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 -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 -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 -neighborhood is constructed. Hence, using PF beta -neighborhood and PF complementary beta -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 -neighborhood is examined. Three new Cq-ROFRS models are differentiated using the principles of q-ROF beta -neighborhood and q-ROF complementary beta -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.
Highlights
Rough set (RS) theory was established for adapting the ambiguity and granularity in data via Pawlak [1,2]
(1) We extend the study of CPFRS through PF complementary β-neighborhood
Zhan et al.’s paper is a generalization to the notions on covering method by IFS and Hussain et al.’s article is a generalization to the last studies on CPFRS by Zhan et al.’s, so it is already generalized to IFS
Summary
Rough set (RS) theory was established for adapting the ambiguity and granularity in data via Pawlak [1,2]. It is utilized in various areas such as neighborhood systems, graphs, kernel, reduction, granulation, probabilistic rough set, variable precision and so on [3,4,5,6,7,8,9,10,11,12,13]. Ma [35] discovered kinds of fuzzy covering rough set (FCRS) using the fuzzy β-neighborhood. The notions of a fuzzy complementary β-neighborhood and fuzzy β minimal and maximal description were found by Yang et al [36,37]
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