4538

4272

كارشناسي ارشد

آمار﴿ اقتصادي - اجتماعي﴾

اصفهان: دانشگاه صنعتي اصفهان، دانشكده علوم رياضي

1387

[هشت]، 120، [II] ص: جدول، نمودار

ص. ع. به:فارسي وانگليسي

محمود طاهري

رضا حجازي

10/4/88

حميد رضا ملكي سروستاني، ايرج كاظمي

رياضي

ID4272

به فارسي وانگليسي : قابل رويت در نسخه ديجيتال

Fuzzy Regression Based on L1 Norm Maryam Kelkinnama m kelkinnama@math iut ac ir February 18 2009 Master of Science Thesis in Farsi Department of Mathematical Sciences Isfahan University of Technology Isfahan 84156 83111 IranSupervisor Dr Seyed Mahmoud Taheri Taheri@cc iut ac ir2000 MSC 04A72 62J05 Key words Fuzzy regression Goodness of t Least absolute deviations Metric on fuzzy numbers AbstractIn this thesis we present an expanded account of Fuzzy Regression Based on L1 Norm basedon an article by Choi and Buckley 2008 Regression analysis is an important tool in eval uating the functional relationship between a certain variable called dependent variable anda set of other variables called explanatory variable s In statistical regression we can makeestimates and predictions for the dependent variable based on a set of observed data But in systems in which human intelligence participates we usually encounter the following twocases 1 the relationship between variables is imprecise and2 the observations due to the variables are fuzzy So we need to consider and investigate some fuzzy regression models to deal in such fuzzyenvironments In this thesis fuzzy linear regression based on least absolute deviations approach is in vestigated First we introduce a metric DLR on the space of LR fuzzy numbers whichmeasures the distance between such fuzzy numbers based on L1 norm Afterwards we usethe metric DLR to obtain unknown coe cients of fuzzy regression models In order to ndthe fuzzy linear model we minimize the sum of distances between observed and estimatedfuzzy outputs for all observations using the metric DLR For simplifying the minimizationproblem we translate it to a standard mathematical programming problem In present thesis we consider three well known fuzzy regression models The rst modelis the model with crisp inputs and fuzzy coe cients the second model is the model withfuzzy inputs and crisp coe cients and the third one is the model with fuzzy inputs andfuzzy coe cients All of the above models have fuzzy outputs We use arithmetic operations based on minimum T norm for dealing with fuzzy numbersin working with three mentioned models Since these operations don t preserve the shapeof fuzzy numbers during the multiplication we also use the weakest T norm for algebraicoperations in another chapter Also we use three indices of goodness of t of fuzzy regression models the mean of errorscriterion the sum of similarity measures criterion and the sum of distances DLR criterion We assess the performance of the proposed models by several common data set based ongoodness of t criteria The result of numerical computations shows the performance of theproposed method in comparison with some usual fuzzy regression methods especially whenthe data set includes some outlier data point s 1

محمود طاهري

رضا حجازي

حميد رضا ملكي سروستاني، ايرج كاظمي