Study On The Generalized Fuzzy Rough Set Model And Its Application

Rough set theory and formal concept analysis are two complementary mathematical toolswhich process imprecise, incomplete and vague information. No needing any prior knowledgeis a great advantage of rough set theory and the conclusion from which is objective, whilethe membership function of a fuzzy set is often given by experts and the result from which issomewhat subjective. The combination of the two tools can mine the hidden knowledge fromthe database more sufficiently. For this reason, the fuzzy rough set theory is one of the mainissues in data mining at the present time. However, since in the database there are usuallysmall errors on one hand and the attribute set often can't re?ex the knowledge completely onthe other hand, the fuzzy rough set model can't adapt such database very well. Aiming at theabove drawbacks, this thesis proposes the variable precision fuzzy rough set model, and thefuzzy rough set is expanded to the generalized fuzzy rough set. Then the inclusion measureand similarity measure on the generalized fuzzy rough sets are investigated, and the methods toconstruct a fuzzy concept lattice using a special generalized fuzzy rough set are proposed. Theconcrete results are as follows:1. The variable precision (θ,σ)?fuzzy rough set model is proposed. The definitions ofvariable precision (θ,σ)?fuzzy rough set and generalized fuzzy rough set are introduced firstly.The computational approach and basic properties of variable precision (θ,σ)?fuzzy rough setare then investigated. Based on which, the definition ofβ?fuzzy lower approximation reduct isgiven and the attribute reduction method is proposed.2. The hybrid monotonic inclusion measure and similarity measure on generalized fuzzyrough sets are investigated. Firstly, the definition of the hybrid monotonic inclusion measure isshown. Then several kinds of inclusion measures are constructed, and the rationalities of whichare proved. Furthermore, certain distributivity and transitivity of some special inclusion mea-sures are investigated. Finally, the concrete similarity measures based on the hybrid monotonicinclusion measure are given and their use in pattern matching of knowledge is discussed.3. The approaches to constructing fuzzy concept lattices based on generalized fuzzy roughapproximation operators are investigated. For a residual implicatorθsatisfyingθ(a,b) =θ(1 ?b,1 ? a) and its dualσ, a pair of fuzzy rough approximation operators is defined. We thenpropose three kinds of fuzzy operators, and examine some of their basic properties. Finally, thefuzzy concept lattice introduced by Beˇlohla′vek is constructed by three approaches.