On Interval-Valued Fuzzy Soft Preordered Sets and Associated Applications in Decision-Making

Recently, using interval-valued fuzzy soft sets to rank alternatives has become an important research area in decision-making because it provides decision-makers with the best option in a vague and uncertain environment. The present study aims to give an extensive insight into decision-making processes relying on a preference relationship of interval-valued fuzzy soft sets. Firstly, interval-valued fuzzy soft preorderings and an interval-valued fuzzy soft equivalence are established based on the interval-valued fuzzy soft topology. Then, two crisp preordering sets, namely lower crisp and upper crisp preordering sets, are proposed. Next, a score function depending on comparison matrices is expressed in solving multi-group decision-making problems. Finally, a numerical example is given to illustrate the validity and efficacy of the proposed method.