarity of continuous functions is analyzed theoretically and intuitively. Then, a grey incidence degree is constructed for multivariable continuous functions. The model employs the gradient to measure the local similarity, as incidence coefficient function, of two functions, and combines local similarity into global similarity, as grey incidence degree by double integral. Third, the gradient incidence degree model for behavior matrix is proposed by discretizing the continuous models. Furthermore, the properties and satisfaction of grey incidence atom of the proposed model are research, respectively. Finally, a financial case is studied to examine the validity of the model.

Findings

The proposed model satisfies properties of invariance under mean value transformation, multiple transformation and linear transformation, which proves it is a model constructed from similarity perspective. Meanwhile, the case study shows that proposed model performs effectively.

Practical implications

The method proposed in the paper could be used in financial multivariable time series clustering, personalized recommendation in e-commerce, etc., when the behavior matrixes need to be analyzed from trend similarity perspective.

Originality/value

It will promote the accuracy of multivariate grey incidence model.

Details

Grey Systems: Theory and Application, vol. 7 no. 2
Type: Research Article
ISSN: 2043-9377

Keywords

Article
Publication date: 10 April 2009

Qiao‐Xing Li and Si‐Feng Liu

The purpose of this paper is to explain the connotation of grey number, which is the basic unit of grey mathematics and the key to establish the mathematic framework of grey

565

Abstract

Purpose

The purpose of this paper is to explain the connotation of grey number, which is the basic unit of grey mathematics and the key to establish the mathematic framework of grey system theory.

Design/methodology/approach

From the grey hazy set, the paper re‐defines grey number and the operation of grey‐number element, then some properties are obtained. Based on them, the operation of greymatrix element is given. The general definition of grey function and its operation are also proposed.

Findings

The connotation of grey number is elaborated and the elementary framework of grey mathematics can be established.

Research limitations/implications

The researched object, objective and techniques of grey system theory have not been logically proposed and they may influence the comprehension of grey system theory. The obtained results of grey mathematics may significantly promote its development.

Practical implications

The paper can enable managers to control the complex system with missing information by using the quantitative approaches.

Originality/value

Grey mathematics may become a branch of mathematics to deal with proximate calculation.

Details

Kybernetes, vol. 38 no. 3/4
Type: Research Article
ISSN: 0368-492X

Keywords

Article
Publication date: 10 April 2009

Qiao‐Xing Li and Si‐Feng Liu

The purpose of this paper is to propose the input‐occupancy‐output analysis for grey situations and to manage the economic systems with missing information. The situation is…

376

Abstract

Purpose

The purpose of this paper is to propose the input‐occupancy‐output analysis for grey situations and to manage the economic systems with missing information. The situation is realistic in practice.

Design/methodology/approach

During the decision‐making process of an economic system, the managers often get some uncertain data for the missing information. Then, it becomes difficult to analyze the complex system by using the input‐occupancy‐output analysis. Since the uncertain data are grey numbers, the decision maker can control it by using grey system theory and the input‐occupancy‐output analysis.

Findings

Get the grey direct consumption and occupancy coefficient matrices and the computational formulas of their matrix‐covered sets. The grey model of input‐occupancy‐output analysis and its covered solution are also obtained.

Research limitations/implications

The chaos of the grey statistic data should satisfy a level of accuracy and it is key to get the number‐covered set that the true data belongs to.

Practical implications

A feasible approach to control the economic system that the accurate data are difficult to be obtained.

Originality/value

Give a new approach to study an economic system by using grey system theory.

Details

Kybernetes, vol. 38 no. 3/4
Type: Research Article
ISSN: 0368-492X

Keywords

Article
Publication date: 25 January 2013

Xueshan Han, Thi Dieu Linh Nguyen and Haiyan Xu

The purpose of this paper is to propose a complete theory of grey conflict analysis model based on grey game and the graph model for conflict resolution and also, to illustrate a…

Abstract

Purpose

The purpose of this paper is to propose a complete theory of grey conflict analysis model based on grey game and the graph model for conflict resolution and also, to illustrate a case of “prisoner's dilemma” in the traditional grey game as an example.

