Generalized hesitant fuzzy N-soft sets and their applications

The N-soft Set as a generalization of the Soft Sets was introduced in 2018 by Fatimah et al. The concept of the N-soft Sets combined with the hesitant fuzzy sets is called hesitant fuzzy N-soft sets. On the other hand, the concept of fuzzy soft sets as a combination of soft sets and fuzzy sets was generalized by Majumdar and Samanta in 2010, called Generalized fuzzy soft sets, where many scholars have studied their properties and characteristics. This paper aims to extend the hesitant fuzzy N-soft set to a generalized hesitant fuzzy N-soft set that incorporates some characteristics of generalized fuzzy soft sets. Definition of the generalized hesitant fuzzy N-soft set, complements, and some of their operations are defined. Moreover, some of their properties, such as associative and distributive related to binary operations, are studied. Finally, we propose two algorithms for decision-making problems by extending the TOPSIS method to apply under generalized hesitant fuzzy N-soft set information.