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By introducing covering rough sets to Pythagorean fuzzy environment, we construct a new rough set model called the Pythagorean fuzzy &#x03BB;-covering rough set. Based on the rough set model, we adopt the discernibility matrix method to obtain its attribute reduction. First, we give the definitions of Pythagorean fuzzy &#x03BB;-coverings and &#x03BB;-neighborhoods and then establish a Pythagorean fuzzy &#x03BB;-covering rough set model. Second, from the perspective of decision systems, Pythagorean fuzzy &#x03BB;-covering decision systems are divided into two categories: consistent Pythagorean fuzzy &#x03BB;-covering decision systems and inconsistent Pythagorean fuzzy &#x03BB;-covering decision systems. We further investigate the attribute reductions in the two systems and some equivalent conditions of the reductions and then design the reduction algorithms by using the discernibility matrix. Finally, numerical examples are provided to demonstrate the effectiveness of the proposed design methods. In addition, we reveal the superiority of the Pythagorean fuzzy &#x03BB;-covering rough set in attribute reduction by numerical experiments.

Attribute Reduction Methods Based on Pythagorean Fuzzy Covering Information Systems