Group decision-making methods based on probabilistic hesitant N-soft sets

In this paper, we introduce a new hybrid model called probabilistic hesitant N-soft sets by a suitable combination of probability with hesitant N-soft sets, a model that extends hesitant N-soft sets. Our novel concept extends the ability of hesitant N-soft set by considering the occurrence probability of hesitant grades, which could effectively avoid the loss of decision-making information. Moreover, we investigate some basic properties of probabilistic hesitant N-soft sets and construct fundamental operations on them. Then we describe group decision-making methods including TOPSIS, VIKOR, choice value and weighted choice value based on probabilistic hesitant N-soft sets. The corresponding algorithms are put forward and their validity is proved by examples.