Pessimistic multigranulation rough bipolar fuzzy set and their application in medical diagnosis

Multigranulation rough sets have recently attracted a lot of attention, and numerous multigranulation rough set models have been created from differing viewpoints. The set is approximated using a collection of binary relations in a basic multigranulation rough set technique. The most common examples of such techniques are optimistic and pessimistic multigranulation rough sets. Though numerous optimistic multigranulation rough sets have been proposed in earlier studies, they cannot meet the condition that the lower approximation is contained in the upper approximation. This study aims to present the concept of pessimistic multigranulation roughness for a bipolar fuzzy set over dual universes. As a result, two sets of bipolar fuzzy soft sets are obtained with respect to aftersets and foresets. The proposed pessimistic multigranulation rough set not only meets the condition that the lower approximation is contained in the upper approximation but also defines the accuracy measures and roughness measures. Next, we investigate a number of basic properties of the new pessimistic granulation rough set model. We present the concepts of accuracy measure and roughness measure, which are used to measure uncertainty in multigranulation rough bipolar fuzzy sets, and we look at some of the fundamental characteristics of these measures. Finally, we give two decision making algorithms with an example in medical diagnosis.