在知識經濟之社會，多元思維逐漸取代傳統二元邏輯的思考與分析方法。過去使用單一數值的樣本來計算中位數的方法，已漸不符現今複雜多變的智慧科技時代之需求。尤其是在具有多變性、不確定性、與訊息不完整性的財金與經濟環境下，過分強調對於數值之運算及數學假設的前提，反而更容易造成與現實環境及條件的背離、甚至是脫節。故在進行財金與經濟方面問題的研究時，利用隸屬度函數與模糊統計的分析將會是一種較為進步的測度方法。本文在此提出模糊中位數的分析理論，並將其應用於財務金融的分析測度上，期望能對複雜的財金經濟現狀提供一套更有效且精確合理的分析方法。 / In the society of economic knowledge, Multi-valued logic goes to replace binary logic gradually. In the traditional way, we usually ask the task-taker to response the answer according to the thinking of binary logic. But such kind of response is improper since the human thinking is fuzzy and uncertain. So it should be an improved measurement using membership functions and fuzzy statistics. 　　In this paper, we will propose the definition of fuzzy median, and present some of its application. According to the above theoretical contents, we give some examples, which is used frequently in financial and economic assessment. From the explanation and discussion of fuzzy median in these examples, we can recognize that fuzzy statistics is more meaningful and proper for research of finance and economics. At last, based upon the findings of this study, certain recommendations for further research are suggested.

High quality image /video has become an integral part in our day-to-day life ranging from many areas of science, engineering and medical diagnosis. All these imaging applications call for high resolution, properly focused and crisp images. However, in real situations obtaining such a high quality image is expensive, and in some cases it is not practical. In imaging systems such as digital camera, blur and noise degrade the image quality. The recorded images look blurred, noisy and unable to resolve the finer details of the scene, which are clearly notable under zoomed conditions. The post processing techniques based on computational methods extract the hidden information and thereby improve the quality of the captured images. The study in this thesis focuses on deconvolution and eventually blind de-convolution problem of a single frame captured at low light imaging conditions arising from digital photography/surveillance imaging applications. Our intention is to restore a sharp image from its blurred and noisy observation, when the blur is completely known/unknown and such inverse problems are ill-posed/twice ill-posed. This thesis consists of two major parts. The first part addresses deconvolution/blind deconvolution problem using Bayesian approach with fuzzy logic based gradient potential as a prior functional. In comparison with analog cameras, artifacts are visible in digital cameras when the images are enlarged and there is a demand to enhance the resolution. The increased resolution can be in spatial, temporal or even in both the dimensions. Super resolution reconstruction methods reconstruct images/video containing spectral information beyond that is available in the captured low resolution images. The second part of the thesis addresses resolution enhancement of observed monochromatic/color images using multiple frames of the same scene. This reconstruction problem is formulated in Bayesian domain with an aspiration of reducing blur, noise, aliasing and increasing the spatial resolution. The image is modeled as Markov random field and a fuzzy logic filter based gradient potential is used to differentiate between edge and noisy pixels. Suitable priors are adaptively applied to obtain artifact free/reduced images. In this work, all our approaches are experimentally validated using standard test images. The Matlab based programming tools are used for carrying out the validation. The performance of the approaches are qualitatively compared with results of recently proposed methods. Our results turn out to be visually pleasing and quantitatively competitive.