Abstract
We lay the theoretical foundations of a novel model, termed picture hesitant fuzzy rough sets, based on picture hesitant fuzzy relations. We also combine this notion with the ideas of multi-granulation rough sets. As a consequence, a new multi-granulation rough set model on two universes, termed a multi-granulation picture hesitant fuzzy rough set, is developed. When the universes coincide or play a symmetric role, the concept assumes the standard format. In this context, we put forward two new classes of multi-granulation picture hesitant fuzzy rough sets, namely, the optimistic and pessimistic multi-granulation picture hesitant fuzzy rough sets. Further, we also investigate the relationships among these two concepts and picture hesitant fuzzy rough sets.
Highlights
Vague and incomplete information poses many challenges to the researchers in science and engineering
Rough sets and picture hesitant fuzzy sets are two mathematical models that deal with uncertainty and imprecision in data analysis from different viewpoints
The authors lay the theoretical foundations of a novel model, called picture hesitant fuzzy rough sets (PHFRS), defined from a picture hesitant fuzzy relation
Summary
Vague and incomplete information poses many challenges to the researchers in science and engineering. It is sometimes difficult for a doctor to recognize whether a patient is suffering from a given disease These situations are better handled by rough sets over two universes, one for the set of patients and the other for the set of clinical symptoms. Qian et al [22] expanded rough set theory with the introduction of multi-granulation rough sets (MGRS) Their structure was clarified by She and He [23], who introduced the optimistic and pessimistic specifications of MGRS. Picture hesitant fuzzy rough sets are introduced using this relation, and an example is provided. Some conclusions and additional directions of research are provided in the concluding section of the paper
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