Time-Series Forecasting via Complex Fuzzy Logic

Abstract

Adaptive neuro-complex-fuzzy inference system (ANCFIS) is a neurofuzzy system that employs complex fuzzy sets for time-series forecasting. One of the particular advantages of this architecture is that each input to the network is a windowed segment of the time series, rather than a single lag as in most other neural networks. This allows ANCFIS to predict even chaotic time series very accurately, using a small number of rules. Some recent findings, however, indicate that published results on ANCFIS are suboptimal; they could be improved by changing how the length of an input window is determined, and/or subsampling the input window.We compare the performance of ANCFIS using three different approaches to defining an input window, across six time-series datasets. These include chaotic datasets and time series up to 20,000 observations in length. We found that the optimal choice of input formats was dataset dependent, and may be influenced by the size of the dataset. We finally develop a recommended approach to determining input windows that balances the twin concerns of accuracy and computation time. IntroductionTime-series forecasting has emerged as the first major application of complex fuzzy sets and logic, which were first described by Ramot in [1]. Beginning in 2007, complex-valued neuro-fuzzy systems were developed to inductively learn forecasting models; these include the adaptive neuro-complex-fuzzy inference system (ANCFIS) architecture [2], and the family of complex neuro-fuzzy system (CNFS) architectures [3]. Both ANCFIS and CNFS are modifications of the well-known ANFIS architecture, in which complex fuzzy sets and complex-valued network signals are used. These architectures showed that complex fuzzy sets were naturally useful in creating very accurate forecasting models. ANCFIS in particular is also very parsimonious;

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“…Their experimental results have demonstrated that the ANCFIS based approach was more accurate in predicting power output on a simulated solar cell. Additionally, in a recent paper Yazdanbaksh et al presented a recommended approach to determining input windows that balances the accuracy and computation time [77].…”

Condition Monitoring and Fault Detection in Small Induction Motors Using Machine Learning Algorithms

“…Finding d allows us to get an optimal level of autocorrelation within each delay vector (by taking each successive value, or every second, every third, etc.) [45]. d is determined heuristically, guided by taking the first minimum of the time-delayed mutual information statistic [42].…”

A Method to Multi-Attribute Group Decision-Making Problem with Complex q-Rung Orthopair Linguistic Information Based on Heronian Mean Operators

“…While, Alkouri and Salleh [3] proposed the notions of linguistic variable, hedges and several distances on CFS. Yazdanbakhsh and Dick [4] proposed time-series forecasting via complex fuzzy logic and a systematic review of CFS. Recently, Bi et al [5] proposed complex fuzzy geometric aggregation operators.…”

“…To precisely cope with such kind of problems, Yager [22] proposed the framework of q-rung orthopair fuzzy set (q-ROFS) whose restriction is that the sum of q-power of membership and q-power of non-membership grade is belonging to [0,1]. Obviously, the q-ROFS can describe effectively such kinds of information, i.e., 0.9 4 + 0.7 4 = 0.7 + 0.24 = 0.94 ≤ 1. The FS, IFS, and PFS all are the special cases of q-ROFS, this characteristic makes q-ROFS more general than existing FSs.…”

“…Develop some extended HM operators, such as complex q-rung orthopair linguistic Heronian mean operator (Cq-ROLHM), complex q-rung orthopair linguistic weighted Heronian mean operator Cq-(ROLWHM), complex q-rung orthopair linguistic geometric Heronian mean operator (Cq-ROLGHM), complex q-rung orthopair linguistic weighted geometric Heronian mean operator (Cq-ROLWGHM), and then verify their some properties. 4. Develop a new MADM method based on the proposed operators.…”