"Mean Values, Measurement of Fuzziness and Variance of Fuzzy Random Variables for Fuzzy Optimization"

抄録

This paper discusses mean values and variance defined by fuzzy measures as evaluation methods of fuzzy numbers/fuzzy random variables, and the methods are applicable to decision making with both randomness and fuzziness. We find the method with lambda-mean functions has proper properties. The variance and the corresponding co-variance and correlation are introduced and their fundamental properties are discussed. The measurement of fuzziness regarding fuzzy numbers is also presented, where fuzziness is another uncertainty different from randomness and comes from the imprecise of data. An example is given as an application in financial engineering of portfolio.