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1 – 10 of 86Qiao‐Xing Li, Nai‐Ang Wang and Shi‐Cheng Chen
This paper attempts to establish the conceptional and computational systems of grey determinant and apply it to solve n grey equations with n grey linear equations, which can be…
Abstract
Purpose
This paper attempts to establish the conceptional and computational systems of grey determinant and apply it to solve n grey equations with n grey linear equations, which can be viewed as the important parts of grey mathematics.
Design/methodology/approach
Starting from the fact that missing information often appears in complex systems, the true values of elements when constructing a determinant and of coefficients when solving n equations with n linear equations cannot be obtained, so they are uncertain. However, their ranges can be obtained by using correct investigation methods. The uncertain elements and coefficients are grey and their ranges are number‐covered sets. On the basis of the results of Li and Wang, the paper systematically proposes the definition system of grey determinant and n grey linear equations, and utilizes the computational rules of grey determinant to solve the n grey equations with n grey linear equations. Some numerical examples are computed to illustrate the results in this paper.
Findings
The results show that the ranges of grey value of grey determinant and grey solutions of grey equations with n grey linear equations can be obtained by using computational rules proposed.
Practical implications
Because the determinant and the linear equations 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 determinant and grey linear equations may have great potential application in the real world. The method realizes the feasibility of system analysis under uncertain situations.
Originality/value
The paper succeeds in providing systematic results of computation of uncertain determinant and n linear equations by using grey systems theory and enriches the contents of grey mathematics.
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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…
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 grey‐matrix 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
Keywords
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.
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Keywords
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…
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.
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Keywords
Abstract
Details
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The purpose of this paper is to obtain the criteria of p‐moment exponential robust stability for a class of grey neutral stochastic delay systems.
Abstract
Purpose
The purpose of this paper is to obtain the criteria of p‐moment exponential robust stability for a class of grey neutral stochastic delay systems.
Design/methodology/approach
By constructing a Lyapunov‐Krasovskii functional and employing the decomposition technique of continuous matrix‐covered sets of grey matrix and using three key inequalities, the paper investigates the p‐moment exponential robust stability for a class of grey neutral stochastic delay systems. A numeric example is given to demonstrate the effectiveness of the criteria presented in the paper.
Findings
The results not only can be used to judge the p‐moment exponential robust stability of the systems researched in the paper, but also can be applied in the stability analysis of grey non‐neutral stochastic systems.
Practical implications
The method exposed in the paper can be used in the analysis and designation of practical stochastic control systems.
Originality/value
The paper succeeds in obtaining the criteria of p‐moment exponential robust stability for grey neutral stochastic delay systems by constructing a Lyapunov‐Krasovskii functional and employing the decomposition technique of continuous matrix‐covered sets of grey matrix and using three key inequalities.
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This paper seeks to investigate the extent of the implementation of annual hours working in Britain and its impact upon employers, organisations and employees.
Abstract
Purpose
This paper seeks to investigate the extent of the implementation of annual hours working in Britain and its impact upon employers, organisations and employees.
Design/methodology/approach
The paper deploys secondary data and sources to establish an overview of the salient issues.
Findings
Although there has been a growth in the extent of annual hours worked in the last decade, the rate of growth has slowed. This is related to the reduction in extant organisations that may consider introducing annual hours in tandem with the problems associated with annual hours worked.
Research limitations/implications
Issues of working time remain a key area of contestation between employers and employees, particularly as in recent years coercive competitive pressures on organisations have increased whilst a discourse about ‘family‐friendly’ working time polices has also emerged.
Practical implications
The plaudits of management consultants and policy groups concerning annual hours worked are revealed to be rather one‐sided, with considerable problems emerging for employers and employees alike.
Originality/value
Brings together an array of data to build up an analysis of annual hours worked.
Details
Keywords
WAS Britain right to resist so strongly the EEC move last month towards the introduction of a much shorter working week?
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In many relatively small industrial firms—and sometimes even in larger concerns—there comes a time when the boss looks round at the motley collection of books, periodicals…
Abstract
In many relatively small industrial firms—and sometimes even in larger concerns—there comes a time when the boss looks round at the motley collection of books, periodicals, pamphlets, catalogues, etc., which have accumulated more or less haphazardly in various corners and other situations in his office, and says to himself, usually after he has failed to find some particular item of information which he knows is somewhere in the collection, ‘I think I'll put somebody on to looking after this stuff’. He then sends for his typist and says to her, ‘Miss Smith, I want you to look after all the books we have, and all those journals and pamphlets and things that keep coming in’. And so another small special library is born.