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This article introduces an approximation space for graded acceptance of proposed models for intelligent system design relative to design patterns that conform to a design standard. A fundamental problem in system design is that feature values extracted from experimental design models tend not to match exactly patterns associated with standard design models. It is not generally known how to measure the extent that a particular intelligent system design conforms to a standard design pattern. The rough set approach introduced by Zdzisław Pawlak provides a ground for concluding to what degree a particular model for an intelligent system design is a part of a set of a set of models representing a standard. The basic assumption made in this research is that every system design can be approximated relative to a standard, and it is possible to prescribe conditions for the construction of a set of acceptable design models. It is also possible to measure the degree that a proposed set of design models is a member of a set of design models that conform to a standard. The neuron and sensor behavioral design patterns are briefly considered by way of illustration of design model approximation. A satisfaction-based approximation space for patterns extracted from intelligent system design models is introduced.

This article introduces an approach to classifying models for intelligent system design in the context of a satisfaction-based approximation space defined in the context of rough sets (Pawlak (1982) and Pawlak (1991)). Considerable work has been done on approximation spaces in the context of rough sets (Skowron, 2001; Skowron and Stepaniuk (1996) and Skowron and Stepaniuk (2001); Stepaniuk, 1998; Peters et al., 2002) as well as generalized approximation spaces (Polkowski, 2002; Pal et al (2004a) and Pal et al (2004b)), which is directly related to a paradigm for approximate reasoning called rough mereology (Polkowski and Skowron (1994) and Polkowski and Skowron (1996)) and recent work on pattern recognition (Skowron and Swiniarski, 2004). It is well known that experimental models for system design in general and intelligent system designs in particular seldom exactly match what might be considered a standard. This is to be expected, since system designs tend to have an unbounded number of variations relative to an accepted design pattern. Consider, for example, the variations in the implementation of design patterns in architecture made possible by pattern languages (Alexander (1964), Alexander (1979) and Alexander (2002); Alexander et al., 1977). This is expected and encouraged. It is this variation in actual system designs that is a source of a difficult classification problem. This problem is acute in reverse engineering a legacy system. It is not generally known how to measure the extent that a particular system design conforms to a standard. It is usually the case that the feature values of a particular intelligent system design, for example, approximately rather than exactly match a standard pattern. An approach to a solution of the system design classification problem is proposed in this article in the context of rough sets and a satisfaction-based form of approximation space. In general, a behavioral model for a system design is represented by a set of interacting objects where each object is an instance of a class (a description of a set of objects that share the same attributes, operations, and semantics). A pattern is a conjunction of feature values that are associated with a decision rule. In particular, a system design pattern is a conjunction of feature values relative to the structure and functionality of a set of classes used in designing components of a system. Patterns commonly found in models for intelligent system designs can be gleaned from class, interaction, and other diagrams (Peters, 2003; Peters and Ramanna, 2003) from UML, the Unified Modeling Language (OMG, 2001), especially in the context of systems engineering (see, e.g., Holt, 2001). In this article, only collaboration diagrams are considered. This paper has the following organization. Basic concepts from rough sets and UML underlying the proposed approach to classifying intelligent system design models are briefly presented in Section 2. Sample system design features and design patterns are briefly considered in 3 and 4, respectively. An approximation space for design patterns is considered in Section 5. A framework for classification of intelligent system design models within a satisfaction-based approximation space is given in Section 6.

This paper has presented a framework for classifying models for intelligent system design in the context of satisfaction-based approximation spaces. The basic goal in this research has been to establish an approach to measuring to what extent a collection of similar intelligent system design models approximate a standard. The construction of sets of similar design models is based on knowledge gained from design patterns. One of the challenges in this work is to develop a methodology for reverse engineering complex systems such as the nervous system of a dinosaur based on knowledge gained fragmentary fossil remains. This is very difficult to accomplish because the features of existing system designs belong to composite design patterns. To make sense of an existing system, it is necessary to unravel the composite patterns in the context of an approximation space, to decompose composite patterns into separate patterns that correspond to well-understood, standard design patterns. Since it common for models of subsystem designs such as sensors, memory and neurons to overlap, a subsystem model extracted from a complete system model of a legacy system has the appearance of a fragment, something incomplete when compared with a standard. Hence, it is appropriate to use approximation methods to measure the extent that experimental models are to a degree a part of a set of models representing a standard.