| The return and risk of security are uncertain where the shoe pinches in decision analysis in an extremely complicated system of stock market. There are mainly two kinds of manifestation in the uncertain event: one is the uncertainty if the event happens, namely, randomicity; the other is the uncertainty of event state, namely, fuzziness. As to the investor, portfolio selection is investment decision problem in uncertain environment. The research on portfolio in random uncertain environment is perfect, and the research on portfolio in fuzzy uncertain environment is gradually noticed. The purpose of this research is to obtain some research results as follows: more accurate value ranges and analysis formula of minimizing portfolio risk and equal weight portfolio risk are given based on the uncertainty of stock market; some necessary and sufficient conditions of equal weight minimizing risk portfolio being optimal portfolio are derived; some effective algorithms are found to solve nonnegative investment proportional coefficients; some interval programming portfolio models are proposed, pertinent algorithms are analyzed, and practical examples are studied; based on possibility theory, the single objective or minimizing bi-objective or hybrid bi-objective portfolio models are proposed which are suitable for investor's requirements satisfying with different constraint investment environments, some effective algorithms are found out, and practical examples of portfolio models are given and analyzed.Matrix theory, fuzzy number theory, optimization theory and possibility theory are powerful tools in solving the above problems. The dissertation combines together theory study and application analysis, and the main contents of this dissertation are as follows:(1) The value ranges of minimizing portfolio risk, upper limit and lower limit, are obtained, and some concrete analysis formulae are presented by rigorous mathematical derivation using matrix theory, optimization theory and positive definiteness of symmetric matrices.(2) Applying matrix theory, the effectiveness of minimizing risk equal portfolio is studied, and the effectiveness of equal weight portfolio and simple weighted portfolio are compared, and some necessary and sufficient conditions of equal weight portfolio being optimal portfolio are presented. The above results are useful to the research on equal portfolio in theory.(3) Applying optimization method and intelligent algorithm, the problem how to solve the nonnegative investment coefficients in portfolio model is studied. In minimum risk portfolio model, nonnegative investment coefficients are solved by penalty function method; in self-financing effective portfolio model, the solutions of this model are obtained by using improved fuzzy genetic algorithm; as to the bi-objective portfolio model with bounded investment coefficients, which is be solved by partial objectives for multiply-divide method and analyzed by practical examples.(4) Applying interval programming model, some related portfolio selection models depicted by three key factors return, risk and turnover rate are studied further. Based on investor's different attitudes: optimistic, pessimistic, compromise, three different interval programming models are given and solved; based on interval number order relationship, the interval number multi-objective minimizing portfolio model is proposed, and the shortest distance method is used to solve it; based on interval inequality satisfaction degree, one kind of portfolio selection model is proposed and analyzed by a numerical example.(5) Based on possibility theory, the single objective portfolio model is studied. Based on the upper-lower possibility theory, maximal utility function portfolio model is solved by multiplier method; one kind of portfolio model with lending is solved by LEMKE method.(6) Based on possibility theory, the bi-objective minimizing portfolio model is studied. Bi-objective fuzzy linear minimizing portfolio model is proposed and solved by ideal point method; one kind of bi-objective linear minimizing portfolio model is studied and analyzed by improved gradually allowance constraint method.(7) Based on possibility theory, the hybrid bi-objective portfolio model is studied. When the return is fuzzy number, the portfolio model with free security is studied by fuzzy two-stage method; the portfolio model with transaction fee is solved by threshold constraint method; the portfolio model with bounded investment coefficients is studied by linear efficacy function method. And the practical examples are verified the feasibility and effectiveness.
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