Based on the characteristics of the complex system, this paper presents a novel method, the monotonic indexes space method, for the effectiveness analysis of the complex system. First, it presents some basic concepts and assumption such as the monotonic indexes space, monotonic indexes requirement locus, etc. Second, based on the assumption that indexes are monotonic for the requirements, an algorithm is proposed and applied to numerical approximation of monotonic indexes requirement locus with hyperboxes. Third, this paper proposes two algorithms for acquiring intersection of several monotonic indexes requirement locus. Fourth, this paper proposes the monotonic-indexspace based system analysis model such as the system evaluation model, the sensitivity analysis model for indexes. Based on the practical requirement, the concept of fuzzy monotonic indexes requirement locus and the corresponding analysis model are introduced. Finally, this paper applies the above-mentioned models to analyze the effectiveness of a notional anti-stealth-air-defense information system. And the outputs show that the method is promising.

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The application of some MVS operations (each dimension of which corresponds to a capability indicator) in system capability analysis and design, including capability indicator requirement analysis, effectiveness analysis, sensibility analysis, fuzzy analysis, stability analysis, capability optimization design, etc., is discussed in the second paper of this series of papers. And some MVS-based models and algorithms for capability analysis and design are put forward. Finally, an example of capability analysis and optimization design is given for explaining the usages of related models and algorithms.

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