Decision-making techniques based on similarity measures of possibility interval fuzzy soft environment

The fuzzy set (FS) is a powerful logic designed to measure uncertain information and plays a crucial role in solving real-life problems such as decision-making. This article is split into two parts. In the first part, we highlight the notion of possibility for interval-valued fuzzy soft sets (PI-VFSSs) by collecting all interval fuzzy sets (IVFSs) with soft sets (SSs) under possibility properties. A basic set theories, some numerical examples, and some properties for this hybrid model have been created. Then, in order to test the efficiency of the proposed method in solving some real-life problems, we construct an algorithm using a PIV-FSS. On the other hand, in the second part, we apply similarity techniques to the proposed model through the analysis of similarity measures of two PIV-FSSs. After that, a new algorithm based on these measures is applied to the medical diagnosis to find out whether or not a patient has a respiratory disease. Finally, some theories that show the relationship between PIV-FSS with some mathematical operations have been proposed.