期刊名称：Journal of Data Analysis and Information Processing
印刷版ISSN：2327-7211
电子版ISSN：2327-7203
出版年度：2017
卷号：05
期号：03
页码：96-114
DOI：10.4236/jdaip.2017.53008
语种：English
出版社：Scientific Research Publishing
摘要：Fuzzy regression provides more approaches for us to deal with imprecise or vague problems. Traditional fuzzy regression is established on triangular fuzzy numbers, which can be represented by trapezoidal numbers. The independent variables, coefficients of independent variables and dependent variable in the regression model are fuzzy numbers in different times and T W , the shape preserving operator, is the only T -norm which induces a shape preserving multiplication of LL -type of fuzzy numbers. So, in this paper, we propose a new fuzzy regression model based on LL -type of trapezoidal fuzzy numbers and TW . Firstly, we introduce the basic fuzzy set theories, the basic arithmetic propositions of the shape preserving operator and a new distance measure between trapezoidal numbers. Secondly, we investigate the specific model algorithms for FIFCFO model (fuzzy input-fuzzy coefficient-fuzzy output model) and introduce three advantages of fit criteria, Error Index, Similarity Measure and Distance Criterion. Thirdly, we use a design set and two reference sets to make a comparison between our proposed model and the reference models and determine their goodness with the above three criteria. Finally, we draw the conclusion that our proposed model is reasonable and has better prediction accuracy, but short of robust, comparing to the reference models by the three goodness of fit criteria. So, we can expand our traditional fuzzy regression model to our proposed new model.
关键词：Fuzzy Sets;LL-Type of Trapezoidal Fuzzy Numbers;Least-Squares Deviations;Shape Preserving Operator;Fuzzy Linear Regression
