On Possibility Analysis For Fuzzy Data

• Main Authors: Liu ,Man Jun, 劉曼君
• Other Authors: Yang, M.S.
• Format: Others
• Language: zh-TW
• Published: 1995
• Online Access: http://ndltd.ncl.edu.tw/handle/37394476899461085668

碩士 === 中原大學 === 應用數學研究所 === 83 === Although there are many researches on statistical analysis for fuzzy data, there are less discussions on possibility analysis for fuzzy data. In this thesis, our goal is to construct a possibility space for the analysis of fuzzy data. Especially we propose the so-called double fuzzy variable. What is " possibility "? Zadeh proposed the concept of fuzzy sets. Then there are two types of description for the uncertainty : one with randomness, the other with fuzziness. The former is dealt with probability, and the latter with possibility. Although the ideas of probability and possibility are different, the constructions are similar. We will make a simple comparision of these two in Chapter 2 and introduce the fuzzy variable which is defined on possibility space. Then we propose the new idea " double fuzzy variable " in Chapter 3 and also present its properties. The combination of statistics and fuzzy data produces fuzzy statistics; the combination of fuzzy theory and fuzzy data produces the possibility analysis for fuzzy data. In Chapter 3, we intepret the implicit features of double level fuzziness and define the double fuzzy variable (d.f.v.). As a result, double fuzzy variable becomes the means of handling fuzzy data in possibility space. Furthermore, we define the possibility distributions and fuzzy modal values of double fuzzy variables. The topic in Chapter 4 is about parameter estimation. Similar to the maximum likelihood principle in statistics, we provide the maximum possibility likelihood principle to estimate the unknown fuzzy parameter. Finally, we take the normal possibility distribution as an example and estimate its fuzzy parameters.