As the most essential feature in problem solving and decision making by humans, uncertainty information occur frequently in business, scientific and engineering disciplines. The explosive growth and diverse forms of uncertainty information in the stored data have generated an urgent requirement for new techniques and tools that can intelligently and automatically assist us in eliciting valuable knowledge from raw data. / The DCIFI is defined based on the Choquet extension of a signed fuzzy measure. A numerical calculation algorithm is implemented to derive the integration result of the DCIFI. A DCIFI regression model is designed to handle the regression problem where heterogeneous fuzzy data are involved. We propose a GA-based Double Optimization Algorithm (GDOA) to retrieve the internal coefficients of the DCIFI regression model. Besides that, A DCIFI projection classifier, which is capable of classifying heterogeneous fuzzy data efficiently and effectively, is established. We proposed a GA-based Classifier-learning Algorithm (GACA) to search the relevant internal parameters of the DCIFI projection classifier. Both the DCIFI regression model and projection classifier are very informative and powerful to deal with heterogeneous fuzzy data sets with strong interaction. Their performances are validated by a series of experiments both on synthetic and real data. (Abstract shortened by UMI.) / This thesis is mainly devoted to a comprehensive investigation on innovative data mining methodologies which merge the advantages of nonlinear integral (Choquet integral) in the representation of nonlinear relationship and fuzzy set theory in the description of uncertainty existed in practical data bases. It proposes two fuzzifications on the classical Choquet integral, one is the Defuzzified Choquet Integral with Fuzzy-valued Integrand (DCIFI), and the other is the Fuzzified Choquet Integral with Fuzzy-valued Integrand (FCIFI). The DCIFI and the FCIFI are regarded as generalizations of Choquet integral since both of them allow their integrands to be fuzzy-valued. The difference lies in that the DCIFI has its integration result non-fuzzified while the FCIFI has its integration result fuzzified. Due to the different forms of integration results, the DCIFI and the FCIFI have their distinct theoretic analyses, implementation algorithms, and application scopes, respectively. / by Rong Yang. / "April 2005." / Advisers: Kwong-Sak Leung; Pheng-Ann Heng. / Source: Dissertation Abstracts International, Volume: 67-01, Section: B, page: 0371. / Thesis (Ph.D.)--Chinese University of Hong Kong, 2005. / Includes bibliographical references (p. 187-199). / Electronic reproduction. Hong Kong : Chinese University of Hong Kong, [2012] System requirements: Adobe Acrobat Reader. Available via World Wide Web. / Electronic reproduction. [Ann Arbor, MI] : ProQuest Information and Learning, [200-] System requirements: Adobe Acrobat Reader. Available via World Wide Web. / Abstract in English and Chinese. / School code: 1307.

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Thesis (Ph. D.)--University of Missouri-Columbia, 2000. / Typescript. Vita. Includes bibliographical references (leaves 133-147). Also available on the Internet.

Thesis (Ph. D.)--University of Missouri-Columbia, 2000. / Typescript. Vita. Includes bibliographical references (leaves 133-147). Also available on the Internet.

The thesis consists of four research papers. The first three deal with the Choquet theory of function spaces. In Chapter 1, a theory on products and projective limits of function spaces is developed. It is shown that the product of simplicial spaces is a simplicial space. The stability of the space of maximal measures under continuous affine mappings is studied in Chapter 2. The third chapter employs results from the previous chapters to construct an example of a function space where the abstract Dirichlet problem is not solvable for any class of Baire-n functions with $n\in N$. It is shown that such an example cannot be constructed via the space of harmonic functions. In the final chapter, the recently introduced class of sequentially Right Banach spaces is being investigated. Connections to other isomorphic properties of Banach spaces are established and several characterizations are given.

In our dissertation we deal with the space H(K) of harmonic functions on a compact space in classical and abstract potential theory. Initially, we prove several equivalent characteristics of this space in classical potential theory. The internal characterization, which describes H(K) as a subspace of those continuous functions on a compact space K which are finely harmonic on the fine interior of K, is then used as the definition of H(K) in abstract potential theory. Further we concentrate on the solution of the Dirichlet problem for open and compact sets mainly with regards to its relation to subclasses of Baire class one functions. The results, proved at first in classical potential theory, are later generalized to abstract potential theory. With a use of more elemen- tary tools we initially prove these results in harmonic spaces with the axiom of dominance and, subsequently, using stronger tools we generalize them to harmonic spaces with the axiom of polarity. We engage also in a more abstract problem of approximation by differen- ces of lower semicontinuous functions in a more general context of binormal topological spaces.