تحليل سري هاي زماني در محيط فازي

چكيده انگليسي :

Analysis of Time Series with Fuzzy Environment Saeedeh Kamgar Sangari s kamgarsangari@math iut ac ir March 10 2010 Master of Science Thesis in Farsi Department of Mathematical Sciences Isfahan University of Technology Isfahan 84156 83111 IranSupervisor Dr S Mahmoud Taheri taheri@cc iut ac ir2010 MSC Primary 03E72 Secondary 37M10 Key words time series fuzzy environment fuzzy random process discretization fuzzy relation AbstractThe aim of time series analysis is to recognize and model structural features in a sequence ofobserved values In classical time series analysis the observed values are real exact numbers If the observed values represent measured values it is often not possible to assign precisenumerical values to the observed data Therefor it needs to generalize the classical methodsfor dealing with such uncertain quantities In this thesis two approaches to time series are investigated under fuzzy imprecise envi ronments The rst approach is based on fuzzy relations In this approach fuzzy relational equationsare employed as the models because the values of fuzzy time series are fuzzy sets and theobservations at time t are the accumulated results of the observations at the previous times That is to say there is a causal relationship between the observations at time t and those atprevious times The second approach is based on discretization method In this approach uncertain dataare described by means of a new incremental fuzzy representation which permits a completeand accurate estimation of uncertainty The fuzzy time series are regarded as realization offuzzy random process In other words a time series of fuzzy data may be viewed as a randomrealization of a fuzzy random process The realizations of this process are uncertain and thusreferred to as fuzzy variables The thesis is organized as follows In the rst chapter we cover some of the basic concepts of fuzzy sets In the second chapter we recall some concepts in classical time series The third chapter demonstrates the rst approach to time series in fuzzy environment i e the approach which is based on fuzzy relations In the fourth chapter rst the fuzzy variables and fuzzy random variables for the mathemat ical description of uncertain data are introduced The mathematical description of uncertaindata is limited to these basic concepts which are essential for forecasting by means of fuzzyrandom processes Then the method of discretization which is an essential for the end ofthesis is explained In addition the method of simulation of f r v is illustrated in thischapter In the last chapter we use discretization method to analyze the time series with fuzzy data also various commonly applied methods of classical time series analysis are extended to dealwith time series comprised of fuzzy data At last the second approach is employed to analysisof the climate report data of the Iranian National Observatory site selection project 1

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تحليل سري هاي زماني در محيط فازي

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