Hierarchical structures and uncertainty measures are two main aspects in granular computing, approximate reasoning and cognitive process. Typical hesitant fuzzy sets, as a prime extension of fuzzy sets, are more flexible to reflect the hesitance and ambiguity in knowledge representation and decision making. In this paper, we mainly investigate the hierarchical structures and uncertainty measure...

Since the seminal paper of fuzzy set theory by Zadeh in 1965, many extensions have been proposed to overcome the difficulty for assigning the membership degrees. In recent years, a new extension, the hesitant fuzzy sets, has attracted a lot of interest due to its usefulness to handle those problems in which it is difficult to provide accurately a single membership value; since for hesitant sets...

Large-scale group decision-making (LS-GDM) problems are common in the daily life of human beings. Both information fusion and computing with words (CWW) technologies LS-GDM suffer from challenges. In current research, a proportional hesitant fuzzy linguistic term set (PHFLTS) will be applied to capture preferences sub-groups LS-GDM, which decreases lost processes. Novel semantic representation ...

In decision making, similarity measure and distance between two objects are crucial to be able to determine the relationship between those objects. Many researchers have received much attention for their research on this subject. In this study, we propose two novel similarity measures between hesitant fuzzy linguistic term sets (HFLTSs). In addition, two extensions of Technique for Order of Pre...

Interval-valued hesitant fuzzy set (IVHFS), which is the further generalization of hesitant fuzzy set, can overcome the barrier that the precise membership degrees are sometimes hard to be specified and permit the membership degrees of an element to a set to have a few different interval values. To efficiently and effectively aggregate the interval-valued hesitant fuzzy information, in this pap...

Probabilistic hesitant fuzzy set (PHFS) is a fruitful concept that adds to hesitant fuzzy set (HFS) the term of probability which is able to retain more information than the usual HFS. Here, we demonstrate that the existing definitions of PHFS are not still reasonable, and therefore, we first improve the PHFS definition. By endowing the set and algebraic operations with a new re-definition of P...

‎Selecting the most suitable robot among their wide range of specifications and capabilities is an important issue to perform the hazardous and repetitive jobs‎. ‎Companies should take into consideration powerful group decision-making (GDM) methods to evaluate the candidates or potential robots versus the selected attributes (criteria)‎. ‎In this study‎, ‎a new GDM method is proposed by utilizi...