Hesitant hierarchical T–S fuzzy system with fuzzily weighted recursive least square

Abstract

Hierarchical fuzzy systems have been an increasingly prevalent research topic, however, most of them are with fixed structures. This could reduce the flexibility of the method in applications and make it difficult to build an elastic multilayer structure for different input information. Hesitant fuzzy set (HFS) consists of rich and flexible hesitant fuzzy elements, which have been widely developed and applied in recent years, and related basic concepts and theories have been constantly developed and improved. By using the flexible expressing capabilities of HFS, we constructively construct a new serial-based hierarchical fuzzy system with flexible and adaptive rules in each layer, named after hesitant hierarchical T–S fuzzy system (HHFS). In the general HHFS, lengths of HFS elements play an important role generating constructions of each layer and consequent parameters of rules are adjusted by fuzzily weighted recursive least square method. It is the first time to build a multilayer fuzzy system using HFS. To adapt HHFS into the application of maneuvering target tracking, another newly adapted one, time-sequential hesitant fuzzy set (TSHFS) is utilized. The function of the conventional HFS is still generating structures of subsystems, and the TSHFS is utilized to optimize parameters of consequent parts with the new proposed approach for fluctuated hesitant information under TSHFS environment. In HHFS, the rules of subsystems are adaptively changeable according to different inputs, namely subsystems of each layer are with variant structures. Compared with state-of-the-art algorithms, the effectiveness and advantage of HHFS are exhibited in various experiments.