# Search results

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Article

## Matrix representation of ideas: stimulating creativity using matrix Algebra

The purpose of this paper is to present a fresh approach to stimulate individual creativity. It introduces a mathematical representation for creative ideas, six creativity…

### Abstract

#### Purpose

The purpose of this paper is to present a fresh approach to stimulate individual creativity. It introduces a mathematical representation for creative ideas, six creativity operators and methods of matrix-algebra to evaluate, improve and stimulate creative ideas. Creativity begins with ideas to resolve a problem or tackle an opportunity. By definition, a creative idea must be simultaneously novel and useful. To inject analytic rigor into these concepts of creative ideas, the author introduces a feature-attribute matrix-construct to represent ideas, creativity operators that use ideas as operands and methods of matrix algebra. It is demonstrated that it is now possible to analytically and quantitatively evaluate the intensity of the variables that make an idea more, equal or less, creative than another. The six creativity operators are illustrated with detailed multi-disciplinary real-world examples. The mathematics and working principles of each creativity operator are discussed.

#### Design/methodology/approach

The unit of analysis is ideas, not theory. Ideas are man-made artifacts. They are represented by an original feature-attribute matrix construct. Using matrix algebra, idea matrices can be manipulated to improve their creative intensity, which are now quantitatively measurable. Unlike atoms and cute rabbits, creative ideas, do not occur in nature. Only people can conceive and develop creative ideas for embodiment in physical, non-physical forms, or in a mix of both. For example, as widgets, abstract theorems, business processes, symphonies, organization structures, and so on. The feature-attribute matrix construct is used to represent novelty and usefulness. The multiplicative product of these two matrices forms the creativity matrix. Six creativity operators and matrix algebra are introduced to stimulate and measure creative ideas. Creativity operators use idea matrices as operands. Uses of the six operators are demonstrated using multi-disciplinary real-world examples. Metrics for novelty, usefulness and creativity are in ratio scales, grounded on the Weber–Fechner Law. This law is about persons’ ability to discern differences in the intensity of stimuli.

#### Findings

Ideas are represented using feature-attribute matrices. This construct is used to represent novel, useful and creative ideas with more clarity and precision than before. Using matrices, it is shown how to unambiguously and clearly represent creative ideas endowed with novelty and usefulness. It is shown that using matrix algebra, on idea matrices, makes it possible to analyze multi-disciplinary, real-world cases of creative ideas, with clarity and discriminatory power, to uncover insights about novelty and usefulness. Idea-matrices and the methods of matrix algebra have strong explanatory and predictive power. Using of matrix algebra and eigenvalue analyses, of idea-matrices, it is demonstrated how to quantitatively rank ideas, features and attributes of creative ideas. Matrix methods operationalize and quantitatively measure creativity, novelty and usefulness. The specific elementary variables that characterize creativity, novelty and usefulness factors, can now be quantitatively ranked. Creativity, novelty and usefulness factors are not considered as monolithic, irreducible factors, vague “lumpy” qualitative factors, but as explicit sets of elementary, specific and measurable variables in ratio scales. This significantly improves the acuity and discriminatory power in the analyses of creative ideas. The feature-attribute matrix approach and its matrix operators are conceptually consistent and complementary with key extant theories engineering design and creativity.

#### Originality/value

First to define and specify ideas as feature-attribute matrices. It is demonstrated that creative ideas, novel ideas and useful ideas can be analytically and unambiguously specified and measured for creativity. It is significant that verbose qualitative narratives will no longer be the exclusive means to specify creative ideas. Rather, qualitative narratives will be used to complement the matrix specifications of creative ideas. First to specify six creativity operators enabling matrix algebra to operate on idea-matrices as operands to generate new ideas. This capability informs and guides a person’s intuition. The myth and dependency, on non-repeatable or non-reproducible serendipity, flashes of “eureka” moments or divine inspiration, can now be vacated. Though their existence cannot be ruled out. First to specify matrix algebra and eigen-value methods of quantitative analyses of feature-attribute matrices to rank the importance of elementary variables that characterize factors of novelty, usefulness and creativity. Use of verbose qualitative narratives of novelty, usefulness and creativity as monolithic “lumpy” factors can now be vacated. Such lumpy narratives risk being ambiguous, imprecise, unreliable and non-reproducible, Analytic and quantitative methods are more reliable and consistent. First to define and specify a method of “attacking the negatives” to systematically pinpoint the improvements of an idea’s novelty, usefulness and creativity. This procedure informs and methodically guides the improvements of deficient ideas.

