Fuzzy time series and its first-order time-invariant model¶

Theory · All theories
Evidence · no claims cited

Description¶

The article defines a fuzzy time series as a sequence of fuzzy sets F(t) defined on the universe of a conventional time series Y(t). A first-order model expresses the relation "F(t-1)-->F(t)" as F(t)=F(t-1)∘R(t,t-1), where R(t,t-1) is a fuzzy relationship; the series is time-invariant when R is independent of t. Theorem 2 gives a matrix formula for computing R from historical fuzzy-set transitions, which the authors use to build the enrollment forecasting model via fuzzy logical reasoning.

Design Implications¶

Context¶

Requirements¶

• Fuzzy sets with memberships must be defined on the universe of the historical data, and historical experience knowledge (or data) is needed to establish the fuzzy logical relationships.

Constraints¶

• The article applies only the first-order, time-invariant model and notes that in cases of quite severe non-linearity different fuzzy time series approaches should be sought.

Target Learners¶

• higher education administrators and planners forecasting university enrollment

Target Learning Objectives¶

• long-range enrollment projection for institutional planning

Claims¶

Related Theories¶

Examples¶

• Two-step fuzzy forecasting pattern: fuzzylise the universe, then interpret the fuzzy output
• Use fuzzy forecasting when historical data are scarce but experience knowledge is available, because the method tolerates imperfect data
• Apply three membership-based principles to translate fuzzy forecast outputs into numeric values
• University enrollment dataset 1971–1990 with fuzzylised universe (13000, 20000)

Key Sources¶

• Song, Qiang; Chissom, Brad S. (1991). Forecasting Enrollments with Fuzzy Time Series. https://eric.ed.gov/?id=ED340733