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 Q-hesitant fuzzy sets and soft set theory to Q-hesitant fuzzy soft sets. The 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 Q-hesitant fuzzy soft (MQHFS) set. First, by combining m-pole fuzzy sets, soft set models, and 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.