Abstract
Ordinary time series analysis operates on time series data measured on interval scale, and/or ratio scale. In the study of psychology, sociology, ethnology, and so on, we often encounter fuzzy time-series data related to human judgement, or recognition in the process of data colletction. In such cases, investigating the trend of responses is one of the most important research activity. One of the ways to clarify the trend is visualize the variation. In order to achieve this purpose, "fuzzy time-series analysis of qualitative data" is proposed as a extention of "time series analysis of qualitative data (Inagaki, 1997). The basic idea behind the method is to assign numerical scores to categories so as to maximize correlation between the category scores and function of times. In the method, the three models, i.e., irreversible model, reversible model, and circulative model, are provided for expressing the trend. The method can be widely used as a tool for analyzing not only time-series data but also fuzzy category data in order to explore the relationship between numerical variables and fuzzy categories. In this paper, mathematical formulation and algebraic solution are showed and some technical problems and relation to other methods are also discussed.