### Details

International Journal of Innovation Science, vol. 11 no. 4
Type: Research Article
ISSN: 1757-2223

Article

## Delay-independent stabilization of nonlinear systems with multiple time-delays and its application in chaos synchronization of Rössler system

– The purpose of this paper is with delay-independent stabilization of nonlinear systems with multiple time-delays and its application in chaos synchronization of Rössler system.

### Abstract

#### Purpose

The purpose of this paper is with delay-independent stabilization of nonlinear systems with multiple time-delays and its application in chaos synchronization of Rössler system.

#### Design/methodology/approach

Based on linear matrix inequality and algebra Riccati matrix equation, the stabilization result is derived to guarantee asymptotically stable and applicated in chaos synchronization of Rössler chaotic system with multiple time-delays.

#### Findings

A controller is designed and added to the nonlinear system with multiple time-delays. The stability of the nonlinear system at its zero equilibrium point is guaranteed by applying the appropriate controller signal based on linear matrix inequality and algebra Riccati matrix equation scheme. Another effective controller is also designed for the global asymptotic synchronization on the Rössler system based on the structure of delay-independent stabilization of nonlinear systems with multiple time-delays. Numerical simulations are demonstrated to verify the effectiveness of the proposed controller scheme.

#### Originality/value

The introduced approach is interesting for delay-independent stabilization of nonlinear systems with multiple time-delays and its application in chaos synchronization of Rössler system.

### Details

International Journal of Intelligent Computing and Cybernetics, vol. 9 no. 2
Type: Research Article
ISSN: 1756-378X

Book part

## Building Generalizable Case-Based Theory in Human Resources Management

This study applies asymmetric rather than conventional symmetric analysis to advance theory in occupational psychology. The study applies systematic case-based analyses to…

### Abstract

This study applies asymmetric rather than conventional symmetric analysis to advance theory in occupational psychology. The study applies systematic case-based analyses to model complex relations among conditions (i.e., configurations of high and low scores for variables) in terms of set memberships of managers. The study uses Boolean algebra to identify configurations (i.e., recipes) reflecting complex conditions sufficient for the occurrence of outcomes of interest (e.g., high versus low financial job stress, job strain, and job satisfaction). The study applies complexity theory tenets to offer a nuanced perspective concerning the occurrence of contrarian cases – for example, in identifying different cases (e.g., managers) with high membership scores in a variable (e.g., core self-evaluation) who have low job satisfaction scores and when different cases with low membership scores in the same variable have high job satisfaction. In a large-scale empirical study of managers (n = 928) in four (contextual) segments of the farm industry in New Zealand, this study tests the fit and predictive validities of set membership configurations for simple and complex antecedent conditions that indicate high/low core self-evaluations, job stress, and high/low job satisfaction. The findings support the conclusion that complexity theory in combination with configural analysis offers useful insights for explaining nuances in the causes and outcomes to high stress as well as low stress among farm managers. Some findings support and some are contrary to symmetric relationship findings (i.e., highly significant correlations that support main effect hypotheses).

### Details

Improving the Marriage of Modeling and Theory for Accurate Forecasts of Outcomes
Type: Book
ISBN: 978-1-78635-122-7

Article

## Energy Theorems and Structural Analysis: A Generalized Discourse with Applications on Energy Principles of Structural Analysis Including the Effects of Temperature and Non‐Linear Stress‐Strain Relations Part I. General Theory

THE general theorems given in Sections 4 and 6 include, from the fundamental point of view, all that is required for the analysis of redundant structures. However, to…

### Abstract

THE general theorems given in Sections 4 and 6 include, from the fundamental point of view, all that is required for the analysis of redundant structures. However, to facilitate practical calculations it is helpful to develop more explicit methods and formulae. To find these is the purpose of this Section.

### Details

Aircraft Engineering and Aerospace Technology, vol. 27 no. 2
Type: Research Article
ISSN: 0002-2667

Article

## Using interpretive structural modelling in strategic decision‐making groups

The purpose of this paper is to apply interpretive structural modelling in the clarification of the perceptions of different individuals in a managerial group in order to…

### Abstract

#### Purpose

The purpose of this paper is to apply interpretive structural modelling in the clarification of the perceptions of different individuals in a managerial group in order to improve group decision making. To limit conflict and increase shared knowledge in group decision making, there is a need to explain differences among group members at the cognitive level.

