Statistical Methods to Determine Variables Based on Fuzzy Data
Regression analysis is a statistical technique to arrive at the best mathematical expression that can correctly determine the relationship between independent variables depending upon a response. The parameters of the regression are determined by minimizing the difference between the real value and observed data, which may have errors. As observations are dependent on human appraisal besides other physical conditions, these always contain the possibility of errors and the regression analysis is used to estimate the value of these errors in order to reach a correct value.
Fuzzy regression analysis for fuzzy data may be done with three categories of dependent variables. The first is where both the input and the resultant output are clear numbers. The second case may be where in spite of the input data being non-fuzzy and clear, the output obtained is of a fuzzy nature. The third and most likely case is where both input and output data are fuzzy and dependent on certain conditions for their values.
In such fuzzy regression analysis for fuzzy data, it is quite likely that the greater the value of the independent variables, the greater will be the width of the dependent variables in determining the value of the center point for the correct regression, which may be vague.
Fuzzy logic is just a different way of determining the probability of an event or value. In fuzzy logic, the value of a variable is determined by logic that governs the variable and is, therefore, determined by the IF and THEN equation that governs it. Probability theory, on the other hand, is based on determining the value based on its probable correctness in a given situation. While fuzzy logic determines values based on possibilities, the probability theory decides these values based on the application to a particular problem.
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