Differential evolution algorithm-based regression model in Z-information environment and its applications

Decision problems in real life basically involve uncertainties. These uncertainties can be found in all components of decision-making processes, such as judgemental discrepancies, crisp structure of data, and computational approximation. Fuzzy sets and their extensions provide powerful problem-solving approaches for modeling and inferring the aforementioned uncertainties. Z-number, one of the fuzzy set extensions, resolves the uncertainties based on knowledge and perception in decision-making processes with its ability to measure reliable information. A Z-number is defined as an ordered pair that consists of a restriction on a random variable and the reliability of this restriction. Z-valuation expresses that a random variable takes its value with a certain probability. The Z-information environment presented by Z-valuation provides information about the value of the random variable. Hybrid approaches including Z-numbers need to be developed to make decisions in a reliable information environment. In this thesis, building a mathematical model under information reliability is examined for system components of decision problems. In this context, the differential evolution algorithm-based regression analysis approach in the Z-information environment was investigated. In this approach, the computational complexity related to the system components (output and inputs) defined by Z-numbers and the model coefficients is eliminated by the bandwidth method. Besides, differential evolution algorithm was used to minimize the differences between the model prediction values and the observed output values under Z-information environment. Differential evolution algorithm-based regression analysis in Z-information environment was applied to single-input/multiple-input and single-output system data for digital maturity evaluation in a technology company. The regression model performances in classical, fuzzy, and Z-information environments were compared. Generally, it has been seen that differential evolution algorithm-based regression analysis in Z-information environment has better performance than other methods. A Matlab interface enriched with data visualization was created to demonstrate performance results and observed-predicted output comparisons of regression approaches in classical, fuzzy, and Z-information environments.