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This paper intends to introduce mathematical tools for aggregation of the generalized hesitant fuzzy numbers in order to increase the use of them in the real world. The proposed operators, are based on general form of t-norm and t-conorm functions, enable us to do some mathematical computations and aggregate the given generalized hesitant fuzzy numbers. At first, some famous Archimedean t-norms and t-conorms, i.e., Algebraic, Einstein, Hamacher, and Frank t-norms and t-conorms, and their properties, have been developed to be employed with generalized hesitant fuzzy numbers. Then, several averaging and geometric-based aggregation operators for generalized hesitant fuzzy numbers have been proposed. Later on, a decision-making algorithm has been defined based on such operators to address the problems. The necessity and application of the proposed concepts have been explained by some numerical examples. [ABSTRACT FROM AUTHOR]

In this paper, we considered the defined intuitionistic fuzzy numbers (IFNs) on real numbers and proposed a new method based on Hamacher operators to operate with membership and non-membership degrees of the given IFN in aggregation process. Also, a new method will be introduced to compute the distance between IFNs. These methods will be applied to solve multi-attribute group decision-making (MAGDM) problems, in which IFNs were used to model the arising uncertainty from human judgments or assessments. To do it, Choquet integral, as a powerful tool in both independent and interactive criteria, will be used individually or as a tool to provide appropriate conditions for application of TOPSIS method. The applicability of these methods is illustrated by numerical examples. [ABSTRACT FROM AUTHOR]

Uncertainty has long been explored as an objective and inalienable reality, and then modeled via different theories such as probability theory, fuzzy sets (FSs) theory, vague sets, etc. Hesitant fuzzy sets (HFSs) as a generalization of FSs, because of their flexibility and capability, extended and applied in many practical problems very soon. However, the above theories cannot meet all the scientific needs of researchers. For example, in some decision-making problems we encounter predetermined definite data, which have inductive uncertainties. In other words, the numbers themselves are crisp in nature, but are associated with varying degrees of satisfaction or fairness from the perspective of each decision-maker/judge. To this end, in this article, hesitant fuzzy numbers as a generalization of hesitant fuzzy sets will be introduced. Some concepts such as the operation laws, the arithmetic operations, the score function, the variance of hesitant fuzzy numbers, and a way to compare hesitant fuzzy numbers will be proposed. Mean-based aggregation operators of hesitant fuzzy numbers, i.e. hesitant fuzzy weighted arithmetic averaging (HWAA), hesitant fuzzy weighted geometric averaging (HWGA), hesitant fuzzy ordered weighted arithmetic averaging (HOWAA), and hesitant fuzzy ordered weighted geometric averaging (HOWGA) operators have been discussed in this paper, too. These new concepts will be used to model, and solve an uncertain multi-attribute group decision making (MAGDM) problem. The proposed method will be illustrated by a numerical example and the validity of the obtained solution will be checked by test criteria. [ABSTRACT FROM AUTHOR]