Double-quantitative $γ^{\ast}-$fuzzy coverings approximation operators
This work addresses a theoretical gap in rough set theory for AI applications, but appears incremental as it builds on existing fuzzy covering models.
The paper tackles the problem of bridging fuzzy covering rough set theory with Pawlak's model by introducing new approximation operators, including $\\gamma-$fuzzy covering based probabilistic, grade, and double-quantitative operators, and extends these to multi-granulation versions, with examples provided to illustrate their construction.
In digital-based information boom, the fuzzy covering rough set model is an important mathematical tool for artificial intelligence, and how to build the bridge between the fuzzy covering rough set theory and Pawlak's model is becoming a hot research topic. In this paper, we first present the $γ-$fuzzy covering based probabilistic and grade approximation operators and double-quantitative approximation operators. We also study the relationships among the three types of $γ-$fuzzy covering based approximation operators. Second, we propose the $γ^{\ast}-$fuzzy coverings based multi-granulation probabilistic and grade lower and upper approximation operators and multi-granulation double-quantitative lower and upper approximation operators. We also investigate the relationships among these types of $γ-$fuzzy coverings based approximation operators. Finally, we employ several examples to illustrate how to construct the lower and upper approximations of fuzzy sets with the absolute and relative quantitative information.