#### Design/methodology/approach

Qualitative research has suggested methods that involve personal narratives and in‐depth interviews. The effectiveness of such methods can be enhanced using the techniques of formal logic. The approach used for the case is a simulation of a strategic group decision‐making process using interpretive structural modelling. The simulation contemplates a typical business scenario. It was done using role‐play in strategic corporate problem solving: four functional managerial roles and one general managerial role were assigned. Individual and group relationships were portrayed.

#### Findings

After analysing the results the authors found major differences in priority orderings of the different roles. As there are differences in the perception of the priority of the issues in the different managerial roles, it would be more difficult to take a decision.

#### Research limitations/implications

The limitations of this research are that it was done with assigned roles instead of real executives. Further research could provide ways of identifying schools of thought in decision‐making groups for strategic issues.

#### Practical implications

The practical application of this paper would be in the hypothetical decision‐making arena, improving the decision‐making process among executives working in different functional areas.

#### Originality/value

The application of formal logic methods to a decision‐making process is the prime contribution of this paper.

### Details

Management Decision, vol. 43 no. 6
Type: Research Article
ISSN: 0025-1747

Article

## Convergence of ADGI methods for solving systems of linear matrix equations

The linear matrix equations have wide applications in engineering, physics, economics and statistics. The purpose of this paper is to introduce iterative methods for…

### Abstract

#### Purpose

The linear matrix equations have wide applications in engineering, physics, economics and statistics. The purpose of this paper is to introduce iterative methods for solving the systems of linear matrix equations.

#### Design/methodology/approach

According to the hierarchical identification principle, the authors construct alternating direction gradient-based iterative (ADGI) methods to solve systems of linear matrix equations.

#### Findings

The authors propose efficient ADGI methods to solve the systems of linear matrix equations. It is proven that the ADGI methods consistently converge to the solution for any initial matrix. Moreover, the constructed methods are extended for finding the reflexive solution to the systems of linear matrix equations.

#### Originality/value

This paper proposes efficient iterative methods without computing any matrix inverses, vec operator and Kronecker product for finding the solution of the systems of linear matrix equations.

### Details

Engineering Computations, vol. 31 no. 4
Type: Research Article
ISSN: 0264-4401

Article

## Performance of minimum energy controllers on tiltrotor aircraft

### Abstract

#### Approach

Minimum energy controllers are designed for tiltrotor aircraft models for helicopter and airplane modes. Performance of minimum energy controllers is evaluated with respect to several criteria.

#### Findings

Minimum energy controllers can be used for tiltrotor aircraft flight control system design. These controllers show satisfactory performance when noise intensities and variance bounds vary.

#### Practical implications

Minimum energy controllers can be implemented for tiltrotor aircraft flight control system design.

#### Originality/value

In this paper, minimum energy controllers are applied for tiltrotor aircraft flight control system design and the performance of minimum energy controllers is evaluated deeply on a complex physical system (i.e. tiltrotor aircraft).

### Details

Aircraft Engineering and Aerospace Technology: An International Journal, vol. 86 no. 5
Type: Research Article
ISSN: 0002-2667

Book part

## Spatial Dependence in Regressors and its Effect on Performance of Likelihood-Based and Instrumental Variable Estimators

Most spatial econometrics work focuses on spatial dependence in the regressand or disturbances. However, Lesage and Pace (2009) as well as Pace and LeSage2009 showed that…

### Abstract

Most spatial econometrics work focuses on spatial dependence in the regressand or disturbances. However, Lesage and Pace (2009) as well as Pace and LeSage2009 showed that the bias in β from applying OLS to a regressand generated from a spatial autoregressive process was exacerbated by spatial dependence in the regressor. Also, the marginal likelihood function or restricted maximum likelihood (REML) function includes a determinant term involving the regressors. Therefore, high dependence in the regressor may affect the likelihood through this term. In addition, Bowden and Turkington (1984) showed that regressor temporal autocorrelation had a non-monotonic effect on instrumental variable estimators.

