A novel fuzzy linear regression model based on a non-equality possibility index and optimum uncertainty |
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| Authors: | H. Shakouri G. R. Nadimi |
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| Affiliation: | 1. Instituto de Alta Investigación, Universidad de Tarapacá, Casilla 7D, Arica, Chile;2. Instituto de Biociências, Letras e Ciências Exatas, UNESP – Univ. Estadual Paulista, Câmpus de São José do Rio Preto, Departamento de Matemática Aplicada, São José do Rio Preto, SP, Brazil;3. Departamento de Estadística e I.O., Universidad de Sevilla, Spain;1. Department of Radiology, Affiliated Hospital of Chengdu University, Chengdu, 610081, China;2. Department of Cardiology, Affiliated Hospital of North Sichuan Medical College, Sichuan 637000, China;3. Department of Radiology, Deyang City People''s Hospital, 618000, China;4. Department of Interventional Radiology, Tenth People''s Hospital of Tongji University, Shanghai 200072, China;5. Department of General Surgery, Affiliated Hospital of Chengdu University, Chengdu 610081, China;6. Department of Urology, Affiliated Hospital of Chengdu University, Chengdu, 610081, China;1. Program for Evolutionary Dynamics, Harvard University, Cambridge, MA 02138, USA;2. Computational Biology Group, Eindhoven University of Technology, 5600 MB Eindhoven, The Netherlands;3. Department of Electrical Engineering and Computer Science, Massachusetts Institute of Technology, Cambridge, MA 02139, USA;1. Innovative Information Industry Research Center, Harbin Institute of Technology Shenzhen Graduate School, Shenzhen, China;2. Development Center, China Hua Rong Holdings Corporation LTD, Beijing, China;3. Innovative Information Industry Research Center, Harbin Institute of University Shenzhen Graduate School, Shenzhen, China;1. Radiation Oncology, Nayati Healthcare and Research Centre, Block 3A, 3rd Floor, DLF Corporate Park, DLF City, Gurgaon, Haryana 122002, India;2. Biostatistics, Nayati Healthcare and Research Centre, Block 3A, 3rd Floor, DLF Corporate Park, DLF City, Gurgaon, Haryana 122002, India;1. Department of Econometrics, Faculty of Computer Science and Statistics, University of Economics, Prague, Winston Churchill Square 4, 13067 Prague, Czech Republic;2. Department of Probability and Mathematical Statistics, Faculty of Mathematics and Physics, Charles University, Prague, Sokolovská 83, 18675 Prague, Czech Republic;3. Department of Applied Mathematics, Faculty of Mathematics and Physics, Charles University, Prague, Malostranské náměstí 25, 11000 Prague, Czech Republic |
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| Abstract: | Various kinds of fuzzy regression models are introduced in the literature and many different methods are proposed to estimate fuzzy parameters of the models. In this study, a new approach is introduced to find the parameters of a linear fuzzy regression, with fuzzy outputs, the input data of which is measured by crisp numbers. Based on a non-equality possibility index, a new objective function is designed and solved, by which a minimum degree of acceptable uncertainty (the h-level or h-cut) is found. Four numerical examples are presented to compare the proposed approach with some other methods. Results show superiority of the new approach based on the criterion used by Kim and Bishu in the cases studied here. A realistic application of the proposed method is also presented, by which the total energy consumption of the Residential-Commercial sector in Iran is modeled using three variables of the GDP, number of the Households and an Energy Price index as inputs (exogenous variables) to the model. |
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