Enrollment Forecasting Based on Linguistic Time Series

Abstract

Dealing with the time series forecasting problem attracts much attention from the fuzzy community. Many models and methods have been proposed in the literature since the publication of the study by Song and Chissom in 1993, in which they proposed fuzzy time series together with its fuzzy forecasting model for time series data and the fuzzy formalism to handle their uncertainty. Unfortunately, the proposed method to calculate this fuzzy model was very complex. Then, in 1996, Chen proposed an efficient method to reduce the computational complexity of the mentioned formalism. Hwang et al. in 1998 proposed a new fuzzy time series forecasting model, which deals with the variations of historical data instead of these historical data themselves. Though fuzzy sets are concepts inspired by fuzzy linguistic information, there is no formal bridge to connect the fuzzy sets and the inherent quantitative semantics of linguistic words. This study proposes the so-called linguistic time series, in which words with their own semantics are used instead of fuzzy sets. By this, forecasting linguistic logical relationships can be established based on the time series variations and this is clearly useful for human users. The effect of the proposed model is justified by applying the proposed model to forecast student enrollment historical data.

A Novel High-order Linguistic Time Series Forecasting Model with the Growth of Declared Word-set

“…Definition 4. [35] Let be a set of linguistic words in the natural language of a variable defined on the universe of discourse to describe its numeric quantities. Then, any series ( ), = 0, 1, 2, …, where ( ) is a finite collection of words of , is called a linguistic time series.…”

“…Definition 5. [35] Let T be a LTS. In T, if every time = − 1 , the linguistic value of LTS is and is the linguistic value of T at the time = , then we have linguistic logical relationship of the form → .…”

“…Definition 6. [35] Suppose that we have more than one linguistic logical relationship with the same left-hand side denoted by → 1 , → 2 , … , → , then we can group them into the linguistic logical relationship group denoted by → 1 , 2 , … , .…”

“…Many applications of hedge algebras can be found in the field of fuzzy control [25]- [31], data classification and regression using fuzzy rule-based systems [32], [33], image processing [34] and so on. In 2020, Hieu et al [35], [36] proposed linguistic time series (LTS) forecasting model handling the linguistic words immediately based on the theory of hedge algebras. It is the first time that the constructed linguistic time series can simulate the way human users describe numerical time series in terms of their linguistic words.…”

Improved Fuzzy Time Series Forecasting Model Based on Optimal Lengths of Intervals Using Hedge Algebras and Particle Swarm Optimization

“…In which, the hedge algebra was used to construct linguistic domains and variables instead of performing data fuzzification and defuzzification in the fuzzy approach. In addition, researches in [29,30] proposed the HA-based forecasting models to obtain unequallength intervals in the UoD by mapping the semantics of linguistic variables into fuzziness intervals. However, two these research works only focus on building the first-order forecasting model to apply the number of students annually at the University of Alabama.…”