Generalized Ideals of BCK/BCI-Algebras Based on MQHF Soft Set with Application in Decision Making

Abstract

The purpose of this study is to generalize the concept of $\mathcal{Q}$ -hesitant fuzzy sets and soft set theory to $\mathcal{Q}$ -hesitant fuzzy soft sets. The $\mathcal{Q}$ -hesitant fuzzy set is an admirable hybrid property, specially developed by the new generalized hybrid structure of hesitant fuzzy sets. Our goal is to provide a formal structure for the $m$ -polar $\mathcal{Q}$ -hesitant fuzzy soft (MQHFS) set. First, by combining m-pole fuzzy sets, soft set models, and $\mathcal{Q}$ -hesitant fuzzy sets, we introduce the concept of MQHFS and apply it to deal with multiple theories in $BCK/BCI$ -algebra. We then develop a framework including MQHFS subalgebras, MQHFS ideals, closed MQHFS ideals, and MQHFS exchange ideals in $BCK/BCI$ -algebras. Furthermore, we prove some relevant properties and theorems studied in our work. Finally, the application of MQHFS-based multicriteria decision-making in the Ministry of Health system is illustrated through a recent case study to demonstrate the effectiveness of MQHFS through the use of horizontal soft sets in decision-making.