Research On Some Issues Of Knowledge Acquiring And Uncertainty Measure In Information System

Information systems (Information tables) provide a convenient and useful tool for rep-resenting a set of objects using a group of attributes. Knowledge acquisition in informationsystems is a key issue in the field of information science. Uncertainty measure in informationsystem has also attracted lots of attention in data mining and knowledge discovery. Informationgranulation and entropy theory are two main approaches to research uncertainty of an informa-tion system. Based on the theory of granular computing, rough sets, fuzzy sets and intuitionisticfuzzy sets, this dissertation study on the uncertainty measure and knowledge acquisition of in-formation systems, including uncertainty measure of rough sets, attribute reduction, entropy,inclusion measure, similarity measure, compatibility measure in intuitionistic fuzzy systemsand multiple scale concept lattice. The main contribution of this dissertation can be generalizedas follows:(1) As one of the most important issues in rough set theory, roughness and fuzziness ofrough sets have been widely studied. Uncertainty of rough sets has close relativity with theknowledge granularities of the approximation space. We propose an improved method for mea-suring the uncertainty of rough sets based on fuzzy theory and granular computing theory. Adefinition of relative knowledge granulation and a concept of boundary entropy for an infor-mation system are given, under which the measure functions of roughness and fuzziness aremodified. The roughness of a rough set based on relative knowledge granularities not only re-?ects the action of the approximation space, but also gets rid of the effect of the negative regionof the rough set. Both of roughness and fuzziness are monotonously decreasing with the refin-ing of knowledge granularities in approximation spaces. Two matrix algorithms are presentedfor measuring the roughness and fuzziness of rough sets, which are easy to implement.(2) In intuitionistc fuzzy system, a new kind of entropy for intuitionistic fuzzy sets is pro-posed, and some basic properties are examined. An axiomatic definition of inclusion measurebetween intuitionistic fuzzy (IF for short) sets is established. Some kinds of IF inclusion mea-sures are constructed by different IF operators, especially by IF implicator. Some new methodsfor measuring the degree of similarity between IF sets are proposed. Moreover, the similaritymeasure obtained from IF inclusion measure holds properties of normal similarity measure. Therelationships between similarity measure and entropy of intuitionistic fuzzy sets are analyzed.We then define the compatibility measure by the predicates logical idea and construct severalfunctions to measure compatibility for an intuitionistic t-norm. (3) Intuitionistic fuzzy information systems are generalized models of single-valued fuzzyinformation systems. We propose some novel classification rules, totally ordered methods anduncertainty measures for intuitionistic fuzzy information systems. By introducing an absolutedominance relation in an intuitionistic fuzzy information system, a rough set approach is es-tablished, which can be extended to other forms of dominance relations in intuitionistic fuzzyinformation systems. For a given permissible discernibility degreeα, a novel rough set ap-proach based onα-indiscernibility relations is discussed and theα-determinant reductions areobtained. Furthermore, to evaluate uncertainty of an intuitionistic fuzzy information system,we design a roughness measure of a rough set depend on a relative knowledge granulation, bywhich the effect of the negative region of the rough set can be removed effectively. Then wedeal with attribute reductions of consistent and inconsistent intuitionistic fuzzy ordered decisioninformation systems based on the theory of dependence space.(4) As an effective method for date analysis, formal concept analysis has been applied tomany fields. The method given in this discussion can reduce the number of concepts efficientlywith conserved main formal structure. Based on a kind of Galois connection via a conceptof inclusion degree, a complete lattice, calledα(αis a real number in [0,1]) concept lattice,is produced. A formal context can be converted into an inducedαcontext through a kind ofinclusion degree which is used to cope with a partition of the objects'set. Moreover, it isproved that theαconcept lattice produced by the original context is equal to the concept latticeproduced by the inducedαcontext. Finally, the concept lattices determined by an inclusiondegree is constructed from the induced context by using the well-known software of Galicia.