We provide empirical evidence that many common economic variables used as regressors (e.g., income, race, and employment) exhibit high levels of spatial dependence. Based on this observation, we conduct a Monte Carlo study of maximum likelihood (ML), REML and two instrumental variable specifications for spatial autoregressive (SAR) and spatial Durbin models (SDM) in the presence of spatially correlated regressors.

Findings indicate that as spatial dependence in the regressor rises, REML outperforms ML and that performance of the instrumental variable methods suffer. The combination of correlated regressors and the SDM specification provides a challenging environment for instrumental variable techniques.

We also examine estimates of marginal effects and show that these behave better than estimates of the underlying model parameters used to construct marginal effects estimates. Suggestions for improving design of Monte Carlo experiments are provided.

### Details

30th Anniversary Edition
Type: Book
ISBN: 978-1-78190-309-4

Article

## Executive learning through case discussion

The purpose of this paper is to provide a framework with which to understand the issues that arise in the discussion cases included in this Special Issue and explains the…

### Abstract

#### Purpose

The purpose of this paper is to provide a framework with which to understand the issues that arise in the discussion cases included in this Special Issue and explains the role of case studies in the education of those responsible for leading organizations.

#### Design/methodology/approach

This paper is based upon the review of literature from a range of disciplines, all of which is relevant to executive learning; the analysis of the cases and papers in this Special Issue, and interviews with colleagues who use the case method.

#### Findings

The case method is useful in the education of managerial decision makers who face complex situations, but it is most effective when the cases contain certain essential ingredients and when the instructor is skilled in discussion leadership. These ingredients include the presence of a protagonist, the deep description of a problematic situation, the existence of at least two reasonable courses of action, and sufficient data to evaluate each alternative. The interactive nature of case discussions reinforces those values and behaviors that associate with civility.

#### Research limitations/implications

Since some of the discussion cases were in the process of completion, it was not always possible to evaluate the experience with their use in the classroom.

#### Practical implications

The introductory paper points to broader opportunities for the use of the case method, and for its adaptation to experiential learning, than is generally recognized in academia.

#### Social implications

The use of discussion cases in management schools, where future business leaders interact with professors and classmates in an environment of critical learning and respect for opinions of others, encourages behaviors of civility.

#### Originality/value

This introductory paper is valuable in providing a framework to integrate and make sense of the diverse topics, situations, and contexts described in the cases contained in the Special Issue.

### Details

Management Decision, vol. 52 no. 9
Type: Research Article
ISSN: 0025-1747

Book part

## Four-Corner Outcomes in Strategic Management: Successful and Unsuccessful Paddling Down versus Upstream

This chapter elaborates on the usefulness of embracing complexity theory, modeling outcomes rather than directionality, and modeling complex rather than simple outcomes in…

### Abstract

This chapter elaborates on the usefulness of embracing complexity theory, modeling outcomes rather than directionality, and modeling complex rather than simple outcomes in strategic management. Complexity theory includes the tenet that most antecedent conditions are neither sufficient nor necessary for the occurrence of a specific outcome. Identifying a firm by individual antecedents (i.e., noninnovative vs. highly innovative, small vs. large size in sales or number of employees, or serving local vs. international markets) provides shallow information in modeling specific outcomes (e.g., high sales growth or high profitability) – even if directional analyses (e.g., regression analysis, including structural equation modeling) indicate that the independent (main) effects of the individual antecedents relate to outcomes directionally – because firm (case) anomalies almost always occur to main effects. Examples: a number of highly innovative firms have low sales while others have high sales and a number of noninnovative firms have low sales while others have high sales. Breaking-away from the current dominant logic of directionality testing – null hypothesis significance testing (NHST) – to embrace somewhat precise outcome testing (SPOT) is necessary for extracting highly useful information about the causes of anomalies – associations opposite to expected and “statistically significant” main effects. The study of anomalies extends to identifying the occurrences of four-corner strategy outcomes: firms doing well in favorable circumstances, firms doing badly in favorable circumstances, firms doing well in unfavorable circumstances, and firms doing badly in unfavorable circumstances. Models of four-corner strategy outcomes advance strategic management beyond the current dominant logic of directional modeling of single outcomes.

### Details

Improving the Marriage of Modeling and Theory for Accurate Forecasts of Outcomes
Type: Book
ISBN: 978-1-78635-122-7

### Keywords

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