Analysis of seasonal time series using fuzzy approach

Abstract

A new methodology for the analysis and forecasting of time series is proposed. It directly employs two soft computing techniques: the fuzzy transform and the perception-based logical deduction. Thanks to the use of both these methods, and to the innovative approach, consisting of the construction of several independent models, the methodology is successfully applicable to robust long-time predictions.

Keywords:

• time series
• fuzzy transform
• perception-based logical deduction
• fuzzy partition

Acknowledgement

This work was supported by the project DAR 1M0572 of the MŠMT ČR.

Notes

^1. In many situations, it is advantageous to extend the set of atomic evaluative expressions by the evaluative expression zero (Ze).

^2. Abbreviations of linguistic hedges are listed after their names.

^3. Let us emphasise that the middle value v _M is not required to be in the exact centre of the interval .

^4. It should be stressed that this is a mathematical model of the context, which works well for evaluative linguistic expressions but cannot be considered as a general model of context for arbitrary ones!

^5. More details and explanation can be found in cf. Novák (2008). In this paper, we use a simplified version of this theory.

^6. An evaluative expression A ₁ is sharper than evaluative expression A ₂ if its interpretation is more specific. For example, very small is sharper than small (Figure 2). Details can be found in Novák (2008).

^7. The Łukasiewicz implication is in [0,1], defined by the formula .