【作者】 杨丹丹；

【导师】 刘巍；

【作者基本信息】 大连海事大学 ， 应用数学， 2010， 硕士

【摘要】 可拓数学是以矛盾问题为研究对象、以矛盾问题的智能化处理为主要研究内容、以可拓方法论为主要研究方法的一门新兴学科。本文在可拓数学理论、多属性决策理论与方法的基础上,主要对以下几个方面的问题进行了研究。在可拓关联函数方面,引入了一种非线性K次抛物型的关联函数,这种非线性关联函数,既能反映各属性间的非线性关系,又能反映各属性值在不同区间内变化对被评事物的影响程度。在区间数多属性决策中,对一类需要进行点与区间数距离计算的多属性决策,应用可拓数学距的概念拓展了经典数学中点与区间的距离的概念,从而决策也更加科学。在决策模型求解方面,根据可拓逆向思维方法对期望-方差决策的求解属性权重模型进行改进,提高了属性权重计算的精确度,决策更加合理。在可拓层次分析法中,为了把可拓判断矩阵中的每个元素定量化,一般取可拓区间数的中值作为定量化的数字。但是有时候属性的权重的实际值可能在可拓区间数中值的左侧或者右侧,由于中值的选取可能使得属性权重的确定偏离实际。为了克服上述缺陷,对可拓判断矩阵定量化进行改进,使得属性权重的确定在实际应用中更加有效。更多还原

【Abstract】 Extension mathematics is a new study which takes contradiction problems as research object, take the intelligent processing of contradiction problems as the main research contents and take the extension methodology as main research method. Based on the extension mathematics theory and multi-attribute decision-making theory, this paper mainly studied the following problem.In the study of extension correlation function, this paper introduce a new correlation function, non-linear parabolic of Kth order. This non-linear correlation function can reflect not only the non-linear relationship between the attributes, but also the influence that the values of each attributes in different intervals exert on the things which are evaluated.In the interval multi-attribute decision-making, for the kind of multi-attribute decision-making which need to calculate the distance between dot and interval, the distance in extension mathematics is introduced to expand the classical mathematical concept of distance between dot and interval, which make decision-making more scientific.In the aspect of solving the model of decision-making, through improving the solving attribute weights in expectation-variance decision-making model using extension reverse thinking, make calculating more accurate and decision-making more rational.In extension analytic hierarchy process (EAHP), in order to quantify every elements of the extension judgment matrix, generally take the median of extension interval as a quantitative number. But sometimes the actual value of attribute weights maybe on the left or right of median of extension interval, because the select of median may make the attribute weights deviate the actual value. To overcome these shortcomings, the quantification of the extension judgment matrix is improved. And this can make the selection of the attribute weights more effective in practical applications.更多还原