A Study on the Development and Application of Fuzzy Evaluation Algorithm to Complex System
The evaluation structure of complex system is composed of multiple attributes and hierarchies. Many studies have been done based upon the assumption that the evaluation elements were independent. The actual evaluation structure of complex system, however, has complexity, ambiguity and inter-linkage among the elements. In this regard, the fuzzy evaluation process is well known to be effective way with which the complex system can be dealt.
Introducing fuzzy evaluation process into the complex system, the problems which might be encountered can be categorized into two kinds: the one originated from existing fuzzy evaluation process and the other from extensive evaluation procedure by Multiple Decision-Making Group(MDMG). The latter is concerned with adjusting and integrating the measures and evaluation values by MDMG which shows a variety of viewpoints on the evaluation of complex system. The former, on the other hand, is closely related to identifying the evaluation hierarchy, the interaction among system elements, and the evaluation value.
The main objective of this study is to develop the Fuzzy Evaluation algorithm to Complex System(FECS) which can be universally adapted to the complex system by both enhancing the existing fuzzy evaluation process and solving the problems in evaluation procedures by MDMG. This study also aims to confirm the effectiveness of FECS by applying to the evaluation of national maritime power system. These were fulfilled, first of all, by suggesting the framework of which the multiple hierarchical evaluation structure system can be efficiently composed, and identifying the superiority of fuzzy measure to linear measure.
The detailed results of this study are as follows:
Firstly, the framework which can logically consist of the multiple hierarchical evaluation structure has been suggested in order to find the interactions among attributes, maintain the consistency of structures, and abstract the hierarchies in structural model of complex system. In this framework, instead of using the existing through evaluation method from bottom level to top, in particular, the integrated evaluation of total hierarchy has been accomplished by the Efficient Hierarchy(EH) only.
Secondly, for the purpose of clarifying the characteristics of measures, the property and differences between linear and fuzzy measures were discussed through two level-down evaluation process. Making the integrated evaluation process which keeps reversibility among hierarchical levels, some necessary conditions for reversibility of fuzzy evaluation were obtained.
Thirdly, the development of FECS has mainly focused on:
ⅰ) Identification process of fuzzy measure for considering the interactions.
ⅱ) Adoption of uncertainty process for considering the confidence degree of each evaluator.
ⅲ) Integration process for integrating the measures of each evaluators by DS(Dempster-Shafer) theory.
ⅳ) Level process for adjusting the excessive different of measures per each evaluation group.
The FECS steps are as follows:
[Step 1] Abstract the attributes composing the evaluation system.
[Step 2] Construct the hierarchical structure of evaluation space.
[Step 3] Determine the efficient hierarchy(EH) in the hierarchical evaluation structure.
[Step 4] Calculate the measures(w) and interaction(λ) of attributes in EH by eigen-vector method.
[Step 5] Adjust and integrate the measures by uncertainty process, DS integration process and level process. Calculate the fuzzy measure by w and λ.
[Step 6] In case of the evaluation of Low EH(LEH), calculate the evaluation value by Sub Fuzzy Integral(SFI) process(in case of evaluation by unit decision-making group) and Group Fuzzy Integral(GFI) process(in case of evaluation by multiple decision-making group).
[Step 7] Calculate the integrated evaluation value by fuzzy integral process. And set the order of alternatives by integrated evaluation value.
For obtaining measures, interactions and some evaluation values of qualitative attributes, a questionnaire survey has been made to the 69 experts who have been engaging in maritime-related area. From the questionnaire survey, the average interaction coefficient among evaluation attributes was found -0.199, and the order of fuzzy measures(fuzzy measure value) was as follows: the power of ocean research and development(0.134) the fundamental power of maritime(0.132) shipping and port power(0.122) naval power(0.117) the protection power of ocean environment(0.106), the will and inclination of government(0.106) shipbuilding power(0.089) fishing power(0.061), dependency on seaborne trade(0.061).
As the results of fuzzy integral, the order of national maritime power of 20 nations was as follows: U. S. Japan U. K. France Germany, Russia Canada, Netherlands China, Italy, Spain Taiwan R. O. K., Belgium Australia Brazil India Mexico Argentina Indonesia.
It was known that R. O. K. ranks the 13th position among 20 nations.