Separable N-soft sets: A tool for multinary descriptions with large-scale parameter sets

Soft set theory builds on the idea of a parameterized family of subsets of a universal set, where for each pertinent characteristic, any specific member of the universe either satisfies it or not. The concept of an N-soft set sharpens this model with the aid of multinary parameterized descriptions; that is, N-soft sets categorize the options in terms of multiple classifications of the characteristics. The aim of this research is fourfold. First, this research focuses on daily-life decision-making problems that involve both positive and negative attributes that can be naturally distributed among classes. Each comparable group of attributes produces an N-soft set, and we can represent all these N-soft sets using separable N-soft sets. We show that this structure facilitates decision-making in the presence of large numbers of attributes. Second, to develop tools that provide a mechanism for the selection of an alternative in this new model, we first develop a complement operator for N-soft sets to uniformize the data, and then, we propose strategies for taking advantage of the qualities of the attributes. Aggregation operators are employed to aggregate the data into a resultant N-soft set, a fuzzy N-soft set, or a hesitant N-soft set. Several algorithmic procedures are proposed to define these methods. Third, we define the novel notion of a multihesitant N-soft set. This loosely defined concept is helpful for representing data with multiple and repetitive entries while avoiding information loss. Finally, we provide solutions to several real-life decision-making problems to illustrate the versatility of our approaches. We apply this theory to construct a new method for ranking countries participating in the Olympic Games. Our motivation is that the existing lexicographic procedure is unable to distinguish among gold, silver, and bronze medals won at sports with very different characteristics.