Multi-Attribute Three-Way Decision Approach Based on Ideal Solutions under Interval-Valued Fuzzy Soft Environment

The interval-valued fuzzy soft set (IVFSS) model, which combines the benefits of the soft set model with the interval-valued fuzzy set (IVFS) model, is a growing and effective mathematical tool for processing hazy data. In detail, this model is characterized by symmetry, which has the lower and upper membership degree. The study of decision-making based on IVFSS has picked up more steam recently. However, existing multi-attribute decision-making (MADM) methods can only sort alternative schemes, but are not able to classify them, which is detrimental to decision-makers’ efficient decision-making. In this paper, we propose a multi-attribute three-way decision-making (MATWDM) algorithm based on ideal solutions for IVFSS. MATWDM is extended to the IVFSS environment by incorporating the concept of the ideal solution, offering a more adaptable and comprehensive approach for addressing uncertain MADM issues. The method not only obtains the ranking results of the alternatives, but also divides them into acceptance domain, rejection domain, and delayed-decision domain, which makes the decision results more reasonable and effective, facilitating decision-makers to make better decisions. We apply the proposed three-way decision algorithm to two practical cases as diverse as mine emergency decision and Homestay selection decision. Additionally, the effectiveness and viability of the suggested method are confirmed by experimental findings.