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Received Aug 18, 2017; Revised Nov 23, 2017; Accepted Dec 5, 2017
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1. Introduction
For Efthymiou et al. [1] a complex system is composed of a structure defined for a great amount of elements, with different types of interactions and characterized by a behavior with uncertainty. Preliminary studies published by Alfaro and Sepulveda [2] consider the manufacturing systems as complex systems. A manufacture system consists of many entities: flexible machines, hundreds of products, thousands of operations, location of the operations, variable context in the political, economic, and environmental factors, and uncertainty of the demands; these features define the structure of a complex system. In Elmaraghy et al. [3] other sources of complexities in the manufacturing systems are defined: customer requirements, products complexity, control systems, product structure, and manufacturing technology.
Complex systems are also found in natural, social, and economic systems. Nonlinear relations of the variables composing the system structured its complex behavior. Abarbanel and Lall [4] studied the time series of the aquifer volume of the Great Salt Lake of Utah, using the theory of nonlinear systems, and obtained as a result the chaotic behavior of the series. Other natural complex systems are presented in the patterns of natural formation of lands [5], in systems consisting of multiple natural and human subsystems [6] and Holling [7] develops the term panarchy to expose the evolution of adaptive systems formed by interconnected natural, human, and socioecological systems.
The measures of complexity in the manufacturing system can be separated into two types of metrics: (1) metric oriented to the measure of the static or structural complexity and (2) metric directed to determine the dynamic complexity of the system. According to Modrak et al. [8] the static complexity is defined by the configuration of the system and the number of components. The dynamic complexity studies the uncertainty of the behavior of the system. The research is centered in the metric of the complexity of a manufacture system and of a dynamic system, independent of the variables and the structure of the system.
To measure the structural complexity, [9–12] have...