A New Likert Scale Based on Fuzzy Sets Theory

Date of Completion

January 2010


Education, Tests and Measurements|Applied Mathematics|Education, Educational Psychology




In social science research, the Likert method is commonly used as a psychometric scale to measure responses. This measurement scale has a procedure that facilitates survey construction and administration, and data coding and analysis. However, there are some problems with Likert scaling. This dissertation addresses the information distortion and information lost problems arising from the closed-form scaling and the ordinal nature of the Likert method. To overcome these problems, a novel fuzzy Likert scale developed based on fuzzy sets theory is proposed. Compared with the traditional Likert method, the fuzzy Likert approach has the advantage of permitting partial agreement of a scale point. By incorporating this advantage into its measurement process, this new Likert scale is able to capture the lost information and regulate the distorted information. A quantitative analysis based on Consensus, a mathematical term measuring agreement among group members, is used to prove that the fuzzy Likert scale can provide more accurate measurement. The implementation feasibility of the fuzzy Likert scale is demonstrated via a simulated case study. Another challenge in obtaining high measurement accuracy using the fuzzy Likert scale lies in the proper assignment of membership functions to the fuzzy scales. A novel assignment method based on the ordinal regression modeling is proposed. Compared with the other existing assignment approaches developed mainly based on empirical knowledge, the proposed assignment method is proved to be more reliable and accurate, and the assigned membership functions more interpretable. The applicability of the ordinal regression based membership function assignment approach is also demonstrated through a case study. ^