Distance measures and δ-approximations with rough complex fuzzy models

• Published in: Granular computing (Internet) 2023-09, Vol.8 (5), p.893-916
• Main Authors: Sarwar, Musavarah, Akram, Muhammad, Shahzadi, Sundas
• Format: Article
• Language: English
• Subjects: Artificial Intelligence; Computational Intelligence; Engineering; Original Paper
• ISSN: 2364-4966; 2364-4974
• DOI: 10.1007/s41066-023-00371-4

Rough set theory is a key approach to model and apprehend the situations involving uncertainty without additional information and suppositions. Complex fuzzy sets are useful in developing parsimonious models in various fields such as image processing, machine learning and data mining. To manipulate the subjectivity and fluctuation in decision making problems, the integration of rough sets and complex fuzzy sets can provide more objective description of the collected data in terms of upper and lower approximations. In this research, we integrate two powerful mathematical techniques, namely rough sets and complex fuzzy sets, to initiate a hybrid model named rough complex fuzzy sets. We describe some basic properties of rough complex fuzzy set operations using t -norms and s -norms. We study algebraic properties and relations of certain operations of rough complex fuzzy sets. Based on different types of distance measures, we investigate the effects and properties of δ -approximations of complex fuzzy sets under rough information. We demonstrate the feasibility of rough complex fuzzy sets with a pragmatic application regarding the classification of unknown building materials. We illustrate certain relations of δ -approximations with different types of rough complex fuzzy sets. Finally, we compare our rough complex fuzzy set based method with several well-established approaches to show its validity and superiority.