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Article
Publication date: 1 January 1979

JOHN A. SCHULTZ

During the twentieth century mathematics has expanded at an unprecedented rate. This expansion has been accompanied by the increased application of mathematics to science…

Abstract

During the twentieth century mathematics has expanded at an unprecedented rate. This expansion has been accompanied by the increased application of mathematics to science. At a time when pure mathematics has been placing more and more emphasis on abstraction and the analysis of broad concepts there has been a corresponding proliferation of practical applications. This seems to have resulted from the fact that the sciences, too, have become more concerned with the discernment of general patterns in the study of nature. This search for simplifying ideas has increased the demand for ever more abstract tools of analysis.

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Studies in Economics and Finance, vol. 3 no. 1
Type: Research Article
ISSN: 1086-7376

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Article
Publication date: 1 October 1996

George J. Klir and David Harmanec

Provides an overview of major developments pertaining to generalized information theory during the lifetime of Kybernetes. Generalized information theory is viewed as a…

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531

Abstract

Provides an overview of major developments pertaining to generalized information theory during the lifetime of Kybernetes. Generalized information theory is viewed as a collection of concepts, theorems, principles, and methods for dealing with problems involving uncertainty‐based information that are beyond the narrow scope of classical information theory. Introduces well‐justified measures of uncertainty in fuzzy set theory, possibility theory, and Dempster‐Shafer theory. Shows how these measures are connected with the classical Hartley measure and Shannon entropy. Discusses basic issues regarding some principles of generalized uncertainty‐based information.

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Kybernetes, vol. 25 no. 7/8
Type: Research Article
ISSN: 0368-492X

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Article
Publication date: 11 April 2008

Yi Lin, Wujia Zhu, Ningsheng Gong and Guoping Du

The paper aims to show the existence of the systemic yoyo structure in human thoughts so that the human way of thinking is proven to have the same structure as that of the…

Abstract

Purpose

The paper aims to show the existence of the systemic yoyo structure in human thoughts so that the human way of thinking is proven to have the same structure as that of the material world.

Design/methodology/approach

Parallel comparison is used to reveal the underlying structure existing in human thoughts.

Findings

After highlighting all the relevant ideas and concepts, which are behind each and every crisis in the foundations of mathematics, it becomes clear that some difficulties in the authors' understanding of nature are originated from confusing actual infinities with potential infinities, and vice versa. By pointing out the similarities and differences between these two kinds of infinities, then some hidden contradictions existing in the system of modern mathematics are handily picked out. Then, theoretically, using the authors' yoyo model, it is predicted that the fourth crisis in the foundations of mathematics has appeared. And, a plan of resolution of this new crisis is provided.

Originality/value

This paper shows the first time in history that human thought, the material world, and each economic entity, share a common structure – the systemic yoyo structure. And it proves the arrival of the fourth crisis in mathematics by using systems modeling and listing several; contradictions hidden deeply in the foundations of mathematics.

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Kybernetes, vol. 37 no. 3/4
Type: Research Article
ISSN: 0368-492X

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Article
Publication date: 21 March 2016

Mitchell J. Neubert and Bruno Dyck

This paper responds to ongoing calls to develop alternative management theory to guide management practice. In particular, the purpose of the paper is to demonstrate the…

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11569

Abstract

Purpose

This paper responds to ongoing calls to develop alternative management theory to guide management practice. In particular, the purpose of the paper is to demonstrate the merit of developing sustainable management theory and organizational practices that parallel conventional management theory and practices. Sustainable theory is based on a variation of virtue theory that seeks to achieve multiple forms of well-being for multiple stakeholders in the immediate as well as distant future. To illustrate the approach, the authors develop a sustainable variation of goal setting theory.

Design/methodology/approach

The paper includes three parts. First, the authors establish the need for developing sustainable management theory (based on virtue theory) that parallels conventional management theory. Second, the authors identify and briefly review the main tenets of goal setting theory and then describe a Sustainable variation of this theory. Finally, the authors discuss the implications of the paper for management and organization theory and practice.

Findings

The conceptual arguments for a sustainable version of goal setting theory based in virtue are supported by research and practitioner examples.

Originality/value

Although there is growing concern regarding the shortcomings of management theory and practice based on a materialist-individualist moral-point-of-view, few alternatives have been discussed in detail. This paper presents an alternative based in virtue theory and illustrates how it relates to goal setting theory and practice.

