Cq-ROFRS: covering q-rung orthopair fuzzy rough sets and its application to multi-attribute decision-making process
Harish Garg, Mohammed Atef · Complex & Intelligent Systems · 2022
Abstract Pythagorean fuzzy sets (briefly, PFSs) were created as an upgrade to intuitionistic fuzzy sets (briefly, IFSs) which helped to address some problems that IFSs couldn’t solve. The definition of q-rung orthopair fuzzy sets (briefly, q-ROFS) is then declared to generalize and solve PFS and IFS failures. Using the concept of PF $$\beta $$ β -neighborhood, Zhan et al. defined the description of the covering through the Pythagorean fuzzy rough set (briefly, CPFRS). Hussain et al. also developed the concept of q-ROF $$\beta $$ β -neighborhood to build the concept of covering through q-rung orthopair fuzzy rough sets (Cq-ROFRS). To enhance the results in Zhan et al.’s and Hussain et al.’s method and in a related context, the concept of PF complementary $$\beta $$ β -neighborhood is constructed. Hence, using PF $$\beta $$ β -neighborhood and PF complementary $$\beta $$ β -neighborhood, three novel kinds of CPFRS are investigated and the related characteristics are analyzed. The interrelationships between Zhan et al.’s approach and our approaches are also discussed. Besides, the concept of q-ROF complementary $$\beta $$ β -neighborhood is examined. Three new Cq-ROFRS models are differentiated using the principles of q-ROF $$\beta $$ β -neighborhood and q-ROF complementary $$\beta $$ β -neighborhood. As a result, the related properties and relationships between these various models and Hussain et al.’s model are established. Because of these correlations, we may consider our approach to be a generalization of Zhan et al.’s and Hussain et al’s approaches. Finally, we developed applications to solve MADM problems using CPFRS and Cq-ROFRS, as well as variances of the two methods using numerical examples are presented.