RETRACTED: Hesitant fuzzy <i>N</i> -soft sets: A new model with applications in decision-making

Abstract

Hesitant fuzzy set theory is a renowned approach to the formal modeling of uncertain data. An evidence of its success is that it has been extensively used in multi-attribute decision-making problems. Hesitant fuzzy computations make the decision-makers’ assessments more flexible and rich, thus impr oving reliability of the decisions that depend on them. In this research article we introduce a novel hybrid model called hesitant fuzzy N-soft sets, which further enhances the virtues of hesitant fuzzy set theory with the benefits of N-soft sets. This theoretical model is capable of incorporating information about the occurrence of ratings or grades in a hesitant environment. We investigate some useful properties of hesitant fuzzy N-soft sets and construct fundamental operations on them. By doing so we lay the groundwork for subsequent analyses and applications. We then develop novel approaches to decision-making including TOPSIS (Technique for Order Preference by Similarity to an Ideal Solution), choice value and L-choice value based on hesitant fuzzy N-soft sets. Finally, we describe potential applications of our model and present the proposed methods as algorithms.