Research On ANP Alternative Ranking Approaches For Complex Systems And Its Application

Socioeconomic complex system is a complicated huge system, it refers to every aspect, furthermore refers to economic activity, social activity and natural intricacy, which need us to adopt the methodology of system science to study and analyze.Socioeconomic complex system has the basic tributes of openness, complicated, hierarchy, nonlinear and dynamic.Holistic viewpoint is important in the field of complex system. For evaluating effectively the complex decision problem, it is essentially to let expert make logical judgments from the holistic viewpoint. However, human's acquaintances with the complex socioeconomic system are not very enough to make relatively accurate evaluations on the holistic behavior. As has been pointed out in the theory of complex system, what experts can do is only to give the semi-theoretical and semi-experiential opinions full of indeterminacy, based on their knowledge, experience and even intuition.Analytic network process is a effective tool to analyze the complex decision problems. Five basic types are divided in the ANP, i.e. the hierarchy system with inner independence, the circular system with inner independence (CSII), the hierarchy system with inner dependence (HSID), hierarch system with inner dependence and feedback and circular system with inner dependence. However, only the CSII and the HSID systems are discussed in this paper. First, In the ANP analysis, the supermatrix of reflecting the mutual influence among GC, CC, and AC, is very vital to the final LIP ranking. As suggested by Saaty, the submatrix is constructed by making paired comparisons among the elements in GC, respective to alternatives, and represented by the point estimates. It is intended that the point estimate approach for the relative preference of compared elements, is not reasonable for constructing the influence submatrix of AC to GC. The reason lies in that the comparison pattern is in essence to let experts make point estimates of logical judgments from the holistic viewpoint, and thus make experts feel very difficult to express their uncertain judgments on the complex characteristics of socioeconomic systems. To solve the above problem, the concept of interval estimate on the relative preference is presented in this paper, with the CSII system referred. For applying the concept to the real world problems, based on the technological core of relative efficiency evaluation used in DEA, namely, selecting a set of favorable weights to maximize the DMU's relative efficiency score, a modified ranking approach to alternatives is presented. The illustrative example proves that the approach is dependable. Since the interval estimates can well reflect the indeterminacy and the difficulty that experts can meet during constructing the influence submatrix of AC to GC, the presented approach is regarded as more practical to the real world problem.