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Abstract

The fuzzy set (FS) is a powerful logic designed to measure uncertain information and plays a crucialrole in solving real-life problems such as decision-making. This article is split into two parts. In the first part, wehighlight 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 someproperties for this hybrid model have been created. Then, in order to test the efficiency of the proposed method insolving 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 nota patient has a respiratory disease. Finally, some theories that show the relationship between PIV-FSS with somemathematical operations have been proposed

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