Preference Intuitionistic Fuzzy Rough Relation and its Theoretical Approach

Relations on intuitionistic fuzzy sets (IFSs) and rough sets (RSs) have recently received a lot of attention for uncertainty. IFSs can effectively represent and simulate the uncertainty and diversity of judgment information offered by decision-makers. In comparison to fuzzy sets (FSs), IFSs are highly beneficial for expressing vagueness and uncertainty more accurately. In this paper, we introduce a novel concept of preference intuitionistic fuzzy rough relation (PIFRR) as an extension of intuitionistic fuzzy rough relation (IFRR) and partially included intuitionistic fuzzy rough relation (PIIFRR). Based on the concepts of IFRR and PIIFRR a theoretical approach of the PIFRR is established and some useful properties are investigated. Finally, we introduce the concepts of Semi-connected and totally semi-connected IFRRs and study under which assumptions PIFRRs fulfil these properties.