Design/methodology/approach

Based on the theories of grey game and graph model for conflict resolution, this paper concentrates on the model of grey conflict analysis in a case of two players under the condition of symmetrical loss information. By analyzing decision makers, strategies, states, graph model and grey potential, and the number of decision makers' steps, the pure strategy Nash equilibrium is extended to grey potential‐general metarationality, grey potential‐symmetrical metarationality, and grey potential‐sequential stability. Meanwhile, the logical relationships between solutions are discussed. A specific case study is carried out to illustrate how the proposed grey conflict analysis model is used in practice.

Findings

The results in this paper indicate that more stable solutions are found when one considers the grey potential‐general metarationality, the grey potential‐symmetrical metarationality, and the grey potential‐sequential stability, and then solve the paradox of “prisoner's dilemma”.

Practical implications

This new grey conflict analysis model could be used to provide useful information for policy makers during existing conflicts or negotiations among parties or enterprises.

Originality/value

The paper succeeds in constructing a new grey conflict analysis model, in which the solution concepts are studied; and the two‐player grey game will be extended to n‐players in the near future.

Details

Grey Systems: Theory and Application, vol. 3 no. 1
Type: Research Article
ISSN: 2043-9377

Keywords

Article
Publication date: 28 October 2014

Om Ji Shukla, Gunjan Soni and G. Anand

In the current customer-driven market, the manufacturers have to be highly responsive and flexible to deliver a variety of products. Hence, to meet this dynamic and uncertain…

Abstract

Purpose

In the current customer-driven market, the manufacturers have to be highly responsive and flexible to deliver a variety of products. Hence, to meet this dynamic and uncertain market changes, the production system, which enables the manufacturing of such variety of products should be able to meet such diverse, dynamic changes. Hence, selecting a suitable manufacturing system is a key strategic decision for today's manufacturing organization, which needs to survive in these uncertain market conditions. Hence, the purpose of this paper is to present a decision-making model for selecting the best manufacturing system and also discuss the criteria on the basis of which the management can select the same.

Design/methodology/approach

A case of small- and medium-sized company is presented, in which the management is deciding to establish a most suitable manufacturing system. To supplement this, a suitable multi-criteria decision-making model (MCDM), the grey approach is used to analyze manufacturing system alternatives based on various decision criteria to arrive a comparative ranking.

Findings

An extensive analysis of grey-based decision-making model described grey decision matrix, grey normalized decision matrix, grey weighted normalized decision matrix and grey possibility degrees for three alternatives revealed that lean manufacturing systems was found to be the most suitable manufacturing system among three alternatives for a given case.

Research limitations/implications

The same study can be extended by including sub-criteria with main criteria for selection of manufacturing system by utilizing two MCDM techniques such as AHP or ANP with Grey approach.

Practical implications

The Grey approach has been discussed in a detailed way and it will be useful for the managers to use this approach as a tool for solving similar type of decision-making problems in their organizations in the future.

Originality/value

Although, the problem of selecting a suitable manufacturing system is often addressed both in practice and research, very few reports are available in the literature of Grey-based decision models that demonstrated its application for selecting a suitable manufacturing systems.

Details

Grey Systems: Theory and Application, vol. 4 no. 3
Type: Research Article
ISSN: 2043-9377

Keywords

Article
Publication date: 29 July 2020

Xiumei Hao, Mingwei Li and Yuting Chen

This paper takes the seven overcapacity industries such as the textile industry, electricity and heat, steel, coal, automobile manufacturing, nonferrous metals and petrochemical…

Abstract

Purpose

This paper takes the seven overcapacity industries such as the textile industry, electricity and heat, steel, coal, automobile manufacturing, nonferrous metals and petrochemical industry as research objects and proposes a TOPSIS grey relational projection group decision method with mixed multiattributes, which is used for the ranking of the seven industries with overcapacity and provided relevant departments with a basis for decision-making.

