Dissertation > Mathematical sciences and chemical > Mathematics > Computational Mathematics > Mathematical modeling, approximate calculation

The Study of Rough Set Theory and Its Extended Model

Author LuAiGuo
Tutor LiuSanYang;MaoYongCai
School Xi'an University of Electronic Science and Technology
Course Applied Mathematics
Keywords Rough sets theory Ordering rules Rule acquisition Multi-attribute decision making (Multigraded) Dominace relation
CLC O242
Type Master's thesis
Year 2004
Downloads 235
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Rough Set Theory, introduced by Z.Pawlak early 1980’s, is a new mathematical tool to deal with vagueness and uncertainty whose basic idea is to derive classification rules of conception by knowledge reduction with the ability of classification unchanged. In recent years, rough set theory has become one of the most active research fields of artificial intelligence and information science, and has been successfully applied to many areas such as data mining, pattern recognition, machine learning, knowledge discovery, decision analysis, and so on. Firstly, the traditional rough sets based on the indiscernibility relation is introduced, which approximates sets of object by upper and lower set approximations. Secondly, the method of data mining in ordering information tables is discussed and some basic theory about ordering information table is introduced in detail. Then a novel rule acquisition approach rough set-based in interval valued decision table is presented. An example shows that this algorithm is effective and scientific. Finally, as an extension of rough set, multigraded dominance-based rough set model is introduced which can deal with multi-attribute decision making problems with preference information instead of the traditional rough sets. An approach in uncertain multi-attribute decision making is presented and an example is given to illustrate the effectivity.

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