Research On Multi-attribute Decision Method Based On Extension Mathematical Theory

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.