Complex Fuzzy Rough Set: An Application in Digital Marketing for Business Growth
Jinxiu Yi, Jabbar Ahmmad, Tahir Mahmood, Ubaid ur Rehman, Shouzhen Zeng
Abstract
Two-dimensional approach is very important in real-life scenarios. To address situations where two-dimensional information is involved, the theory of complex fuzzy set (CFS) is a reliable and applicable structure. The CFS gives a more expressive structure for modeling uncertainty and imprecision where 2 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">nd</sup> dimension is included. On the other hand, the notion of rough set (RS) is interpreted by two components that is upper and lower approximation, that provide more space in decision-making (DM) dilemmas. To get the benefits and advantages of the CFS and RS, in this manuscript, we interpret the theory of a complex fuzzy rough set (CFRS) by employing complex fuzzy relations. We also devise the operations such as addition, product, scalar product, scalar power, union, intersection and complement for the theory of CFRS. Further, in the structure of CFRS, we devise the aggregation operators (AOs) that are complex fuzzy rough weighted averaging (CFRWA), complex fuzzy rough ordered weighted averaging (CFROWA), complex fuzzy rough weighted geometric (CFRWG) and complex fuzzy rough ordered weighted geometric (CFROWG). We initiate a technique identified as “weighted aggregates sum product assessment” (WAPAS) by employing devised AOs in the environment of CFRS. After that, to reveal the applicability of the anticipated theory and WASPAS technique, we identify and order digital marketing for business growth. Finally, to demonstrate the superiority of the introduced concept, we compare our work to some already-existing ideas.