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Management Decision, vol. 54 no. 2
Type: Research Article
ISSN: 0025-1747

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Article
Publication date: 1 July 2004

Chengdong Wu, Yong Yue, Mengxin Li and Osei Adjei

This paper presents a comprehensive review of the available literature on applications of the rough set theory. Concepts of the rough set theory are discussed for…

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2077

Abstract

This paper presents a comprehensive review of the available literature on applications of the rough set theory. Concepts of the rough set theory are discussed for approximation, dependence and reduction of attributes, decision tables and decision rules. The applications of rough sets are discussed in pattern recognition, information processing, business and finance, industry, environment engineering, medical diagnosis and medical data analysis, system fault diagnosis and monitoring and intelligent control systems. Development trends and future efforts are outlined. An extensive list of references is also provided to encourage interested readers to pursue further investigations.

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Engineering Computations, vol. 21 no. 5
Type: Research Article
ISSN: 0264-4401

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Book part
Publication date: 13 August 2018

Robert L. Dipboye

Abstract

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The Emerald Review of Industrial and Organizational Psychology
Type: Book
ISBN: 978-1-78743-786-9

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Article
Publication date: 12 July 2011

Albrecht Reibiger

Different axiomatizations of network theory are considered. Kirchhoff networks are regarded with priority. Multipole and multiport networks are introduced as alternative…

Abstract

Purpose

Different axiomatizations of network theory are considered. Kirchhoff networks are regarded with priority. Multipole and multiport networks are introduced as alternative variants. Additionally, Minty and Paynter networks, which are always dualizable are discussed briefly. The latter are special cases of Kirchhoff as well as of multiport networks. This paper seeks to discuss these issues.

Design/methodology/approach

The paper develops network theory inside of set theory, i.e. networks, multipoles, etc. are defined as objects of set theory. As such objects we use preferably ordered pairs, ordered triples, etc. The objects of network theory are then separated from the class of all these set theoretical objects by means of some defining conditions. These conditions are the axioms of our approaches to network theory.

Findings

It is shown that all presented variants of axiomatizations can be developed on the basis of a uniform representation for the time functions for voltages and currents. All these variants allow interdisciplinary applications of network theory and they can be generalized to multidimensional networks. An interesting byproduct is the relationship between multiport networks, networks in Belevitch normal form, Paynter networks, and bond graphs.

Originality/value

For applications it is essential that Kirchhoff and multipole networks are with respect to their modeling capability of equal value. But from the foundational point of view the multipole terminology has a number of crucial disadvantages compared with that based on Kirchhoff networks. This fact is important both for the conception of circuit simulation software packages and for the development of basic circuit theory curricula.

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COMPEL - The international journal for computation and mathematics in electrical and electronic engineering, vol. 30 no. 4
Type: Research Article
ISSN: 0332-1649

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Article
Publication date: 1 June 1993

C. Musès

Incorporates a unified basis for both set and system theory, and also makes a clear case for topology as the science which both underlies and includes logic. Indeed…

Abstract

Incorporates a unified basis for both set and system theory, and also makes a clear case for topology as the science which both underlies and includes logic. Indeed, careful topological analysis reveals the problems besetting the so‐called “law of the excluded middle”. Basically, the middle is there, whether we try to ostracize it or not. Interestingly, makes clear that Buddhist logicians almost two millennia before L. Brouwer's critique of formalistic proofs, had discovered the non‐exclusion of the middle term. Also discusses the related and neglected matter of the tangency between two sets, as distinct from their intersection or disjunction in a Boolean context. These renovated foundations make for new cybernetics and system theory as well.

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Kybernetes, vol. 22 no. 6
Type: Research Article
ISSN: 0368-492X

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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…

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

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Article
Publication date: 1 August 2004

D. Dutta Majumder and Kausik Kumar Majumdar

In this paper, we present a brief study on various paradigms to tackle complexity or in other words manage uncertainty in the context of understanding science, society and…

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1067

Abstract

In this paper, we present a brief study on various paradigms to tackle complexity or in other words manage uncertainty in the context of understanding science, society and nature. Fuzzy real numbers, fuzzy logic, possibility theory, probability theory, Dempster‐Shafer theory, artificial neural nets, neuro‐fuzzy, fractals and multifractals, etc. are some of the paradigms to help us to understand complex systems. We present a very detailed discussion on the mathematical theory of fuzzy dynamical system (FDS), which is the most fundamental theory from the point of view of evolution of any fuzzy system. We have made considerable extension of FDS in this paper, which has great practical value in studying some of the very complex systems in society and nature. The theories of fuzzy controllers, fuzzy pattern recognition and fuzzy computer vision are but some of the most prominent subclasses of FDS. We enunciate the concept of fuzzy differential inclusion (not equation) and fuzzy attractor. We attempt to present this theoretical framework to give an interpretation of cyclogenesis in atmospheric cybernetics as a case study. We also have presented a Dempster‐Shafer's evidence theoretic analysis and a classical probability theoretic analysis (from general system theoretic outlook) of carcinogenesis as other interesting case studies of bio‐cybernetics.

Details

Kybernetes, vol. 33 no. 7
Type: Research Article
ISSN: 0368-492X

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