Double hierarchy linguistic term set (DHLTS) is a powerful tool when expressing the real thoughts of experts and handling complex linguistic information considering that it divides complex linguistic information into two simple linguistic hierarchies in which the first hierarchy linguistic term set (LTS) is the main linguistic hierarchy and the second hierarchy LTS is the linguistic feature or detailed supplementary of each linguistic term in the first hierarchy LTS. Some extensions of DHLTS have been developed, such as the double hierarchy hesitant fuzzy LTS, the unbalanced DHLTS, the linguistic preference ordering, the double hierarchy linguistic preference relation, and the double hierarchy hesitant fuzzy linguistic preference relation. In recent years, DHLTS and its extensions have been researched by scholars in lots of fields, including the extended concepts, the operational laws, the comparative methods, the measure methods, the consistency and consensus methods, the decision-making methods, the applications, and so forth. Therefore, the purpose of this paper is to review all the researches of DHLTS and its extensions, as well as proposing some challenges in the future.

With the rapid development of society and continual progress of science and technology, large-scale group decision-making (LSGDM) problems are very commonly encountered in real-life situations. Considering that the information required for decision-making and people's cognition processes is becoming more and more complex, double hierarchy linguistic preference relation (DHLPR) can be used to express complex linguistic information reasonably and intuitively. Sometimes experts in LSGDM unwillingly modify their preferences or even modify them on purpose in a contrary way to the other experts. Thus, differing opinions or minority preferences are often referred to as obstacles to decision-making. This article develops a consensus model to manage minority opinions and noncooperative behaviors in LSGDM with DHLPRs. In addition, to establish the consensus model, some basic tools, such as the clustering method, weights-determining method, and adjustment coefficients-determining method, are developed. Finally, a practical LSGDM problem is set up to prove that the proposed consensus model is feasible and effective, and some comparative analyses are made to highlight the advantages of these methods and models, as well as to analyze current deficiencies.

Tracking a maneuvering target is an important technology. Due to complex environment and diversity of sensors, errors need to be optimized with respect to various motion states during the tracking process. In this paper, we first propose how to unify the coordinate system and data preprocessing in case of tracking using multiple sensors. We then combine fuzzy sets with a novel trace optimization method based on extended Kalman filter (EKF) with nested probabilistic-numerical linguistic information (NPN-EKFTO). We present a case study of trace optimization of an unknown maneuvering target in Sichuan province in China. We solve the case by using both the proposed method and the traditional EKF and offer comparative analysis to validate the proposed approach.

In practical decision-making processes, we can utilize various types of fuzzy sets to express the uncertain and ambiguous information. However, we may encounter such the situations: the sum of the support (membership) degree and the against (nonmembership) degree to which an alternative satisfies a criterion provided by the decision maker may be bigger than 1 but their square sum is equal to or less than 1. The Pythagorean fuzzy sets (PFS), as the generalization of the fuzzy sets, can be used to effectively deal with this issue. Therefore, to enrich the theory of PFS, it is very necessary to investigate the fundamental properties of Pythagorean fuzzy information. In this paper, we first describe the change values of Pythagorean fuzzy numbers (PFNs), which are the basic components of PFSs, when considering them as variables. Then we divide all the change values into the eight regions by using the basic operations of PFNs. Finally, we develop several Pythagorean fuzzy functions and study their fundamental properties such as continuity, derivability, and differentiability in detail.