Rough Set Theory And Its Extension Model

Rough set theory, a new mathematical tool dealing with vagueness an uncertainty, was introduced by Zdzislaw Pawlak in 1982. The primary idea is to make use of the known knowledge or information as an approximation for the unprecise concepts or phenomena. Since the nineties of the twentieth century, the continuous perfecting in theory and the wide extending in application for the rough set became a very hot research spots in the world academe. Nearly the same era, as well as a powerful tool for data analyses, the theory of the fuzzy set and the concept lattice were advanced by Aadeh in 1965 and by Wille R. in 1982, respectively. Though the two theories are different from the rough set's, they bear some common consistency and comparability in the processes of data analyses. Further developments have been achieved by using the theories and methods of rough set, concept lattice and the fuzzy set for reference one another.According to the present applications of the rough set, continuous generalization studies for rough model will be done in this paper, it mainly adopts the formation ways and associates with this uncertainty theories of probability, fuzzy set, concept lattice which are referred to as follows:(1) Analyze the comparability and the relation between the rough set and concept lattice in the processes of data analyses. This text developed the concept lattice under the information system and gained the fuzzy concept lattice expressed by different residuated implications, The text is established on the concept lattice which bases on rough set and aims at the limitations that the classification described by rough set iscompletely precise. By introducing the threshold value~β, we broaden the rigorousdefine of the approximate bound demanded in former rough set with probability classification. We also promise certain error of classification in upper and lower approximation. Consequently, we illuminate the concept lattice based on VPRS and its properties.(2) The existing fuzzy rough sets are all defined with respect to fuzzy min-similarity relation so that they have not some properties as the crisp rough sets do, and the condition needed for the fuzzy min-transitivity in the fuzzy min-similarity relation R defined too strict so that the similar degree between two object in Ucannot be measured effectively by means of the fuzzy min-similarity relation. Due to these characteristics, the application fields of the existing fuzzy rough sets are limited. Aimed at these limitations, we make some improvements for the former fuzzy rough set model and introduce the fuzzy T- similarity relation, construct a new fuzzy information system. Then, we obtain a fuzzy T- rough set based on the new fuzzy information granule. Its corresponding properties and the relationship between the new lower and upper approximations are also discussed in detail.