Design/methodology/approach

First, an evaluation index system from four aspects is established. Secondly, the attributes of linguistic information are converted into two-dimensional interval numbers and triangular fuzzy numbers, and an evaluation matrix is constructed and normalized. This paper uses the AHP method to determine the subjective weights and uses the coefficient of variation method to determine the objective weights. Moreover, this paper sets up the optimization model with the largest comprehensive evaluation value to determine the combined weights. Finally, the TOPSIS grey relational projection method is proposed to calculate the closeness of grey relational projections and to rank them.

Findings

This paper analyzes the problem of overcapacity in seven industries with the TOPSIS grey relational projection method. The results show that the four industries of automobile manufacturing, textile, coal and petrochemical are all in serious overcapacity levels, while the three industries of steel, nonferrous metals and electric power are relatively in weak overcapacity level in the three years of 2016–2018. TOPSIS grey relational projection method ranks the overcapacity degree of the seven major overcapacity industries, making the relative overcapacity degree of each industry more clear and providing a reference for the government to formulate targeted policies and measures for each industry.

Practical implications

By using TOPSIS grey relational projection method to evaluate the overcapacity of the seven major overcapacity industries, on the one hand, it makes the relative overcapacity degree of each industry more clear, on the other hand, it can provides the basis for the government and decision-making departments. This helps them promote better the healthy and orderly economic development of the seven major industries and avoid resource waste caused by overcapacity.

Originality/value

This article solves the single evaluation method caused by the limited indicators in the past, combines TOPSIS and the grey relational projection method and applies it to the overcapacity evaluation of the industry, not only applies it to the evaluation of overcapacity for the first time but also involves novel problems and methods, which expands the scope of application of the model.

Details

Grey Systems: Theory and Application, vol. 11 no. 2
Type: Research Article
ISSN: 2043-9377

Keywords

Article
Publication date: 2 November 2015

Dilip Kumar Sen, Saurav Datta and Siba Sankar Mahapatra

Decision making is the task of selecting the most appropriate alternative among a finite set of possible alternatives with respect to some attributes. The attributes may be…

Abstract

Purpose

Decision making is the task of selecting the most appropriate alternative among a finite set of possible alternatives with respect to some attributes. The attributes may be subjective or objective (or combination of both), depending upon the situation; requirements may also be conflicting. In practice, most of the real-world decision-making problems are based on subjective evaluation criteria which are basically ill-defined and vague. Since subjective human judgment bears ambiguity and vagueness in the decision making; application of grey numbers set theory may be proved fruitful in this context. The paper aims to discuss these issues.

Design/methodology/approach

Owing to the advantages of grey numbers set theory in tackling subjectivity in decision making; the crisp-TODIM needs to be extended by integrating with grey numbers set theory in order to facilitate decision making consisting of subjective data. Hence, the unified objective of this paper is to propose a grey-based TODIM approach in the context of decision making.

Findings

Application potential of grey-TODIM has been demonstrated through a case empirical robot selection problem. Result obtained thereof, has also been compared to that of existing grey-based decision support systems available in literature.

Originality/value

Application potential of grey-based decision support systems (grey-TOPSIS, grey analysis, grey-MOORA) have been highlighted in available literature resource. However, the shortcoming of these approaches is that they do not consider decision-makers’ risk attitude while decision making. TODIM method is derived from the philosophy of Cumulative Prospect Theory (CPT) which considers risk averting attitude of the decision maker in case of gain and risk seeking attitude in case of loss, while comparing dominance between two alternatives with respect to a particular criterion. Hence, this paper contributes a mathematical foundation of TODIM coupled with grey numbers set theory for logical decision making.

Details

Grey Systems: Theory and Application, vol. 5 no. 3
Type: Research Article
ISSN: 2043-9377

Keywords

1 – 10 of over 8000