A comparison of fuzzy forecasting and Markov modeling

These models are compared with each other and with a time-invariant Markov model using linguistic labels with probability distributions and compared with three traditional time series models, a first-order autoregressive (AR) model and two second-order auto-regressive (AR(2) models, all of which are time- Invariant.

Abstract

Fuzzy time series models were introduced by Song and Chissom [Fuzzy Sets and Systems 54 (1993) 269–277, 54 (1993) 1–9, 62 (1994) 1–8] to model and forecast processes whose values are described by linguistic variables. Song and Chissom used as an application the forecasting of educational enrollments. This paper reviews the two methods set forth by Song and Chissom, a first-order time-invariant fuzzy time series model and a first-order time variant model. These models are compared with each other and with a time-invariant Markov model using linguistic labels with probability distributions. The results of these methods for the enrollment data are compared with three traditional time series models, a first-order autoregressive (AR(1)) model and two second-order auto-regressive (AR(2)) models, all of which are time-invariant.