Strong (α, k)-cut and computational-based segmentation based novel hesitant fuzzy time series forecasting model

Abstract

Hesitant fuzzy set (HFS) is an ideal tool to deal with hesitancy situation arises due to collection of membership values for each time series datum. Many researchers developed HFS based fuzzy time series forecasting (FTSF) models in past years. In this article, a novel method is proposed to deal with critical factors affecting the HFS based FTSF and name as strong (α,k)-cut and computational-based segmentation based hesitant fuzzy time series forecasting (SCS-FTSF). Computational-based segmentation (CBS) approach is developed to determination of number of intervals and generating intervals. Proposed method uses Gaussian and triangular membership functions to construct HFS and uses aggregation operator aggregating the membership values to construct aggregate HFS. A novel fuzzification procedure is proposed by taking all aggregate HFSs with non-zero aggregated membership value relative to data points. Strong(α,k)-cut is employed to selection of suitable aggregate HFLRs. Further, a defuzzification approach is also proposed to obtaining numerical value. In order to assess the performance of proposed SCS -FTSF method two time series datasets are used. Results of error measures and validation tests confirms that superiority of the proposed SCS-FTSF method.