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allocation of competitive sports resources is foundation and premise for the brilliant
achievements. The so-called competitive sports resources is the sum of all the input
resources for competitive sports activities, including human, financial and material
resources, as well as some tangible and intangible resources like training techniques,
physical fitness, moral laws, customs and culture [1]. With human development, so-
cial progress, economic system transition and transformation of social institutions, the
original sports resource allocation pattern has shown many limitations and drawbacks.
How to adjust the allocation mode of competitive sports resources in China should be
given priorities. In this regard, there is considerable need for methods and indicators
to diagnose the allocation efficiency of competitive sports resources for adjusting the
allocation mode, management and regulation.
As a kind of multi-attribute assessment, the evaluation of the allocation efficiency
of competitive sports resources is conducted mainly through the use of proxy indica-
tors. These indicators are then aggregated into a composite index by certain weight
determination procedure. The indices aggregation procedure is a continuous process
of optimization, the transition of the equilibrium state from instability to stability [2].
The analytic hierarchy process (AHP) has been used widely for determining weights
of indices in multi-attribute assessment studies [3-4]. However, the weight determina-
tion procedure of AHP is treaded as a discontinuous process, given that the impor-
tance of the indicators is divided into certain grades [2]. Despite its popularity and
simplicity in concept, this method is often criticized for its inability to adequately
incorporate the inherent uncertainty and imprecision associated with quantifying deci-
sion maker's perceptions using discrete (crisp) values [5-6].
Thom (1975) [7] proposed the catastrophe theory (CT), a mathematical model
studies systems that, under particular conditions, show sudden changes in the steady
equilibrium state as a consequence of small changes in the value of certain input pa-
rameters [8]. Due to its dialectic characteristics and advantages as a simple mathe-
matical construct with clear physical meaning, the catastrophe theory has recently
found home in multi-attribute assessment studies [2, 9]. The catastrophe-based as-
sessment model considers the whole problem as a particular catastrophic behavior, a
small and gradual change in the steady equilibrium state of a sub-system can rapidly
cause the whole system to reach the crush state [2]. This thus serves to avoid the
disadvantages associated with the weight determination procedure. Given the charac-
teristics of competitive sports resources and the advantages of catastrophe-based as-
sessment models, this paper aims to propose a catastrophe model for the assessment
of allocation efficiency of competitive sports resources in China.
2 Development of a Catastrophe Assessment Model
2.1 Indices Selection
From the view of system theory, China's competitive sport resources system is an
open giant system, and relates tightly with the environment through a wide range
of resources inflow and outflow. The optimal allocation of competitive sport re-
sources is to improve the use and allocation efficiency of competitive sport resources,
at a certain time and space scales, with the minimum consumption of human, financial
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