Mohamed A. Abd Elgawad

The Molodtsov-initiated soft set theory plays an important role as a powerful mathematical tool for handling uncertainty. As an extension of the soft set, the fuzzy soft set can be seen to be more generic and flexible than utilizing the soft set only that fails to represent problem parameters fuzziness. Through this progress, the fuzzy soft set theory cannot deal with decision-making problems involving multi-attribute sets, bipolarity, or some effective considered parameters. Therefore, the goal of this article is to adapt effectiveness and bipolarity concepts with the multi-fuzzy soft set of order n. One can see that this approach generates a novel, extended, effective decision-making environment that is more applicable than any previously introduced one. In addition, types, concepts, and operations of effective bipolar-valued multi-fuzzy soft sets of dimension n are provided, each with an example. Furthermore, properties like absorption, associative, distributive, commutative, and De Morgan’s laws of those new sets are investigated. Moreover, a decision-making methodology under effective bipolar-valued multi-fuzzy soft settings is established. This technique facilitates reaching the final decision that this student is qualified to take a certain education level, or this patient is suffering from a certain disease, etc. In addition, a case study represented in a medical diagnosis example is discussed in detail to make the proposed algorithm clearer. Applying matrix techniques in this example as well as using MATLAB®, not only makes it easier and faster in doing calculations, but also gives more accurate, optimal, and effective decisions. Finally, the sensitivity analysis, as well as a comparison with the existing methods, are conducted in detail and are summarized in a chart to show the difference between them and the current one.