Complex fuzzy linear systems

In paper the complex fuzzy linear equation nbspnbspin which nbspis a crisp complex matrix and nbspis an arbitrary complex fuzzy numbers vector, is investigated. The complex fuzzy linear system is converted to a equivalent high order fuzzy linear system . Numerical procedure for calculating the complex fuzzy solution is designed and thenbsp sufficient condition for the existence of strong complex fuzzy solution is derived. A example is given to illustrate the proposed method.nbs

What Makes Complex Systems Complex?

This paper explores some of the factors that make complex systems complex. We first examine the history of complex systems. It was Aristotle’s insight that how elements are joined together helps determine the properties of the resulting whole. We find (a) that scientific reductionism does not provide a sufficient explanation; (b) that to understand complex systems, one must identify and trace energy flows; and (c) that disproportionate causality, including global tipping points, are all around us. Disproportionate causality results from the wide availability of energy stores. We discuss three categories of emergent phenomena—static, dynamic, and adaptive—and recommend retiring the term emergent, except perhaps as a synonym for creative. Finally, we find that virtually all communication is stigmergic

Complex City Systems

Information and communications technology (ICT) is being exploited within cities to enable them to better compete in a global knowledge-based service-led economy. In the nineteenth and twentieth centuries, cities exploited large technical systems (LTSs) such as the telegraph, telephony, electrical networks, and other technologies to enhance their social and economic position. This paper examines how the LTS model applies to ICT deployments, including broadband network, municipal wireless, and related services, and how cities and city planners in the twenty-first century are using or planning to use these technologies. This paper also examines their motivations and expectations, the contribution to date, and the factors affecting outcomes. The findings extend the LTS model by proposing an increased role for organizations with respect to an individual agency. The findings show how organizations form themselves into networks that interact and influence the outcome of the system at the level of the city. The extension to LTS, in the context of city infrastructure, is referred to as the complex city system framework. This proposed framework integrates the role of these stakeholder networks, as well as that of the socioeconomic, technical, and spatial factors within a city, and shows how together they shape the technical system and its socioeconomic contribution. The CCS framework has been presented at Digital Cities Conferences in Eindhoven, Barcelona, Taiwan, London and at IBM’s Global Smart Cities Conference in Shanghai between 2010 and 2012. Its finding are timely in the context of major policy decisions on investments at regional, national and international level on ICT infrastructure and related service transformation, as well as the governance of such projects, their planning and their deployment

Why Risk Models should be Parameterised

Risk models using fault and event trees can be extended with explicit factors, which are states of the system, its users or its environment that influence event probabilities. The factors act as parameters in the risk model, enabling the model to be re-used and also providing a new way to estimate the overall risk of a system with many instances of the risk. A risk model with parameters can also be clearer

Evolution in complex systems

What features characterise complex system dynamics? Power laws and scale invariance of fluctuations are often taken as the hallmarks of complexity, drawing on analogies with equilibrium critical phenomena[1-3]. Here we argue that slow, directed dynamics, during which the system's properties change significantly, is fundamental. The underlying dynamics is related to a slow, decelerating but spasmodic release of an intrinsic strain or tension. Time series of a number of appropriate observables can be analysed to confirm this effect. The strain arises from local frustration. As the strain is released through "quakes", some system variable undergoes record statistics with accompanying log-Poisson statistics for the quake event times[4]. We demonstrate these phenomena via two very different systems: a model of magnetic relaxation in type II superconductors and the Tangled Nature model of evolutionary ecology, and show how quantitative indications of ageing can be found.Comment: 8 pages, 5 figures all in one fil

Complex Systems: A Survey

A complex system is a system composed of many interacting parts, often called agents, which displays collective behavior that does not follow trivially from the behaviors of the individual parts. Examples include condensed matter systems, ecosystems, stock markets and economies, biological evolution, and indeed the whole of human society. Substantial progress has been made in the quantitative understanding of complex systems, particularly since the 1980s, using a combination of basic theory, much of it derived from physics, and computer simulation. The subject is a broad one, drawing on techniques and ideas from a wide range of areas. Here I give a survey of the main themes and methods of complex systems science and an annotated bibliography of resources, ranging from classic papers to recent books and reviews.Comment: 10 page