Formulating Intuitionistic Fuzzy Regression Models by a Two-Stage Method

Abstract

Regression analysis is one of the most widely used decision-making tools It allows decision-makers to determine the relationship between input variables and output variables In the complex real-world environment data may be uncertain written in linguistic terms or based on personal subjective attitudes Therefore fuzzy set theory was developed to deal with this datatype To express the essence of uncertainty better scholars proposed the concept of intuitionistic fuzzy sets (IFS) as a generalization of fuzzy set theory In addition to positive information it also includes negative information In this study the regression coefficients are crisp values and the input variables and output variable are intuitionistic fuzzy numbers (IFN) IFN multiplied with each other will lead to an over-increase in the spread of IFN In other words the fuzziness of the numbers will be over-increased Differing from previous studies on intuitionistic fuzzy regression (IFR) this study proposes a two-stage approach to construct IFR model based on the distance concept In the first stage the fuzzy observations are defuzzified so that the classical least-squares method can be applied to find a crisp regression line In the second stage the adjustment variable of the model which represents the fuzziness of the data is determined to give the model the best explanatory power and the smaller estimation error between the observed and estimated values The predictive ability of the obtained models is evaluated using similarity and distance measures The results indicate that the model proposed in this study has better performance than those in previous studies As for the robustness of the model the cross-validation of the model also proves that the rationality of this method is sufficient Furthermore this study demonstrates the applicability of the proposed two-stage approach in handling a problem with asymmetric intuitionistic fuzzy numbers

Date of Award	2019
Original language	English
Supervisor	Liang-Hsuan Chen (Supervisor)